Answer:
3.16 square units
Step-by-step explanation:
Find the area of the triangle with vertices: Q(-5,5,-3), R(-6,8,-4), S(-8,2,-4).
Step 1
We find QR and QS
QR = R - Q
= R(-6,8,-4) - Q(-5,5,-3)
= (-1, 3, -1)
QS = S - Q
= S(-8,2,-4) - Q(-5,5,-3)
= (-3, -3, -1)
Step 2
QR × QS
(-1, 3, -1) × (-3, -3, -1)
Using the formula:
a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k
Where a = (a1, a2, a3)
b = (b1, b2, b3)
QR = a
QS = b
(-1, 3, -1) × (-3, -3, -1)
a x b = (a2b3 – a3b2)i + (a3b1 – a1b3)j + (a1b2 – a2b1)k
= ((3 × -1) – (-1×-3))i + ((-1)×-3) – (-1) × -1)j + (-1 × -3) – (3×-3)k
= (-3 - 3)i + (3 – 1)j + (3 – 9)k
= 0i + 2j - 6k = (0,2,-6)
QR × QS = (0,2,-6)
Area of the triangle = √0² + 2² + 6²/ 2
= √0 + 4 + 36/2
= √40/2
= 6.324555320336759 /2
3.1622776602 square units
Approximately = 3.16 square units
A local brewery produces three premium lagers named Half Pint, XXX, and Dark Night. Of its premium lagers, they bottle 40% Half Pint, 40% XXX, and 20% Dark Night lagers. In a marketing test of a sample of consumers, 27 preferred the Half Pint lager, 29 preferred the XXX lager, and 24 preferred the Dark Night lager. Using a chi-square goodness-of-fit test, decide to retain or reject the null hypothesis that production of the premium lagers matches these consumer preferences using a 0.05 level of significance. State the value of the test statistic. (Round your answer to two decimal places.) $ \chi_{obt}^2 $
Answer:
reject the null hypothesis
Step-by-step explanation:
Total observation = 27+49+24 = 100
Expected Frequency :
Half Pint = 100 × 0.4 = 40
XXX = 100 × 0.4 = 40
Dark night = 100 × 0.2 = 20
The Chi-square goodness-of-fit test can be computed as follows:
Observed Expected [tex]X^2 = \dfrac{(O- E)^2}{E}[/tex]
Frequency(O) Frequency (E)
Half- 27 40 4.225
Pint
XXX 29 40 3.025
Dark- 24 20 0.8
night
Total 100 100 8.05
The test statistics [tex]X^2[/tex] = 8.05
8.05
degree of freedom = n -1
degree of freedom = 3 - 1
degree of freedom = 2
The p-value can be computed by using the EXCEL FORMULA (=CHIDIST(8.05,2)
p-value = 0.01786
Since the p-value is less than the level of significance, we reject the null hypothesis
Also using the critical value approach from the EXCEL FUNCTION;
critical chi-square (=CHIINV(0.05,2) = 5.99
[tex]X^2 > 5.99[/tex], therefore, we reject the null hypothesis
Items 2-4. Points P, Q, and Sare
collinear.
(3x - 5)
0
(x + 1)
s
2. What is the value of x?
3. What is m ZPQR?
will
11. M
4. If a ray QT bisects ZRQS, what
will be the measure of one of the
resulting angles?
m
of
5. Points L, M, and N are collinear.
You are given LM = 5 and LN = 17.
What is a possible value of MN?
Flb
6. Ray BD bisects ZABC so that
mZDBC = x + 6 and
mZABD = 2x - 12. What is x?
Answer:
See below
Step-by-step explanation:
2......................
∠PQR and ∠RQS are supplementary, which add up 180°
∠PQR = 3x - 5∠RQS = x + 1Sum:
3x - 5 + x + 1 = 1804x - 4 = 1804x = 184x = 46°3......................
∠PQR = 3x - 5 = 3*46° - 5° = 138° - 5° = 133°4......................
From the picture and the value of x we got above:
∠RQS = x + 1 = 46 + 1= 47°QT bisects ∠RQS and we get two equal angles
Each will measure:
47°/2 = 23.5°5......................
LM = 5, LN = 17, MN = ?
If L is between M and N, then
MN = LM + LN = 5 + 17 = 22M is between L and N, then
MN = LN - LM = 17 - 5 = 125......................
Ray BD bisects ∠ABC, then formed angles are equal:
m∠DBC = x + 6 m∠ABD = 2x - 12m∠DBC = m∠ABD
x + 6 = 2x - 122x - x =6 + 12x = 18°Find the point (x1,x2) that lies on the line x1 +5x2 =7 and on the line x1 - 2x2 = -2.
Given :
Two equation [tex]x_1 +5x_2 =7[/tex] and [tex]x_1 - 2x_2 = -2[/tex] .
To Find :
The point of intersection of these lines .
Solution :
We will use elimination method :
From equation 1 :
[tex]x_1=7-5x_2[/tex]
Putting value of [tex]x_1[/tex] in equation 2 we get :
[tex](7-5x_2)-2x_2=-2\\\\7-7x_2=-2\\\\x_2=\dfrac{9}{7}[/tex]
Putting value of [tex]x_2[/tex] in equation 1 we get :
[tex]x_1+5\times \dfrac{9}{7}=7\\\\x_1=\dfrac{4}{7}[/tex]
Therefore , point of interaction is [tex](\dfrac{4}{7},\dfrac{9}{7})[/tex] .
Hence , this is the required solution .
The point is: [tex]\left(x_{1},x_{2}\right)=\left(\frac{4}{7},\frac{9}{7}\right)[/tex]
We will solve the given system of equations.
Subtract the second equation from the first one:
[tex]\left(x_{1}+5x_{2}\right)-\left(x_{1}-2x_{2}\right)=7-\left(-2\right)\\x_{1}+5x_{2}-x_{1}+2x_{2}=7+2\\7x_{2}=9\\x_{2}=\frac{9}{7}[/tex]
Then we plug [tex]x_{2}=\frac{9}{7}[/tex] in the given first equation.
[tex]x_{1}+5x_{2}=7\\x_{1}+5\left(\frac{9}{7}\right)=7\\x_{1}+\frac{45}{7}=7\\x_{1}=7-\frac{45}{7}\\x_{1}=\frac{4}{7}[/tex]
So the point is: [tex]\left(x_{1},x_{2}\right)=\left(\frac{4}{7},\frac{9}{7}\right)[/tex]
Learn more: https://brainly.com/question/16236436
Which expression is equivalent to 1/2 x + (-70) - 2 1/4 x - (-2) *
Answer:
-7/4x-68
Step-by-step explanation:
Help i dont understand Pls help :( Given g(x)=-4x-2g(x)=−4x−2, find g(-2)g(−2).
Answer:
[tex]g(-2)=6[/tex]
Step-by-step explanation:
Hi again!
So we have the equation:
[tex]g(x)=-4x-2[/tex]
To find g(-2), substitute -2 for x. Thus:
[tex]g(-2)=-4(-2)-2[/tex]
Multiply. -4 times -2 is positive 8:
[tex]g(-2)=8-2[/tex]
Subtract:
[tex]g(-2)=6[/tex]
And we're done!
what is the 3rd square root of 1000
Answer:
10
Step-by-step explanation:
The third square root is the cube root. This means we are looking for the number that multiplies by itself 3 times to get to 1000, which is 10. (10x10x10=1000)
Hope this helped!
a. Plot 13.58 on a number line on which the long
tick marks are whole numbers.
b. Plot 0.193 on a number line on which the long
tick marks are tenths.
c. Plot 26.9999 on a number line on which the
long tick marks are thousandths.
Answer:
Se attached for plots and here is position of the numbers:
a. Plot 13.58 on a number line on which the long
tick marks are whole numbers.
13 < 13.58 < 14b. Plot 0.193 on a number line on which the long
tick marks are tenths.
0.1 < 0.193 < 0.2c. Plot 26.9999 on a number line on which the
long tick marks are thousandths.
26.999 < 26.9999 < 27.000David and Amrita had an equal number of marbles. After Amrita gave 50 marbles to David, he had 5 times as many marbles as her. Find the total number of marbles they had.
Answer:
Step-by-step explanation:
a = d before Anna gives away 50 marbles.
5 (a-50) = a +50 after Anna gives away 50 marbles.
5a - 250 = a + 50
4a = 300
a = 75
Anna has 75 marbles at the beginning and so did David.
Together they have 150 marbles.
:)
Answer:
150
Step-by-step explanation:
Originally, they had the same number, so they both had x marbles each.
David: x
Amrita: x
Amrita gives 50 marbles to David. Now they have:
David: x + 50
Amrita: x - 50
"he had 5 times as many marbles as her"
x + 50 = 5(x - 50)
x + 50 = 5x - 250
-4x = -300
x = 75
Each had 75 marbles to start with.
75 + 75 = 150
The total is 150.
Which type of cell contains Cell Membrane?
Answer:
Eukaryotic cells contain cell membrane!
historians label an event as a turning point when it
Answer:
F
Step-by-step explanation:
Answer:
Historians label an event as a turning point when it marks the beginning of a distant historical period
Step-by-step explanation:
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. The actual dimensions of the building are 30 feet long by 55 feet wide. true or false
1 inch = 10 feet.
3 inches x 10 = 30 feet
5.5 inches x 10 = 55 feet
The actual room is 30 feet x 55 feet.
The answer is true.
Answer:
Round up to the Nernst number
Step-by-step explanation:
45 inches
Frank needs 3.6 meters of ribbon to wrap gifts for friends this year. If each spool contains 90 cm of ribbon,how many spools will Frank need to purchase?
Answer:a lot
Step-by-step explanation:
Solve for x: 3(x + 1) = −2(x − 1) − 4. (1 point)
Answer:
X=2.5 (btw im a rising 5th grader just saying) i hope i helped u
Step-by-step explanation:
3x+3=-2x+2-4 (get rid of the parenthesis)
+2x +2x (get rid of 2x)
5x+3=2-4
+4 +4 (get rid of 4)
5x+7=2
-7 -7 (get rid of 7)
5x=2
5/2=2.5 (solve)
which fraction represents 56 shares evenly distributed among 12 people
Answer:
14/3
Step-by-step explanation:
When 56 shares are evenly distributed between 12 people, each person gets equal number of shares.
The number of shares gotten by each person is the ratio of the total number of shares to the total number of people. It is given by the formula:
number of shares gotten by each person = total number of shares / total number of people
number of shares gotten by each person = 56 shares / 12 people
number of shares gotten by each person = 14/3 shares
3
Type the correct answer in each box. Use numerals instead of words.
Complete the table of inputs and outputs for the function.
f(x) = -5(x + 7)
-9
0
0
-60
Reset
Next
Answer:
(-9,10),(-7,0)(0,-35)(5,-60)
Step-by-step explanation:
plz help quicky.......................................
A car drives with an average velocity of 20.1 m/s . After some time, it has traveled 34.2 km. How long has the car been traveling?
Answer:
time = distance / velocity
time = 34,200 meters / 20.1 meters per second
time = 1,701.4925373134 seconds
time = 28.36 minutes
Step-by-step explanation:
Find the area and perimeter of a court with dimensions of 50ft by 84ft.
Answer:
Area: 4200
Perimeter: 268
Step-by-step explanation:
To find the area, multiply length and width (50 x 84)
To find perimeter, add up the lengths of all the sides (50+50+84+84)
Hope this helps!
0.01 is...........0.01
Answer:
=
Step-by-step explanation:
0.01 is = to 0.01
Plot the point then draw the shape
they create. What shape does it
create?
(2,5)
(7, 1)
(5,5-)
(-1,-5)
(-3,1)
Find the population mean or sample mean as indicated.Sample: 19, 15, 6, 11, 24Required:Compute the sample mean for this data set.
Answer:
The sample mean is 15.
Step-by-step explanation:
We have given data 19, 15, 6, 11, 24.
We are required to find the sample mean. The sample mean can be determined by adding all the given value and then divide by the total numbers or how many numbers. Below is the calculation of the mean.
Sample mean = (19+ 15 +6 +11 +24) / 5
Sample mean = 75 / 5
Sample mean = 15
Therefore the sample mean of the given data is 15.
A survey of 500 farmers showed that of the farmers, 121 grew only wheat, 108 grew only corn, 92 grew only oats, 195 grew wheat, 59 grew wheat and corn, 48 grew wheat and oats, and 176 grew corn. Determine the number of farmers who a) grew at least one of the three, b) grew all three, c) did not grow any of the three, and d) grew exactly two of the three.
Answer:
The farmers in regions II, IV, and VI had exactly two of the three Summing the numbers in these regions 25 + 15 + 10 we find the that 50 farmers grew exactly two of the three.
An observer (O) spots a plane flying at a 55° angle to his horizontal line of sight. If the plane is flying at an altitude of 21,000 ft., what is the distance (x) from the plane (P) to the observer (O)?
Answer:
Step-by-step explanation:
The givens form a right triangle. The operational definition is The opposite over the hypotenuse, where the hypotenuse is the unknown.
sin(x) = 21000/hypotenuse
sin(55) = 21000 / hypotenuse
hypotenuse * sin(55) = 21000
hypotenuse = 21000/sin(55)
hypotenuse = 25636 feet.= 26000 feet rounded.
The answer does make sense. The hypotenuse is larger than the given height.
63x^12-35x^6 help pls
Answer:
7x^6×(9×^6-5)
Step-by-step explanation:
63x^12-35x^6
7x^6×(9×^6-5)
Answer:I dont know
Step-by-step explanation: Can you pls rate this good I am in 2 grade
a rectangle is 41 cm on one side and 12 cm on the other side.what is the perimeter?
Answer:
106
Step-by-step explanation:
4+y when y = 18 would the answer be 22
Yes you are correct.
You replace y with 18 to get 4+y = 4+18 = 22.
The temperature in a town is 24.8 during the day and -8.1 at night. Find the difference in the temperatures.
The difference is exactly 32.9 degrees
Guess and win math cash 0 and 99999
Answer:
12345
Step-by-step explanation:
乁[ ◕ ᴥ ◕ ]ㄏฅ^•ﻌ•^ฅ▼・ᴥ・▼
0-99999
(IT COULd Be aNy?) This writing was a joke. BUT WHAT IS THE ANSWER!!!!!!!!
15 = x + 13
which property could be used to solve this equation
Steps to solve:
15 = x + 13
~Subtract 13 to both sides
2 = x
Best of Luck!
Ahmed wrote two numbers the first number has a seven and it’s tenths place the second number has a seven with a value that is 1000 times greater than the value of the seven in the first in which place is a seven and the second number
Answer: I think the answer is thousands
Step-by-step explanation:
Answer:
100,000
Step-by-step explanation:
first # = 70, 2 digits
second # = 1,000 times greater than 70 1,000 = 4 digits
4 + 2 = 6, 100,000 = 6 digits