Answer:
\(d=4\sqrt{5}\approx8.94\)
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)
Let (-1, -2) be (x₁, y₁) and let (-9, 2) be (x₂, y₂).
Substitute appropriately:
\(d=\sqrt{(-9-(-1))^2+(2-(-2))^2\)
Evaluate:
\(d=\sqrt{(-8)^2+(4)^2\)
Square and evaluate:
\(d=\sqrt{64+16}=\sqrt{80}=4\sqrt{5}\approx8.94\)
Therefore, the distance between the two points is approximately 8.94 units.
The number of small air bubbles per 3 feet by 3 feet plastic sheet has a Poisson distribution with a mean number of two per sheet. What percent of these sheets have no air bubbles
The percentage of the sheets with no air bubbles is given as follows:
13.53%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:
\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)
The parameters are listed and explained as follows:
x is the number of successes that we want to find the probability of.e = 2.71828 is the Euler number\(\mu\) is the mean in the given interval or range of values of the input parameter.The mean for this problem is given as follows:
\(\mu = 2\)
The proportion of these sheets with no air bubbles is P(X = 0), hence it is given as follows:
P(X = 0) = e^-2 = 0.1353 = 13.53%.
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Manny begins the summer with $200 in his savings account. Each week he adds $85 to his account. Susan begins the summer with $95 in a savings account and adds $100 each week. When will Manny and Susan have the same amount of money in their accounts?
Answer:
7 weeks
Step-by-step explanation:
200 + 85w = 95 + 100w
-95 -85w -95 -85w
105 = 15w (divide both sides by 15)
7 = w
Which place value first determines which of the numbers 6.399 or 6.400 is the larger number?
thousandths
hundredths
tenths
ones
Comparing the numbers, it is found that the tenths value first determines which of the numbers 6.399 or 6.400 is the larger number.
The decimal numbers are 6.399 and 6.400.
The ones value for each is 6.For the first value, the tenths digit is of 3, while for the second is of 4.The tenths digit is the first in which there is a difference, hence, it determines which of the numbers 6.399 or 6.400 is the larger number.
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Borrow 1 from the whole number part to rewrite 8 10/24.
We will get 7 34/24 after borrowing 1 from the whole number part to rewrite 8 10/24.
What is whole number ?
All of the fundamental counting numbers as well as the number zero are grouped together as whole numbers. Natural numbers are the term used in mathematics to describe counting numbers. Consequently, we can define the whole number as a combination of all natural numbers and 0. Along with zero, all positive integers are considered whole numbers.
Given : 8 10/24
We have to borrow 1 from the whole number, So, we also need to add 1 to the fraction part.
Hence, 8 10/24 - 1 = 7 (1+ 10/24)
= 7 ( 24+10 / 24 )
= 7 34/24.
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What is 2 3/7 minus 5 6/7
Step-by-step explanation:
\( = 2 \frac{3}{7} - 5 \frac{6}{7} \\ \)
\( = \frac{2 \times 7 + 3}{7} - \frac{5 \times 7 + 6}{7} \\ \)
\( = \frac{17}{7} - \frac{41}{7} \\ \)
\( = \frac{17 - 41}{7} \\ \)
\( = \frac{ - 24}{ \: 7} \\ \)
☘☘☘...
Can you plz help me with this, because I don’t know how to do this and can u plz explain how to do it
Answer:
Step-by-step explanation:
You can start this in may ways but let's start by isolating one of the parenthesis:
x (x² - 5) = - (x - 3)
x³ - 5x = -x + 3 (here I multiplied x for what's inside the parenthesis and the "minus" signal by the other parenthesis which was (x - 3))
x³ - 5x + x = 3
x³ -4x = 3
x³ -4x -3 = 0 (now this right here is a "depressed cubic equation" and it's one of the toughest sit of all time, so good luck with that, you might wanna take a look at this:
ytb/watch?v=rNDy2ZFvG1E
or maybe I'm doing something wrong and it's simpler than that, but whaterver...)
1/2(-2x -10) > 3(4 -6x)
Answer:
x>1
Step-by-step explanation:
\(\frac{1}{2}\) × (-2x - 10) > 3(4-6x)
-2x - 10 > 6(4-6x)
-2x - 10 > 24 - 36x
-2x + 36x > 24 + 10
34x > 34
x>1
Answer:
10 > -6x
Step-by-step explanation:
1/2(-2 x -10) > 3(4 - 6)
PEMDAS
do the work in the parentheses:
1/2(20) > 3(-2)
multiply (you multiply when a number is next to parentheses fyi):
1/2 x 20 = 10, 3 x -2 = -6
answer: 10 > -6x
Are the expressions –0.5(3x + 5) and –1.5x + 2.5 equivalent? Explain why or why not.
Answer:
It is
-0.5(3x+5)= -1.5x+2.5
Step-by-step explanation:
-0.5(3x+5)
multiply-0.5 with 3x and 5 to get rid of the brackets.
-0.5×3x= -1.5x
-0.5×5= 2.5
-1.5x+2.5
Answer:
Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.
Step-by-step explanation:
The product of¾ xy and 3/4is ____________.
Answer:
9/16xy
Step-by-step explanation:
Multiply through by 3/4
(3/4xy) × (3/4)
numerator =(3×3) = 9
denominator = (4×4) = 16
Simplifying = 9/16xy
What is the area of the composite shape?
The sum of the measures of the interior angles of a
convex quadrilateral is
a. 180°
b. 270°
c. 540°
d. 360°
Answer:
d. 360°
Hope this help!
consider the following. x = sin(t), y = csc(t), 0 < t < ????/2 (a) eliminate the parameter to find a cartesian equation of the curve.
The cartesian equation of the curve defined by x = sin(t) and y = csc(t), 0 < t < π/2, is y = √(1 - x²).
To eliminate the parameter t, we can use the trigonometric identity
csc(t) = 1/sin(t).
Substituting this into the equation y = csc(t), we have y = 1/sin(t).
Rearranging the equation, we get sin(t) = 1/y. Now, we can substitute the expression for x from the equation x = sin(t) into this equation. This gives sin(t) = 1/y = x.
Taking the square of both sides, we have
sin²(t) = (1/y)²
= x².
Using the Pythagorean identity sin²(t) + cos²(t) = 1,
we can rewrite the equation as cos²(t) = 1 - x².
Since cos²(t) = 1 - sin²(t), we can substitute this into the equation to get
1 - sin²(t) = 1 - x².
Simplifying, we have sin²(t) = x².
Taking the square root of both sides, we get sin(t) = ±x.
Finally, substituting sin(t) with its expression x in the equation y = csc(t), we have y = 1/sin(t) = 1/(±x).
Simplifying further, we have y = ±(1/x).
Hence, the cartesian equation of the curve is y = ±(1/x), or equivalently,
y = √(1 - x²) for the positive root.
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Anna is saving to buy some souvenirs on a family vacation. She has already saved $125, and she saves another $2 from her allowance every day. Formulate and then graph the equation that models the total amount Anna saves, y, in terms of the number of days she adds to her savings, X.
Answer:
125+2x=y (take 125 add 2x for $2 a day and then = y for amount saved)
Points on Graph:
(125,0)
(135,5)
(145,10)
(155,15)
(165,20)
(175,25)
(185,30)
(195,35)
(205,40)
(215,45)
(225,50)
Answer:
Step-by-step explanation:
Solve for x. Please help.
Answer:
x = 11
Step-by-step explanation:
Pre-SolvingWe are given a circle.
We know that arc DC is equal to 95°, and that arc CE is 10x+3.
We also know that m<DCE = 76°.
We want to find the value of x.
Recall that an entire circle is 360 degrees in measure.
Also recall that an angle that is inside a circle (an inscribed angle) is half the value of the arc it intercepts.
We can see that <DCE is an inscribed angle; the arc it intercepts is arc DE.
Based on what we know from above, arc DE is twice the value of <DCE.
This means, arc DE = 2(76°) = 152°
As stated above, a circle's full measure is 360 (degrees).
This means that the sum of all the arcs equals 360.
So, arc CD + arc DE + arc CE = 360
Substitute the values we know to get:
95 + 152 + arc CE = 360
247 + arc CE = 360
arc CE = 113
Recall that the value of arc CE is 10x + 3.
So:
10x + 3 = 113
Subtract 3 from both sides.
10x = 110
Divide by 10.
x = 11
Circle the outliers in the following scatter plots. -5 15 10 L 5 5 -5 10 15 4 3 2 2 3 4 5 - 60 7
The outliers in the following scatterplots need to be circled:--5, 15-60
The points (-5,15) and (-60,7) are outliers.
An outlier is a value that lies outside (is smaller or larger) than most other values in a given data set. An outlier may represent a unique event or error. When examining scatterplots, outliers are the values that appear to be farthest from the trend line. Outliers are labeled as "L" in scatterplots. To answer this question, the outliers in the following scatterplots need to be circled:
--5, 15-60
The points (-5,15) and (-60,7) are outliers.
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I need help with this problem. please and thank you.
The value of f(g(x)) is x^2 + 1/x
How to determine the valueA function is an expression that describes the relationship between an independent variable and dependent variable.
Given the functions;
f(x) =
\( \sqrt[3]{x} \)
g(x) =
\( \frac{ x+ 1}{ {x}^{3} } \)
How to determine the function
Substitute the value do x as the value of the function g(x)
f(g(x)) =
\( \sqrt[3]{ \frac{x + 1}{ {x}^{3} } } \)
Find the cube root of the expression
f(g(x)) =
\( \frac{ {x}^{3} + {1}^{3} }{x} \)
Find the cube of the values
f(g(x)) =
\( \frac{ {x}^{3} + 1 }{x} \)
Divide through by x, we have;
f(g(x)) = x^2 + 1/x
Thus, the value of f(g(x)) is x^2 + 1/x
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Health and safety guidelines set the highest sound intensity level in the workplace to 90. 0 db. One workshop with 32 similar machines produces a sound intensity level of 92. 0 db. How many of them must be shut down to bring the workshop into compliance with the guidelines?.
The sound intensity level should be decreased by 2 dB to carry the studio into consistency with the rules.
A decrease of 2 dB can be accomplished by one or the other by closing down a portion of the machines (since the sound intensity level declines by 6 dB for each splitting of the sound power) or by introducing sound-sealing materials.
Thus, to carry the studio consistent with the rules, 16 machines would need to be closed down.
It's vital to follow well-being and security rules in the working environment to guarantee the prosperity of representatives and forestall hearing harm. Decreasing the number of machines or introducing soundproofing materials can bring the studio into consistency.
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the first 5 terms are -16,-7,2,11,20 what is the eighth number in this sequence
Answer:
29
Step-by-step explanation:
to get from -16 to -7 you have to add 9
to get from -7 to 2 you have to add 9
to get from 2 to 11 you have to add 9
and the same thing for 11 to 20
Answer: The answer
is 29 because the pattern of the number is 999999
Step-by-step explanation:
PLEASE HELP!
Six guinea pigs are released in an area with no natural predators. The guinea pig population quadruples every year. Write a function P that represents the guinea pig population at a given time T measured in years. Choose the function below that represents the inverse function P-1
Use the inverse function to find how long it will take the guinea pig population to reach 1,000 and choose the response that correctly states this information.
The time taken for the population of the pig to reach 1000 will be almost four years.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
Six guinea pigs are released in an area with no natural predators.
The guinea pig population quadruples every year.
Write a function P that represents the guinea pig population at a given time T measured in years.
Then the function will be
\(\rm P = 6 (4)^T\)
Then the inverse function of P will be
\(\rm T = 6 (4)^P\\\\\\P \ln 4 = \ln \left (\dfrac{T}{6} \right )\\\\\\P = \dfrac{\ln (T/6)}{\ln 4}\)
Then the time taken for the population of the pig to reach 1000 will be
\(\rm 1000 = 6 (4)^T\\\\\\166.667 = 4^T\\\\\\T = 3.69 \\\\\\T \approx 4 \ years\)
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H14
113
42
11
-10
H13
12
-11
-40
9
144
H13
H12
-11
10
3
-6
TOA
2
4
1 2 3 4 5 6 7 8 9 1011121314
1 2 3 4 5 6 7 8 9 1011121314
1 2 3 4 5 6 7 8 9 1011121314
94
14
4000
H14
13
Y4
14
13
12
11
10
13
42
11
10
9
8
7
12
8
а со т о р т о су
-11
10
9
8
-7
6
5
No dob
3
2
1
3
2
1
2.
1 2 3 4 5 6 7 8 9 1011121314
1 2 3 4 5 6 7 8 9 1011121314
1 2 3 4 5 6 7 8 9 1011121314
Positive Association
Negative Association
No Association
uh I don't unerstand that :(
How many solutions does the system of equations below have?
y = 8x - 7
y = 8x + 4/5
no solution
one solution
infinitely many solutions
Answer: No Solution
Step-by-step explanation:
To solve this system of equations, set the two equations equal to each other and get: 8x - 7 = 8x + 4/5.
However, notice that if you consolidate the x terms and subtract 8x, you get 0 - 7 = 4/5.
7 can never equal 4/5, so there is no solution :)
A survey was given to people who own a certain type of car. What percent of the people surveyed were completely satisfied with the car?
60% of the people from the survey are completely satisfied
Last month, Henry and Kendra sold candy to raise money for their debate team. Kendra sold 3/10 as much candy as Harry did. If Harry sold 1/2 of a box of candy, how many boxes of candy did Kendra sell? I want the REAL answer!
1/2-3/10=5-3/10=1/5 this is the answer
PLEASE HELP ME!!!!!!!
Step-by-step explanation:
step 1. triangles ABG and ACF are similar.
step 2. triangle ACF is twice the size of triangle ABG.
step 3. if BG = 8 then CF = 16.
Need help pls help me
Answer:
See below, please!
Step-by-step explanation:
We know that 6z-31+something is going to be equal to 180 degrees, because it is supplementary. But what is that something? We see 67 degrees. Do you think this is a corresponding angle to the something that we need to find? Yes, it is! So we know that 6z-31+67 is equal to 180. So, z is 24. Now, since we know the value of the something (67 degrees because of corresponding angles) we can find yet another pair of supplementary angles. 67+x=180! Kind of neat, huh? So, x is equal to 113.
Hope this helped!
how do i find an equation for a line with an x-intercept of 4 and a y-intercept of -2
Answer:
The equation of a line is y = ax + b, where a is the slope and b is the y-intercept.
Since we have the y-intercept, all we need to do is find the slope. To find the slope, you need 2 coordinates.
The y-intercept is where the line crosses the y axis, so it is where x is 0. Since the y intercept is -2, that means the first coordinate is (0, -2)
The x-intercept is where the line crosses the x axis, so it is where y is 0. Since the x intercept is 4, that means the second coordinate is (4, 0)
Since we already have the y-intercept, all we do is put the slope in the equation: y = 1/2x - 2.
Step-by-step explanation:
The vertices of a quadrilateral pqrs lie on circle k. let x be the point on k such that qx bisects angle pqr. let y be the point on k such that xy is a diameter. prove that sy bisects angle psr.
Line SY bisects angle PSR. To prove that line SY bisects angle PSR, we can use the property that an angle inscribed in a circle is half the measure of the intercepted arc. Here's the proof:
Since XY is a diameter, it subtends a 180-degree angle at any point on the circle. Therefore, angle QXY measures 180 degrees.
Angle PQY is an inscribed angle, and its measure is half the intercepted arc PQ. Similarly, angle YSR measures half the intercepted arc SR.
Since angle QXY is 180 degrees and angle PQY and angle YSR are half of their respective intercepted arcs, the sum of angles PQY and YSR must be 180 degrees.
Therefore, angle PQY and angle YSR are equal, and since angle PQY is congruent to angle PQS (as QX bisects angle PQR), it follows that angle YSR is congruent to angle PSR.
Hence, we have proved that line SY bisects angle PSR.
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What is the value of the expression -218 - 72 - (-5)?
Answer:
The answer is -285
Step-by-step explanation:
PLEASE ANSWEEEEERRRR
Natalie solved a system of equations by graphing as shown which of the following is a true statement?
A. One of the equations in the system was y=2x
B. One of the equations in the system was x + y = -6
C. The solution to the system of equations is (-2,-4)
D. All of the above
Answer:
D
Step-by-step explanation:
D
Find two points that belongs to the liney + 4x = -1
We want to find two points that belong to the line
\(y+4x=-1\)The easiest points to calculate are the intercepts. The x-intercept happens when y = 0, to find the corresponding x-value we just need to evaluate y = 0 on the expression for our line.
\(0+4x=-1\Rightarrow x=-\frac{1}{4}=-0.25\)The x-intercept is (-0.25, 0).
Analogously, for the y-intercept(that happens at x = 0), we have
\(y+4\cdot0=-1\Rightarrow y=-1\)The y-intercept is (0, -1).
Two points that belongs to this line are (-0.25, 0) and (0, -1).
The graph of this line is