Basically we need to find the distance between A and B, so:
[tex]\begin{gathered} \mleft\Vert AB\mright||=d=\sqrt[]{(x2-x1)^2+(y2-y1)^2+(z2-z1)^2} \\ where \\ A=(x1,y1,z1)=(-1,-7,0) \\ B=(x2,y2,z2)=(-8,8,-10) \\ \Vert AB||=\sqrt[]{(-8-(-1))^2+(8-(-7))^2+(-10-0)^2} \\ \Vert AB||=\sqrt[]{49+225+100} \\ \Vert AB||=\sqrt[]{374} \\ \Vert AB||\approx19.339 \end{gathered}[/tex]is 26 and 65 relatively prime
No. 26 and 65 both have a common factor of 13, since 26 = 2•13 and 65 = 5•13, so GCD(26, 65) = 13 ≠ 1.
We can also arrive at this using Euclid's algorithm.
65 = 58 + 7 = 2•26 + 13
26 = 2•13 + 0
Since the last remainder is zero, the previous remainder is the GCD.
18
Select the correct answers from each drop-down menu.
Complete the steps in the proof that show quadrilateral KITE with vertices K(0, -2). I(1, 2). T(7,5), and E(4,-1) is a kite.
Using the distance formula, KI = √√(2 – (-2)² + (1 - 0)² = √17. KE =
-
IT =
and TE=
Therefore, KITE is a kite because
→
In the quadrilateral KITE,
The value of side KI = [tex]\sqrt{17}[/tex]
The value of side KE = [tex]\sqrt{17}[/tex]
The value of side IT = [tex]3\sqrt{5}[/tex]
The value of side TE = [tex]3\sqrt{5}[/tex]
The quadrilateral KITE is a kite because , KI = KE and IT = TE
How are the values of the quadrilateral sides calculated?
K (0,-2) , I(1,2) ,T(7,5) , E(4, -1)
KI = [tex]\sqrt{17}[/tex]
What is the value of side KE ?
K (0,-2) and E(4, -1)
The distance formula is:
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\KE =\sqrt{(4-0)^{2} + (-1 +2)^{2} }\\\\KE = \sqrt{(4)^{2} + (1)^{2} }\\\\KE = \sqrt{16+1} \\\\KE = \sqrt{17}[/tex]
The value of side KE of the quadrilateral = [tex]\sqrt{17}[/tex]
What is the value of side IT ?
I(1,2) and T(7,5)
The distance formula is:
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\IT =\sqrt{(7-1)^{2} + (5-2)^{2} }\\\\IT = \sqrt{(6)^{2} + (3)^{2} }\\\\IT = \sqrt{36+9} \\\\IT = \sqrt{45} =3 \sqrt{5}[/tex]
The value of side IT of the quadrilateral =[tex]3\sqrt{5}[/tex]
What is the value of side TE ?
T(7,5) and E(4, -1)
The distance formula is :
[tex]d = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }\\\\TE =\sqrt{(4-7)^{2} + (-1-5)^{2} }\\\\TE = \sqrt{(-3)^{2} + (-6)^{2} }\\\\TE = \sqrt{9+36} \\\\TE = \sqrt{45} =3 \sqrt{5}[/tex]
The value of side TE of the quadrilateral = [tex]3\sqrt{5}[/tex]
The quadrilateral KITE is a kite because :
KI = KE and IT = TE Two sets of a quadrilateral with equal lengths and adjacent edges are kites.To learn more about quadrilaterals, refer:
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Answer:
The answer is in the picture.
Hope this helps!
Step-by-step explanation:
what expression is equal 4to the -2 power multiplied by 7 to the -2 power
Answer:
Step-by-step explanation:
4^-2 * 7^-2
= 1/4^2 * 1/7^2
= 1/16 * 1/49
- 1/784
a human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. to test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000. the following is the setup for this hypothesis test: $ h0: p
The test is one of the form Hₐ < ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀
According to problem ststement : We need to solve an Hypotesis test proportion so:
H₀ P₀ = 0,4 and Hₐ < 0,4 ( Alternative hipotesis)
From a random sample of 700 employes 305 are determined to earn more than $ 50000
Proportion pₐ = 305/700 = 0,4357 pₐ = 0,4357
proportions are p = 0.4 and q = 0,6
We will asume a confidence level of 95 % hence α= 1-0,95 α = 0,05
so from z table we find z(c) = 1,64
Therefore we must calculate our z(p) = ( pₐ-p₀) ÷√(p*q)/n
Calculating z(p) = 0,0357 /0,01851 ⇒ z(p) 1.9286
Our test is one of the form Hₐ < ; that means is a right tail test, and the value z(p) is bigger than our critical value (z(c) = 1.64) so we rejecte H₀
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sammy buys 5 pounds of oranges for 7.50 at this rate how much would 8 pounds of oranges cost
The cost of 8 pounds of oranges based on the total cost of 5 pounds bought is 12.00
What is the cost for a pound of oranges?
The cost of a pound of oranges based on the rate at which 5 pounds were bought and 8 pounds would also be bought is determined as the amount paid for 5 pounds of oranges divided by the number of pounds of oranges bought
cost per pound of oranges=cost of 5 pounds/5 pounds
cost per pound of oranges=7.50/5
cost per pound of oranges=1.50
Based on the 1.50 per pound, the cost of 8 pounds is the cost per pound multiplied by 8 pounds
cost of 8 pounds of oranges=1.50*8pounds
cost of 8 pounds of oranges=12.00
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Solve for x. Please help!!
Answer: x= -16
Step-by-step explanation:
Ray is on the school basketball team. During practice, Ray made 23 out of 40 free throw shots. Which letter on the number line best represents the percent of free throw shots ray made? D E F G
How do you find this??
Answer:
Step-by-step explanation:
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A cylindrical hole cut out of the center has a radius of 6 millimeters.
A cylinder is shown. A smaller cylinder is cut out of the middle of the larger cylinder. Both have a height of 21 millimeters. The diameter of the larger cylinder is 20 millimeters, and the the radius of the smaller cylinder is 6 millimeters.
Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.
21π(10)2 – 21π(6)2
π(20)2(21) – π(6)2
2,100π – 756π
7,644π
1,344
The expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .
In the question ,
it is given that
the diameter of the cylindrical metal pipe = 20mm
so the radius of the cylindrical pipe = 10 mm
height of the cylindrical metal pipe = 21mm
Using the formula of Volume of Cylinder = π*r²*h
the volume of cylindrical metal pipe = π*(10)²*21 .....(i)
the height of smaller cylinder = 21mm
radius of the smaller cylinder = 6mm
So, Volume of the smaller cylinder = π*(6)²*21 .....(ii)
the volume of metal needed to make the pipe = Volume of cylindrical metal pipe - Volume of the smaller cylinder .
Substituting the values from (i) and (ii) , we get
volume of metal needed = π*(10)²*21 - π*(6)²*21
= 21*π*(10)² - 21*π*(6)²
hence , option(a) is correct .
Further Simplifying , we get
= 21*100*π - 21*36*π
= 2100π - 756π
hence , option(c) is also correct
Therefore , the expressions that represent the volume of metal needed , to make the pipe are (a)21*π*(10)² - 21*π*(6)² and (c)2100π - 756π .
The given question is incomplete , the complete question is
A cylindrical metal pipe has a diameter of 20 millimeters and a height of 21 millimeters. A smaller cylinder is cut out of the middle of the larger cylinder. Both have a height of 21 millimeters and the the radius of the smaller cylinder is 6 millimeters.
Which expressions represent the volume of metal needed, in cubic millimeters, to make the pipe? Select two options.
(a) 21*π*(10)² - 21*π*(6)²
(b) π*(20)²*(21) – π*(6)²
(c) 2100π - 756π
(d) 7,644π
(e) 1,344
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Answer: A & C
Step-by-step explanation: Just did it
The ratio of the number of men to the number of woman is 9:5 if there are 63 men how then how many woman are there
Answer:
Step-by-step explation:
if the ratio of 9 contains 63 men then what about the ratio of 5 u do cross multiplication it will be 5 ×63 the answer you get multiply by 9 answer will be 35
Prizes and the chances of winning in a sweepstakes are given in the table below.
Prize Chances
$10,000,000 1 chance in 300,000,000
$350,000 1 chance in 150,000,000
$50,000 1 chance in 10,000,000
$20,000 1 chance in 1,000,000
$400 1 chance in 200,000
A watch valued at $75 1 chance in 6,000
(a) Find the expected value (in dollars) of the amount won by one entry.
(b) Find the expected value (in dollars) if the cost of entering this sweepstakes is the cost of a postage stamp (34 cents)
The expected value of the discrete distribution, for each case, is given as follows:
a) Amount won by one entry: $0.075.
b) If the cost is the cost of a postage stamp: -$0.525.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's probabillity.
In this problem, the distribution for the prizes is given as follows:
P(X = 10,000,000) = 1/300,000,000.P(X = 350,000) = 1/150,000,000.P(X = 50,000) = 1/10,000,000.P(X = 20,000) = 1/1,000,000.P(X = 400) = 1/200,000.P(X = 75) = 1/6,000.Hence the expected value for the prizes is:
E(X) = 10,000,000 x 1/300,000,000 + 350,000 x 1/150,000,000 + 50,000 x 1/10,000,000 + 20,000 x 1/1,000,000 + 400 x 1/200,000 + 75 x 1/6,000 = $0.075.
The cost of a postage stamp is of $0.6, hence the expected value considering this cost would be of:
0.075 - 0.6 = -$0.525.
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Jake currently has 362 g of sugar and then uses 7 ounces for baking a cake. How many grams (g) of sugar does he have left? 1 ounce = 28 g
Solve it please ☹️ hehdhdbssbdvs
A quantity with an initial value of 200 grows continuously at a rate of 55% per day.
What is the value of the quantity after 1 week, to the nearest hundredth?
The value of the quantity after 420 minutes is 1.739
How to calculate the amount of the quantity?
In mathematics, the amount of the quantity can be measured with the help of the exponential function by using its standard equation. But the measured quantity should grow continuously.
According to the question, the growth of the quantity is growing continuously which illustrate the exponential function.
The given parameters are:
Initial value, a = 200; Rate, r = 55%
An exponential growth function is represented as:
y = a(1 + r)^x
Substitute the value in the equation
y = 200(1 + 55%)^x
After 1.55 minutes, x = 7 * 60
So, we have:
y = 200(1 + 55%)^(7 * 60)
Evaluate the expression
y = 1.739
Hence, the value of the quantity after 420 minutes is 1.739
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Of the 300 scarves, 200 are not blue.
(d) Write the number of scarves which are blue as a fraction of the total number
of scarves.
The answer will be: 200/300 of scarves are blue. 200/300 also is equal to 2/3. The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
What does "fraction" mean?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Reduce the fractions if they aren't already in the lowest terms. Then, all that is required is to multiply the denominator by the denominator and the numerator by the numerator. For instance, multiplying 2 by 7 yields the new numerator, which is 14, when multiplying 2/3 and 7/8. The result of multiplying 3 by 8 is 24.
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The temperature rises 2c each hour from 6:00 am to 3:00 pm. What is the total change in temperature during this period of time?
Answer:
20c
Step-by-step explanation:
if the temperature rises 2c every hour u count from 6 to 3 and it would be 10 hours
then u do 10×2=20 or 10×2=20c
pls help ASAP for brainliest
(should have solution)
Answers:
15) x= −1 and y=2
16) x=2 and y= −1
Step-by-step explanation:
15) Solve the system by elimination:
Multiply the first equation by 2 and the second equation by 1.
2(8x−6y=−20)
1(−16x+7y=30)
They then become:
16x−12y=−40
−16x+7y=30
Add the two equations to eliminate x:
−5y=−10
Then solve for y by dividing both sides by -5:
−5y/−5 = −10/−5
The answer for y is y=2
Now Substitute 2 for y in the equation 8x−6y=−20:
8x−(6)(2)=−20
8x−12=−20
Add 12 to both sides:
8x−12+12=−20+12
8x=−8
Divide by 8:
8x/8 = −8/8
The answer for x is x=−1
16) Solve the system by elimination:
Multiply the second equation by 6 and merge the equations together.
(6x−12y=24)
6(−x−6y=4)
They then become:
6x−12y=24
−6x−36y=24
Add the two equations to eliminate x:
−48y=48
Then solve for y:
−48y=48
−48y/−48 = 48/−48
The answer for y is y= −1
Now substitute −1 for y in 6x−12y=24:
6x−(12)(−1)=24
6x+12=24
Add -12 to both sides:
6x+12+−12=24+−12
6x=12
6x/6 = 12/6
The answer for x is x=2
Solved! Please don't forget the Brainliest!!
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Problem 15.) The two equations are :
[tex] \sf \: 8x - 6y = - 20 \: \: \: \: \: \: \: - (1)[/tex][tex]\sf - 16x + 7y = 30 \: \: \: \: \: \: - (2)[/tex]Let's multiply whole equation (1) by 2
[tex]\qquad \sf \dashrightarrow \: 16x - 12y = - 40 \: \: \: \: \: \: - (3)[/tex]
Now, Add equation (3) and equation (2)
[tex]\qquad \sf \dashrightarrow \: 16x - 12y - 16x + 7y = - 40 + 30[/tex]
[tex]\qquad \sf \dashrightarrow \: - 5y = - 10[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - 10 \div - 5[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 2[/tex]
Plug the value of y in equation (1) :
[tex]\qquad \sf \dashrightarrow \: 8x - 6y = - 20[/tex]
[tex]\qquad \sf \dashrightarrow \: 8x - 6(2) = - 20[/tex]
[tex]\qquad \sf \dashrightarrow \: 8x - 12 = - 20[/tex]
[tex]\qquad \sf \dashrightarrow \: 8x = - 20 + 12[/tex]
[tex]\qquad \sf \dashrightarrow \: x = - 8 \div 8[/tex]
[tex]\qquad \sf \dashrightarrow \: x = - 1[/tex]
So, the required values are : x = -1 and y = 2
Problem 16.) The two equations are :
[tex] \sf 6x - 12y = 24 \: \: \: \: \: \: \: - (1)[/tex][tex] \sf - x - 6y = 4 \: \: \: \: \: \: \: \: \: \: \: - (2)[/tex]Multiply equation (2) by 2 :
[tex]\qquad \sf \dashrightarrow \: - 2x - 12y = 8 \: \: \: \: \: \: - (3)[/tex]
Now, subtract equation (3) from equation (1)
[tex]\qquad \sf \dashrightarrow \: 6x - 12y - ( - 2x - 12y) = 24 - 8[/tex]
[tex]\qquad \sf \dashrightarrow \: 6x - 12y + 2x + 12y= 16[/tex]
[tex]\qquad \sf \dashrightarrow \: 8x = 16[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 16 \div 8[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 2[/tex]
Now, plug x = 2, in equation (2) :
[tex]\qquad \sf \dashrightarrow \: - x - 6y = 4[/tex]
[tex]\qquad \sf \dashrightarrow \: - 2 - 6y = 4[/tex]
[tex]\qquad \sf \dashrightarrow \: - 6y = 4 + 2[/tex]
[tex]\qquad \sf \dashrightarrow \: - 6y = 6[/tex]
[tex]\qquad \sf \dashrightarrow \: y = 6 \div - 6[/tex]
[tex]\qquad \sf \dashrightarrow \: y = - 1[/tex]
So, the required values are : x = 2 and y = -1
HELP MEEEEEEEEEEE, Ed's living room is 4 yards wide and 7 yards long. He wants to install yellow carpet that costs $5.00 per square yard. How much will it cost to buy enough carpet for the living room?
It will cost 140 dollars to buy enough carpet for the living room.
What is a rectangle?A rectangle is a four-sided figure in which opposite sides are equal and the diagonals are also of the same length.
Given Ed's living room is 4 yards wide and 7 yards long.
We know that the area of a triangle is the product of its length and width.
∴ The area of Ed's living room is (4×7) sq yards = 28 sq yards.
Also given to install yellow carpet that costs $5.00 per square yard,
∴ For 28 sq yards, the cost of installing a yellow carpet will be,
= (28×5) dollars.
= 140 dollars.
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IF AB = 6x-9 BC = 3x+17 and AC = 5x+16, find BC
Since the point B is between points A and C, the length BC is 22.25 units
How to determine the numerical length of BC?From the question, we have the following parameters that can be used in our computation:
Length AB = 6x - 9
Length BC = 3x + 17
Length AC = 5x + 16
The above implies that the point B is between points A and C
So, we have the following equation
AC = AB + BC
Substitute the known values in the above equation
So, we have the following equation
5x + 16 = 6x - 9 + 3x + 17
Collect the like terms
So, we have the following equation
5x - 6x - 3x = -9 + 18 - 16
Evaluate the like terms
So, we have the following equation
-4x = -7
Divide by -4
x = 7/4
Substitute x = 7/4 in the equation BC = 3x + 17
So, we have the following equation
BC = 3 x 7/4 + 17
Evaluate
BC = 22.25
Hence, the numerical length of BC is 22.25 units
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Write the given equation in slope-intercept form -10x + 2y = 12
Answer:
x-intercept- (-1.2,0)
y-intercept- (0,6)
Step-by-step explanation:
To find the slope-intercept form, we have to find x and y.
First, find x. Get rid of the 2y, and the equation will look like this.
-10x=12
Now, divide both sides by -10.
12/-10=-1.2
The x-intercept would be (-1.2,0)
To find the y-intercept form, do the same thing.
Get rid of the -10x.
2y=12
Divide by 2 on both sides.
y=6
The y-intercept form would be (0,6)
Hope this helps! :D
please help meeeeeeeeeeeeeeeeeeeeee
3. Which point is closest to -3 on the number line?
Answer: D.
Step-by-step explanation:
-2/20 = -0.1, 0.1 is the closet one to -3
What is the slope of the line passing through (0, 5) an d(-12, 2)?
m = 1/4 is the slope of the line .
What is slope in plain English?
Slope and slant both refer to an elevation away from a surface or line that is generally straight and used as a reference. Slope is the verb form for an oblique vertical incline: Here, the land abruptly slopes either upward or downhill.The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b. M represents the line's slope. Additionally, the y-intercept is at a position where b is the b. (0, b). The slope and y-intercept of the equation y = 3x - 7 are, for instance, 3 and 0, respectively.The slope of a line passing through points ( x₁ , y₁ ) ( x₂ , y₂ ) is defined as
m = y₂ - y₁/x₂ - x₁
if the x coordinates are not equal. The slope is not defined if the x
coordinates are equal because that would require dividing by zero.
here ,
( x₁ , y₁ ) = (0, 5)
( x₂ , y₂ ) = ( -12 , 2 )
m = y₂ - y₁/x₂ - x₁
m = 2 - 5/-12 - 0
m = -3/-12
m = 1/4
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Whoever Answers First I will make Brainliest Evaluate
{[(20−32)÷(−6)]2−11}÷(−7)
11. you suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. the outcome of the experiment is listed in the following table. do you think the die is loaded? why?
There is insufficient evidence to prove that the dice are loaded because every number on them has a probability of 1/6.
The likelihood of any number appearing on a six-sided die is 1/6.
It will not be 1/6 if it is loaded.
In order to determine whether the provided distribution complies with the idealized distribution of the dice throw, we do a chi-square test.
Step 1: Form the hypothesis.
H₀ = The likelihood of rolling any number on a six-sided die is one-sixth.
H₁ = The likelihood of getting any number on a six-sided die is not one in six.
Step 2: Indicate the degree of significance.
Alpha = 0.5
Step 3: computation of the chi-square test statistic (Image is attached for this step)
Step 4: Discover the important value.
Critical Value ⇒ 12.8325 =CHISQ.INV[1 - (0.05 / 2), 5]
Step 5: Determine the p-value.
p-value ⇒ 0.853 =1 - CHISQ.DIST(1.97,5,TRUE)
Step 6: Make a choice regarding whether or not to reject H₀
We are unable to reject the null hypothesis since the p-value is higher than 0.05.
As a result, we draw the conclusion that there is a 1/6 chance of getting any number on a six-sided die.
Note: Since the chi-square value is below the threshold, the null hypothesis cannot be rejected.
Because every number on the dice has a probability of 1/6, there is insufficient evidence to support the assertion that the dice are loaded.
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Write an expression for 362 more than the product of 302 and q.
Mathematically we write this as:
=362+(302×q)
The expression is 362+302q
Goodluck.
Please help!!!!!!!! I’ll mark brainliest
The answers to all the equations are:
(A) f(x) = x + 3 when f(4) ⇒ f(x) = 7(B) f(x) = 2x - 9 when f(5) ⇒ f(x) = 1(C) f(x) = -6x + 2 when f(-3) ⇒ f(x) = 20What do we mean by equations?The equals sign is used in mathematical equations to indicate that two expressions are equal.A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.Using 3x + 5 as an example equals 15.Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, f(x):
(A) f(x) = x + 3 when f(4)
f(x) = x + 3f(x) = 4 + 7f(x) = 7(B) f(x) = 2x - 9 when f(5)
f(x) = 2x - 9f(x) = 2(5) - 9f(x) = 10 - 9f(x) = 1(C) f(x) = -6x + 2 when f(-3)
f(x) = -6x + 2f(x) = -6(-3) + 2f(x) = 18 + 2f(x) = 20Therefore, the answers to all the equations are:
(A) f(x) = x + 3 when f(4) ⇒ f(x) = 7(B) f(x) = 2x - 9 when f(5) ⇒ f(x) = 1(C) f(x) = -6x + 2 when f(-3) ⇒ f(x) = 20Know more about equations here:
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If-4y² − x³ + 4 = 0 then find dy/dx in terms of x and y.
True or False
An application of deductive reasoning such that the reasoning is logically correct and undeniably true is a valid argument.
Answer:true
Step-by-step explanation:
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
a
Step-by-step explanation:
