Answers
Answer:
D = -87Dx = 174Dy = -435Dz = 0(x, y, z) = (-2, 5, 0)Step-by-step explanation:
The determinant of the coefficient matrix is ...
[tex]D=\left|\begin{array}{ccc}2&5&3\\4&-1&-4\\-5&-2&6\end{array}\right|\\\\=2(-1)(6)+5(-4)(-5)+3(4)(-2)-2(-4)(-2)-5(4)(6)-3(-1)(-5)\\\\=-12+100-24-16-120-15=\boxed{-87}[/tex]
The other determinants are found in similar fashion after substituting the constants on the right for each of the above matrix columns, in turn.
Those determinants are ...
[tex]D_x=\left|\begin{array}{ccc}21&5&3\\-13&-1&-4\\0&-2&6\end{array}\right|=174[/tex]
[tex]D_y=\left|\begin{array}{ccc}2&21&3\\4&-13&-4\\-5&0&6\end{array}\right|=-435[/tex]
[tex]D_z=\left|\begin{array}{ccc}2&5&21\\4&-1&-13\\-5&-2&0\end{array}\right|=0[/tex]
The solutions are ...
x = 174/-87 = -2
y = -435/-87 = 5
z = 0
That is, (x, y, z) = (-2, 5, 0).
Related Questions
g A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. a. How many simple events are in the sample space
Answers
Answer:
64
Step-by-step explanation:
Let us consider E_abc to be the event that a, b and c appear on the first, second and third slot of the spin machine.
Now, we are told that each slot has 4 possibilities which are a cherry, a lemon, a star, or a bar when spun.
Thus, from mn rule in probability, the total number of simple events in the sample space is = 4³ = 64
Find the value of NT
A. 4
B. 14
C. 12
D. 16
Answers
Answer:
14
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
12*x = 8 * (x+2)
Distribute
12x = 8x+16
Subtract 8x
12x-8x = 8x+16-8x
4x = 16
Divide by 4
4x/4 = 16/4
x = 4
We want NT
NT = 8+x+2
= 10 +x
= 10 +4
= 14
What is the area of polygon EFGH?
Answers
A flagpole is 50 feet high. You are standing a distance from the flag pole. The angle of elevation from where you are standing to the top of the flagpole is 23°. How far away from the flagpole are you standing? Note that the angle of elevation is the angle formed by the ground and the line of sight to the top of the flagpole.
Answers
Answer:
x = 21.2 ft
Step-by-step explanation:
x = tanФ h
h = 50
Ф = 23°
x = tan(23°) * 50
x = 21.2 ft
which of the following greatest
6+(-2)
6-(-2)
6×(-2)
6+(-2)
Answers
4
8
-12
4
8, or 6-(-2) is greatest
If the errors produced by a forecasting method for 3 observations are +3, +3, and −3, then what is the mean squared error?
Answers
Answer:
9
Step-by-step explanation:
The mean squared error (MSE)of a set of observations can be calculated using the formula :
(1/n)Σ(Actual values - predicted values)^2
Where n = number of observations
Steps :
Error values of each observation (difference between actual and predicted values) is squared.
Step 2:
The squared values are summed
Step 3:
The summation is the divided by the number of observations
The difference between the actual and predicted values is known as the ERROR.
(1/n)Σ(ERROR)^2
n = 3
Error = +3, +3, - 3
MSE = (1/3)Σ[(3)^2 + (3)^2 + (-3)^2]
MSE = (1/3) × [9 + 9 + 9]
MSE = (1/3) × 27
MSE = 9
A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml) and a standard deviation of 0.4 ml. Answer the following questions based on this information. Find the dye amount that represents the 9th percentile of the distribution.
Answers
Answer:
4.464 ml
Step-by-step explanation:
Given that:
mean (μ) = 5 mm, standard deviation (σ) = 0.4 ml
The z score is a score in statistics used to determine by how many standard deviation the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if the z score is negative then the raw score is below the mean It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
From the normal distribution table, the 9th percentile (0.09) corresponds to a z score of -1.34
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.34=\frac{x-5}{0.4}\\\\x-5=-0.536\\\\x=5-0.536\\\\x=4.464[/tex]
The dye amount that represents the 9th percentile of the distribution is 4.464 ml
Select the best estimate of the capacity of a bath tub. A. 5 ml B. 500 ml C. 50 cl D. 500 L.
Answers
Answer:
D. 500 L
because ml cl is smaller than L
Answer:
D. 500 L
Step-by-step explanation:
Choice A (5 ml) is basically a teaspoon. A bathtub can most definitely hold much more then one teaspoon of water.
Choice B (500 ml) is about 17 ounces. Which is basically the amount of water in a normal water bottle. A bathtub can hold more then the amount of water in one water bottle.
Choice C (50 cl) is a little bit more then 2 cups of water. I believe a normal bathtub can hold about 1280 cups of water.
That rules out choices A, B, and C. By process of elimination, we can tell choice D is the answer. But let's just take a look at D.
Choice D (500 L) is about 132 gallons. This is the most plausible one, although some bathtubs don't hold as much water as that, it still is the best estimate of the capacity of a bath tub. \
Hope that helped!
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answers
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
Four members from a "55"person committee are to be selected randomly to serve as chairperson, vice-chairperson, secretary, and treasurer. The first person selected is the chairperson; the second, the vice-chairperson; the third, the secretary; and the fourth, the treasurer. How many different leadership structures are possible?
Answers
Answer:
8,185,320 different leadership structures
Step-by-step explanation:
Since the order at which the members of the committee are chosen matters, this is a permutation of 4 out 55 people and it is given by:
[tex]n=\frac{55!}{(55-4)!}=55*54*53*52 \\\\n=8,185,320[/tex]
8,185,320 different leadership structures are possible.
PLEASE HELP ! (2/4) - 50 POINTS -
Answers
Answer:
The correct answer would be 15.5 or C.
plz someone help me with this question
Answers
Answer:
(x+3)^2=-4(y-3)
Step-by-step explanation:
(x-h)^2 = 4p(y-k)
P is the distance between the focus and vertex
P = 1 --> used distance formula for the points of -3,2 -3,3
Vertex is -3,3 --> according to picture
(x+3)^2=-4(y-3)
P is negative since it goes downwards in the picture.
I need help with this question
Answers
Answer:
a. 2
b. x^2 + 10x + 26
c. x^2 + 2x + 2
Step-by-step explanation:
For each part, replace x with the value you are given and simplify.
f(x) = x^2 - 2x + 2
a.
f(2) = 2^2 - 2(2) + 2 = 2
b.
f(x + 6) = (x + 6)^2 - 2(x + 6) + 2
= x^2 + 12x + 36 - 2x - 12 + 2
= x^2 + 10x + 26
c.
f(-x) = (-x)^2 - 2(-x) + 2
= x^2 + 2x + 2
A hockey team is convinced that the coin used to determine the order of play is weighted. The team captain steals this special coin and flips it 14 times to evaluate the hypothesis that the coin is weighted, and it shows up heads 12 times. Test this hypothesis (use alpha=.05).
1. What is the appropriate test?
2. State the null hypothesis:
3. State the alternative hypothesis:
4. Find the critical value:
5. Calculate the obtained statistic:
6. Make a decision:
7. What does your decision mean
Answers
Answer:
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Step-by-step explanation:
Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as
H0 :p 0.5 against Ha: p ≠ 0.5
The significance level is approximately 0.05
The test statistic to be used is number of heads x.
Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution
Heads (x) Probability (X=x) Cumulative Decumulative
0 1/16384 (1) 0.000061 0.000061
1 1/16384 (14) 0.00085 0.000911
2 1/16384 (91) 0.00555 0.006461
3 1/16384(364) 0.02222
4 1/16384(1001) 0.0611
5 1/16384(2002) 0.122188
6 1/16384(3003) 0.1833
7 1/16384(3432) 0.2095
8 1/16384(3003) 0.1833
9 1/16384(2002) 0.122188
10 1/16384(1001) 0.0611
11 1/16384(364) 0.02222
12 1/16384(91) 0.00555 0.006461
13 1/16384(14) 0.00085 0.000911
14 1/16384(1) 0.000061 0.000061
We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).
We observe that P (X≤2) = 0.006461 > 0.025
and
P ( X≥12 ) = 0.006461 > 0.025
Therefore true significance level is
∝= P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122
Hence critical region is (X≤0) and ( X≥14)
Computation x= 12
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
f(x) = -3x + 7
What is f (0)?
Answers
f(0) = 7
Answer:
f(0) = 7
Step-by-step explanation:
f(x) = -3x + 7
Let x =0
f(0) = -3*0 + 7
f(0) = 7
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 7.2 to 4.5
Answers
Answer:
[tex]\frac{8}{5}[/tex]
Step-by-step explanation:
Given
7.2 : 4.5 ← multiply both parts by 10
= 72 : 45 ← divide both parts by 9
= 8 : 5
= [tex]\frac{8}{5}[/tex]
If the mean difference gets larger and sample standard deviation stays the same, what happens to effect size?
Answers
Answer:
The effect size of the sample gets larger
Step-by-step explanation:
The effect size of the sample gets larger when the mean difference gets larger and the sample standard deviation stays the same. because the Cohen's effect size is proportional to mean difference and this can be proven below using the Cohen's formula
Cohen's effect size = Mean difference / standard deviation
form the question standard deviation is constant while the mean difference gets larger, hence the effect size will get larger as well
Let A and B be any two sets. Show that:
Show that (
AUB)', (BUA)' = 0
Answers
Step-by-step explanation:
(AUB)' means they are all outside the set A and B so thats 0. Hope it helps
PLEASE ANSWER ASAP!!!!
Question refers to Table in the picture
Use a proportional reasoning statement like the one in the picture to determine how many feet are in 3 miles. Notice that the conversion fact 1 mile = 5,280 feet is written as a ratio in the picture.
A. x = 15,840 feet
B. x = 10,560 feet
C. x = 21,120 feet
D. x = 26,400 feet
any unrelated answer will be reported
Answers
Answer:
The answer is A 15,840, because 5,280 x 3 is equivalent to A
Answer:
A. x = 15,840 feet.
Step-by-step explanation:
[tex]\frac{5280 feet}{1 mile} =\frac{x feet}{3 miles}[/tex]
[tex]\frac{5280}{1} =\frac{x}{3}[/tex]
1 * x = 5,280 * 3
x = 15,840 feet
So, your answer is A. x = 15,840 feet.
Hope this helps!
Simplify 10 - [14 = (3 + 4) · 2]+3
Answers
Answer:
There is a typo near the equal sign.
There can be two different answers if we think that = sign as + or -.
First way: Making = as +
=> 10 - [14 + (3+4) x 2] +3
=> 10 - [14 + 7 x 2] + 3
=> 10 - [14 + 14] + 3
=> 10 - 28 + 3
=> 10 + 3 - 28
=> 13 - 28
=> -15
=> So, -15 is the answer if we consider "=" sign as "+" sign.
Second way: Making = as -
=> 10 - [14 - (3+4) x 2] + 3
=> 10 - [14 - 7 x 2] + 3
=> 10 - [14 - 14] + 3
=> 10 - 0 + 3
=> 10 + 3
=> 13
=> So, 13 is the answer if we consider "=" sign as "-" sign.
the temperature at which water freezes on the celsius scale is 0 degrees C. It freezes at 32 degrees F on the Fahrenheit scale, write opposites fo these two numbers as integers.
Answers
Answer:
If we have an integer number N, the opposite of N will be:
-1*N = -N.
Then, the opposite of 0°C is:
-1*0°C = 0°C.
The number 0 is it's own opposite.
And for 32F, the opposite is:
-1*32F = -32F
So, while the numbers 0°C and 32F physically represent the same thing (the same temperature), mathematically, they behave differently.
Nour drove from the Dead Sea up to Amman, and her altitude changed at a constant rate. When she began driving, her altitude was 400400400 meters below sea level. When she arrived in Amman 222 hours later, her altitude was 100010001000 meters above sea level. Let yyy represent Nour's altitude (in meters) relative to sea level after xxx hours.
Answers
Answer:
y = 700x - 400
Step-by-step explanation:
A negative number represents an altitude below sea level.
Beginning: -400
y = mx + b
y = mx - 400
In 2 hours the altitude was now 1000 m.
1000 m - (400 m) = 1400 m
The altitude went up 1400 m in 2 hours. The rate of change is
1400/2 m/h = 700 m/h
The rate of change is the slope.
y = 700x - 400
Answer:
The graph answer is below :)
Step-by-step explanation:
In a zoo there are 6 orang-utans for every 3 baboons. There are 27 orang-utans and baboons altogether. How many are orang-utans?
Answers
Answer:
18
Step-by-step explanation:
Okay first we know that for every one baboon there is 2 orang-utans (6 / 3 = 2)
So, I like to play the guess and check:
Lets just use the numbers 12 orang-utans and 6 baboons. We know that those two don't equal 27, so thats not it.
Now we can have 18 orang-utans and 9 baboons. 18 + 9 = 27, which means there are 18 orang-utans.
Hope this helps, and have a good day.
One way to calculate the target heart rate of a physically fit adult during exercise is given by the formula h=0.8( 220−x ), where h is the number of heartbeats per minute and x is the age of the person in years. Which formula is equivalent and gives the age of the person in terms of the number of heartbeats per minute?
Answers
Answer:
The answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Step-by-step explanation:
Given:
[tex]h=0.8( 220-x )[/tex]
Where [tex]h[/tex] is the heartbeats per minute and
[tex]x[/tex] is the age of person
To find:
Age of person in terms of heartbeats per minute = ?
To choose form the options:
[tex]A.\ x=176-h\\B.\ x=176-0.8h\\C.\ x=-1.25h+220\\D.\ x=h-0.8220[/tex]
Solution:
First of all, let us have a look at the given equation:
[tex]h=0.8( 220-x )[/tex]
It is value of [tex]h[/tex] in terms of [tex]x[/tex].
We have to find the value of [tex]x[/tex] in terms of [tex]h[/tex].
Let us divide the equation by 0.8 on both sides:
[tex]\dfrac{h}{0.8}=\dfrac{0.8( 220-x )}{0.8}\\\Rightarrow \dfrac{1}{0.8}h=220-x\\\Rightarrow 1.25h=220-x[/tex]
Now, subtracting 220 from both sides:
[tex]\Rightarrow 1.25h-220=220-x-220\\\Rightarrow 1.25h-220=-x[/tex]
Now, multiplying with -1 on both sides:
[tex]-1.25h+220=x\\OR\\\bold{x = -1.25h+220}[/tex]
So, the answer is:
C. [tex]\bold{x = -1.25h+220}[/tex]
Figure ABCD is a square find the value of x
Answers
Answer:
x=3
Step-by-step explanation:
since its a square all sides equal each other
5x-2=x+10
4x -2 =10
4x=12
x = 3
Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.
Answers
Answer:
Step-by-step explanation:
Given
Garden: [tex]x^2+18x+81[/tex]
One Bag: [tex]x^2 - 81[/tex]
Requires
Determine the number of bags to cover the whole garden
This is calculated as thus;
[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]
Expand the numerator
[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]
[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]
Express 81 as 9²
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]
Evaluate as difference of two squares
[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]
[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
In the diagram, XY bisects ZWXZ.
1
z
2
w
(5x + 3)
(7x - Y
х
mWYZ
type your answer.
Answers
In provided diagram angle WXY = angle YXZ
Angle WXY =( 7x-7)°
Angle YXZ = ( 5x +3)°
We have to find out the value of Angle WXZ
→ 7x-7 = 5x +3
→ 7x - 5x = 7+3
→ 2x = 10
→ x = 10/2
→ x = 5 .
Putting the value of x .
→ Angle WXY = 7(2)-7
→ 14-7 = 7°
→ Angle YXZ = 5(2)+3
→ 10+3 = 13°
Angle WXZ = 13° + 7 ° → 20°
So 20° is the required answer .
Answer:
SI
Step-by-step explanation:
Using the FOIL method, find the product of x - 2 and x - 3 .
Answers
(x - 2)(x - 3)
x^2 -3x - 2x + 6
x^2 - 5x + 6
Answer:
[tex] \boxed{ {x}^{2} - 5x + 6}[/tex]Step-by-step explanation:
[tex] \mathsf{(x - 2)(x - 3)}[/tex]
Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )
[tex] \mathsf{x×x - 3x - 2x - 2 × ( - 3 )}[/tex]
Calculate the product
[tex] \mathsf{ {x}^{2} - 3x - 2x - 2 \times (- 3)}[/tex]
Multiply the numbers
[tex] \mathsf{ {x}^{2} - 3x - 2x + 6 }[/tex]
Collect like terms
[tex] \mathsf{ {x}^{2} - 5x + 6}[/tex]
Hope I helped!
Best regards!
in the factory 25 men working 26 hour can produce 1300 radios . how manny hours must the same group of men work to produce 450 radios
Answers
Answer:
9 hours
Step-by-step explanation:
Since the group of men remains the same, number of hours is proportional to number of radios.
1300/26 = 450/h
h = 26 * 450 / 1300 = 9 hours
Divide. Write the quotient in lowest terms. 3 3/4 ÷ 5/7
Answers
Rewrite 3 3/4 as an improper fraction
3 3/4 = 15/4
Now you have
15/5 / 5/7
When you divide fractions, change the division to multiplication and flip the second fraction over:
15/4 x 7/5
Now multiply the top numbers together and the bottom numbers together:
( 15 x 7) / (4 x 5) = 105/20
Write as a proper fraction:
105/20 = 5 1/4
Explanation:
3 3/4 divide by 5/7
= 15/4 x 7/5
= 105/20
= 21/4 or 5 1/4
