Find the distance from point A (0,5) to the line y = -3x - 5. Round to the nearest tenth
Answer:
3.2
Step-by-step explanation:
Substitute in the equation:
|(mx1-y1+b)| / √(m2 + (1)2) =
= |(0+-5+-5)| / √(9 + 1)
Sum and operate:
|-10| / √10 = 10 / √10
Exact solution is:
√10
Approximate solution is:
3.2
Answered by GAUTHMATH
Explain how you could find the shortest distance from A(6, 5) to the line y = 5x – 10. (Use a diagram, be specific, and list all your steps.
Step-by-step explanation:
I cannot draw a diagram here.
but I can explain what to do in general.
the shortest distance from a point to a line is always via a connecting line that is perpendicular to the given line and his through the given point.
and then the distance from the given point to the intersection point is calculated.
every line is defined in the form like
y = ax + b
where a is the slope of the line, and b is the intersection point on the y-axis (the offset from point 0).
the slope of a line is the ratio y/x defining how many units y changes when x changes a certain amount of units.
in our example,
y = 5x - 10
5 (or rather 5/1) is the slope of the line.
it means that y grows by 5 units every time x grows by 1 unit.
a perpendicular line (cuts the original line with a 90 degree angle) has a related slope : it reverts x and y and flips the sign :
5/1 turns into -1/5
that means at the perpendicular line whenever x grows by 5 units, y goes down by 1 unit.
so, the first approach for the perpendicular line is
y = -1/5 x + b
to get b we use the given point (6, 5) that has to be in the perpendicular line.
5 = -1/5 × 6 + b
25/5 = -6/5 + b
31/5 = b
=> y = -1/5 x + 31/5
the intersecting point is now where both lines are equal
5x - 10 = -1/5 x + 31/5
25x - 50 = -x + 31
26x = 81
x = 81/26
y = 5×(81/26) - 10 = 405/26 - 260/26 = 145/26
the distance of the given point (6, 5) to the line intersection point (81/26, 145/26) is the calculated as
distance² = (6 - 81/26)² + (5 - 145/26)²
distance = sqrt((6-81/26)² + (5-145/26)²)
since the result was not requested here, I save us the calculation.
What is the scale factor of the dilation?
PLEASE BE CORRECT
If 3^2x+1 =3^x+5, what is the value of x?
Answer:
x = 4
Step-by-step explanation:
[tex]3^{2x+1} = 3^{x+5}[/tex]
if the bases are equal then the powers must be equal as well
2x+ 1 = x+5 export like terms to same side of equation
2x - x = 5 - 1 add/subtract like terms
x = 4
The number of bacteria in a second study is modeled by the function b_2(t)=800(1.6)^t.
What is the growth rate, r, for this equation?
Answer:
1.6 = 1 + .6 = 60% growth rate
Step-by-step explanation:
HELP ASAP PLEASE!!!!!!!!
Answer:
1
Step-by-step explanation:
1 : 1 :sqrt(2)
The legs are in the ratio of 1 to 1
tan 45 = opp side / adj side
tan 45 = 1/1
tan 45 =1
Answer:
Step-by-step explanation:
The FDA regulates that fish that is consumed is allowed to contain 1.0 mg/kg of mercury. In Florida, bass fish were collected in 53 different lakes to measure the amount of mercury in the fish. The data for the average amount of mercury in each lake is in the given table ("Multi-disciplinary niser activity," 2013). Do the data provide enough evidence to show that the fish in Florida lakes has more mercury than the allowable amount? Test at the 10% level. Use the framework below to guide your work. Hypotheses:
H0 : u = 1.0 mg/kg
HA: ul > 1.0 mg/kg
Test statistic = -10.09 p-value is approximately 1, would report 0.9999. Since this is not less than or equal to 0.10, we do not favor Ha. We would conclude that there is not enough evidence to show that the mean amount of mercury in fish in Florida lakes is more than the allowable amount Why is the p-value so high when the test statistic seems extreme?
A. The alternative is > so the p-value matches the area to the left. Since the TS is negative, this results in shading most of the curve.
B. The TS is negative so the p-value matches the area to the left and results in a very small area. This p-value reported is not correct.
C. The alternative is > so the p-value matches the area to the right. Since the TS is negative, this results in shading most of the curve.
D. The TS should be positive so the p-value matches the area to the left and results in shading most of the curve.
Answer:
Step-by-step explanation:
H0 : u = 1.0 mg/kg
HA: u > 1.0 mg/kg
Test statistic = -10.09
p-value is approximately 1, would report 0.9999
α = 10% ; 0.1
Using the Pvalue, we can make a decision pattern ;
Recall ; H0 is rejected If Pvalue < α
Here,
Pvalue Given is ' 0.99999 α = 0.1
Pvalue > α ; Hence, we fail to reject the Null ;
The actual Pvalue calculated using the test statistic will be :
Pvalue(-10.09) with test statistic value using a Pvalue calculator
Pvalue < 0.00001
Pls if anyone knows the answer that will be greatly appreciated :)
Answer:
I think the area is 60 but i couldn't figure out the perimeter, sorry.
Step-by-step explanation:
Answer:
perimeter = 36 m
area = 60 m²
Step-by-step explanation:
there is some missing information. for example about the types of the shapes. e.g. if the triangle on the top is an isosceles triangle (2 equal sides). or if the rectangle at the bottom is actually a square with 6 m on all sides. in order to make the sloped side of the top triangle a round, whole number, i assume that the bottom part is a square.
so, the area of this combined shape is the area of the bottom square plus the area of the top triangle.
area square As = 6×6 = 36 m²
so, one side of the triangle is also 6 m, the other is 14-6 = 8 m.
the area of such a right-angled triangle is half of the full rectangle of 6×8.
area triangle At = 6×8/2 = 48/2 = 24 m²
total area = As + At = 36 + 24 = 60 m²
the perimeter of the total shape is the sum of all sides.
so, 14, 6, 6 and ... the baseline/ Hypotenuse of the top triangle.
for that r need the mentioned Pythagoras :
c² = a² + b²
where a and b are the sides, and c is the Hypotenuse (the side opposite of the 90 degree angle).
so, in our case of an isosceles triangle with a 90 degree angle :
c² = 8² + 6² = 64 + 36 = 100
c = 10 m
so, the perimeter is
14+6+6+10 = 36 m
Evaluate f(x) = X - 8 for x = -8
Answer:-16
Step-by-step explanation:
Add 2/5, 3/10 and 1/2. Give your answer as a mixed number
Answer:
I hope this will help you
A number is chosen at random from 1 to 50. What is the probability of selecting
multiples of 10.
Answer: 25
Step-by-step explanation:
please help will give brainliest and points
i need this by tomorrow pleaseeee
Answer:
Step-by-step explanation:
Angle 1 and angle 2 are remote interior angles of angle 6 because angles 1 and 2 are on the inside and it is remote and across from angle six. You can also see this where angle 1 and angle 3 are remote interior angles of angle 5
So in turn angles 2 and 3 are remote interior angles of angle 4 for the same reasoning.
This function is _____over the interval
[tex]x < - 1[/tex]
This function is_____ over the interval l
[tex] - 1 < x < 1[/tex]
Select all of the possible degrees of this polynomial function
2
3
4
5
Answer:
the answer to this question is 1
Step-by-step explanation:
the reason to that is because when the line goes over 2 and -2.
Answer:
first part is decreasing and increasing
second part is 3 and 5
Step-by-step explanation:
edg 2021
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of kg. Interpret your answer in terms of sampling error
Answer:
The result indicates that the percentage of all samples of three men that have mean brain weights within (1.24 * sampling error) of the mean is 78.50%.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question as follows:
According to one study, brain weights of men are normally distributed with mean = 1.20 kg and a standard deviation = 0.14 kg.
Determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg. Interpret your answer in terms of sampling error.
The explanation of the answers is now provided as follows:
Based on the Central limit theorem, it possible to say that the mean of sampling distribution (μₓ) is approximately equal to the population mean (μ) as follows:
μₓ = μ = 1.20 kg …………………………. (1)
Also, the standard deviation of the sampling distribution can be written as follows:
σₓ = (σ/√N) ……………………….. (2)
Where:
σ = population standard deviation = 0.14 kg
N = Sample size = 3
Substituting the values into equation (2), we have:
σₓ = 0.14 / √3 = 0.0808
Since we are to determine the percentage of all samples of three men that have mean brain weights within 0.1 kg of the population mean brain weight of 1.20 kg, this implies that we have:
P(1.10 ≤ x ≤ 1.30)
Therefore, 1.10 and 1.30 have to be first normalized or standardized as follows:
For 1.10 kg
z = (x - μₓ) / σₓ = (1.10 - 1.20) / 0.0808 = -1.24
For 1.30 kg
z = (x - μₓ)/σₓ = (1.30 - 1.20) / 0.0808 = 1.24
The required probability can be determined when P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24).
From the normal distribution table, the following can be obtained for these probabilities:
P(1.10 ≤ x ≤ 1.30) = P(-1.24 ≤ z ≤ 1.24) = P(z ≤ 1.24) - P(z ≤ -1.24) = 0.89251 - 0.10749 = 0.7850, or 78.50%
Therefore, the sampling error is equal to 0.0808 which is the standard deviation of the sampling distribution.
In terms of the sampling error, the result indicates that the percentage of all samples of three men that have mean brain weights within (1.24 * sampling error) of the mean is 78.50%.
A group of 49 randomly selected students has a mean age of 22.4 years with a standarddeviation of 3.8. Construct a 98% confidence interval for the population mean knowing thatthe population standard deviation is 4.2 years.
Answer:
The 98% confidence interval for the population mean is between 21 and 23.8 years.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{4.2}{\sqrt{49}} = 1.4[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 22.4 - 1.4 = 21 years.
The upper end of the interval is the sample mean added to M. So it is 22.4 + 1.4 = 23.8 years.
The 98% confidence interval for the population mean is between 21 and 23.8 years.
Find the y-intercept from the line passing through (1, 3) and having slope m=2.
Answer:
The y intercept is 1
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 2x+b
Substitute the point into the equation and solve for y
3 = 2(1)+b
3 =2+b
1 = b
The y intercept is 1
Part A
What is the relationship between squaring and taking the square root? Because of this relationship, what happens when you square a square
root?
I put 22.5 but it won’t work is there any other way for this to work??
Try rounding off your answer
Find a fraction equivalent to
that has a denominator of 10.
Answer:
1/10
Step-by-step explanation:
any number (1-9) as the number above the fraction line (numerator) with the number 10 below the fraction line is a fraction with a denominator of 10.
if it was 10/10, it will = 1
PLz help!!
What is the degree of the polynomial
Answer:
3 maybe I'm just guessing.
now thats room for an answer again: yeah, 3 is right. its the x³ that defines the degree, its just the biggest power.
Identify the two types of incorrect decisions in a hypothesis test. For each incorrect decision, what symbol is used to represent the probability of making that type of error?
Answer:
Type I error and Type II error
Explanation:
Type I and Type II errors are statistical errors made in hypothesis testing where an accepted hypothesis is actually the false hypothesis and the other true.
Type I error occurs when the chosen hypothesis is the alternative hypothesis which is false since the null hypothesis is true. We reject the null hypothesis which is actually true.
Type II error occurs when we accept or fail to reject the null hypothesis which is false and reject the alternative hypothesis which is true.
The probability of making a Type I error is represented by your alpha level (α)(we reject when below p-value)
The probability of a type-II error is represented by β which is beta.
Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.) f(x, y, z) = yz + xy; xy = 1, y^2 + z^2 = 25
Answer:
pls post pic of question can't understand ur question
I really need help
Dz,2 of X is
(0-4)
(2,-2)
(6,2)
9514 1404 393
Answer:
(6,2)
Step-by-step explanation:
As is often the case with multiple-choice problems, you don't actually need to know the detailed working. You just need to know what the answer looks like.
When point X is dilated by a factor of 2 with point Z as the center of dilation, it will move to a location twice as far from Z. You can tell by looking at the graph that X' will be in the first quadrant, above and to the right of the location of X. The only sensible answer choice is ...
X' = (6, 2)
_____
Additional comment
X is a distance of X-Z = (4, 0) -(2, -2) = (2, 2) from Z Doubling that will put the image point a distance of 2(2, 2) = (4, 4) from Z. When this is added to Z, we find ...
X' = Z + (4, 4) = (2+4, -2+4) = (6, 2)
Find the minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints.
y= √1+x^2 −2x, [0, 1]
Answer:
maximum: y = 1
minimum: y = 0.
Step-by-step explanation:
Here we have the function:
y = f(x) = √(1 + x^2 - 2x)
we want to find the minimum and maximum in the segment [0, 1]
First, we evaluate in the endpoints, which are 0 and 1.
f(0) =√(1 + 0^2 - 2*0) = 1
f(1) = √(1 + 1^2 - 2*1) = 0
Now let's look at the critical points (the zeros of the first derivate)
To derivate our function, we can use the chain rule:
f(x) = h(g(x))
then
f'(x) = h'(g(x))*g(x)
Here we can define:
h(x) = √x
g(x) = 1 + x^2 - 2x
Then:
f(x) = h(g(x))
f'(x) = 1/2*( 1 + x^2 - 2x)*(2x - 2)
f'(x) = (1 + x^2 - 2x)*(x - 1)
f'(x) = x^3 - 3x^2 + x - 1
this function does not have any zero in the segment [0, 1] (you can look it in the image below)
Thus, the function does not have critical points in the segment.
Then the maximum and minimum are given by the endpoints.
The maximum is 1 (when x = 0)
the minimum is 0 (when x = 1)
Annie bought a 2 3/4 pound roast for the family dinner. A total of 9 people will be at dinner. How many pound of roast will each person get if the roast is divided up equally?
Answer:
11 /36 of a pound
Step-by-step explanation:
Take the pounds and divide by the number of people
2 3/4 ÷ 9
Change the mixed number to an improper fraction
(4*2+3)/4 ÷9
11/4 ÷9
Copy dot flip
11/4 * 1/9
11/36
The length of a rectangle is 2 centimeters less than three times its width. Its area is 21 square centimeters. Find the dimensions of the rectangle. Use the formula, area=length*width.
Area = length x width
Area = 21 square cm
Width = x
Length = 3x + 2
21 = 3x+ 2 * x
21 = 3x ^2 + 2x
Subtract 21 from both sides:
3x^2 + 2x -21 = 0
Use the quadratic formula to solve for x:
-2 +/- sqrt(2^2-4*3(-21))/(2*3)
X = 7/3 and -3
A dimension can’t be a negative value so x needs to be 7/3
Width = x = 7/3 = 2 1/3 cm
Length = 3(7/3) + 2 = 9 cm
Check: 9 x 2 1/3 = 21
Dimensions: width 2 1/3 cm length 9 cm
Answer:
The dimensions of the rectangle are 7 by 3 centimeters.
Step-by-step explanation:
We are given that the length of a rectangle is two centimeters less than three times its width. In other words:
[tex]\displaystyle \ell = 3w-2[/tex]
Given that the area of the rectangle is 21 square centimeters, we want to determine the dimensions of the rectangle.
Recall that the area of a rectangle is given by:
[tex]A= w\ell[/tex]
Substitute:
[tex](21)=w(3w-2)[/tex]
Solve foro the width. Distribute:
[tex]3w^2-2w=21[/tex]
Isolate the equation:
[tex]3w^2-2w-21=0[/tex]
Factor. Find two numbers that multiply to 3(-21) = -63 and add to -2.
-9 and 7 suffice. Hence:
[tex]3w^2-9w+7w-21=0 \\ \\ 3w(w-3)+7(w-3) = 0 \\ \\ (3w+7)(w-3)=0[/tex]
Zero Product Property:
[tex]3w+7=0\text{ or } w-3=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle w = -\frac{7}{3}\text{ or } w=3[/tex]
Since width cannot be negative, we can ignore the first solution.
Therefore, our width is three centimeters.
And since the length is two less than three times the width, the length is:
[tex]\ell = 3(3) - 2 = 7[/tex]
The dimensions of the rectangle are 7 by 3 centimeters.
Match each scenario with the type of correlation it shows
Based on experience, the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2935 mm with a standard deviation of 0.000924 mm.
(a) A certain shipment has a diameter of 0.2963. Find the standardized z-score for this shipment.
Answer:
Step-by-step explanation:
the formula attached
HELP ASAP! I have completed everything except for the last box. Can someone please help me on the last box. Thank you for your help!
Answer:
2.35%
Step-by-step explanation:
According to the Empirical Rule,
71 - 79 and 79 - 87 are each 34% of the graph.
63 - 71 and 87 - 95 are each 13.5% of the graph.
55 - 63 and 95 - 103 are each 2.35% of the graph.
Hope this helps.
if one half of a number is 5 more than 6, what is the value when the number is tripled
Answer:
66
Step-by-step explanation:
let's use x to represent the unknown number
1/2x is 5 more than 6:
↓
1/2x=5+6
solve to find x
1/2x=11
x=22
next, it asks us what is the value of the number when the number is tripled
since we already found what x is equal to, we can multiply that by 3 to figure out its value when it's tripled
3(22)=66
Using mathematical equation to model the scenario, the value of the number when tripled is 66
Let the number = n
0.5n = 5 + 6
0.5n = 11
Divide both sides by 0.5
n = 22
When n is tripled :
n = 22 × 3
n = 66
Hence, the value of the number when tripled is 66
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