Answer:
A. x <= 2
Step-by-step explanation:
The domain of a real function should be all real numbers. In
f(x) = sqrt(2-x)
we need 2-x to be non-negative, therefore
2-x >= 0
which implies
x <= 2
Answer:
[tex]\Huge \boxed{{x\leq 2}}[/tex]
Step-by-step explanation:
The function is given,
[tex]f(x)=\sqrt{2-x}[/tex]
The domain of a function are all possible values of x.
There are restrictions for the value of x.
2 - x cannot be equal to a negative number, because the square root of a negative number is undefined. 2 - x has to equal to 0 or be greater than 0.
[tex]2-x\geq 0[/tex]
[tex]-x\geq -2[/tex]
[tex]x\leq 2[/tex]
The domain of the function is x ≤ 2.
We want to estimate the population mean within 5, with a 99% level of confidence. The population standard deviation is estimated to be 15. How large a sample is required? (Round up your answer to the next whole number.)
Answer: 60
Step-by-step explanation:
Formula to calculate sample size (n):
[tex]n=(\dfrac{\sigma\times z^*}{E})^2[/tex]
, where [tex]\sigma[/tex] = population standard deviation, E Margin of error , z* = critical value for the confidence interval.
As per given , we have
E =5
[tex]\sigma=15[/tex]
Critical value for 99% confidence = 2.576
Then,
[tex]n=(\dfrac{15\times2.576}{5})^2\\\\\Rightarrow\ n=59.721984\approx60[/tex]
So, Required sample size = 60 .
4 to the 4th power equals 256. Explain how to use that fact to more quickly evaluate 4 to the 5th power.
Answer: Because 4 is the base of what is being exponentially multiplied, you can multiply 256 by 4 to get 4^5
Hi there! Hopefully this helps!
--------------------------------------------------------------------------------------------------------
So, we know that 4 to the 4th power equals 256.
4 to the 4th power = 4 x 4 x 4 x 4.
So we can add another 4 to the equation to quickly get out answer for 4 to the 5th power.
4 to the 5th power = 4 x 4 x 4 x 4 x 4 = 1024.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Or you could break the equation into parts.
For example, there are FOUR 4s in the equation.
4 x 4 = 16.
4 x 4 = 16.
16 x 16 = 256.
Now since we've added ANOTHER 4, it should look like this:
16 x 16 = 256.
256 x 4 = 1024.
The vertices of a triangle are given in the columns of the matrix T= [0,4,0,0,0,5] If [-1,0,0,-1] is found to preform a transformation, what are the coordinates of the transformed triangle?
Answer:
(0,0), (-4,0), (0,-5).
Step-by-step explanation:
Note: Matrices are not in proper format.
Consider the given matrix is
[tex]T=\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]
It means vertices are (0,0), (4,0) and (0,5).
Transformation matrix is
[tex]A=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}[/tex]
To find the coordinates of the transformed triangle multiply both matrices and calculate matrix AT.
[tex]AT=\begin{bmatrix}-1&0\\0&-1\end{bmatrix}\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}[/tex]
[tex]AT=\begin{bmatrix}\left(-1\right)\cdot \:0+0\cdot \:0&\left(-1\right)\cdot \:4+0\cdot \:0&\left(-1\right)\cdot \:0+0\cdot \:5\\ 0\cdot \:0+\left(-1\right)\cdot \:0&0\cdot \:4+\left(-1\right)\cdot \:0&0\cdot \:0+\left(-1\right)\cdot \:5\end{bmatrix}[/tex]
[tex]AT=\begin{bmatrix}0&-4&0\\ 0&0&-5\end{bmatrix}[/tex]
It means coordinates of the transformed triangle are (0,0), (-4,0), (0,-5).
Answer:
A
Step-by-step explanation:
E2020
a 12- inch ruler is duvided into 3 parts. the large part is 3 times longer than the small. the meddium part is times longer than then small, the medium part is 2 times long as the smallest .how long is the smallest part?
Answer:
2 inches
Step-by-step explanation:
x= smallest
3x=largest
2x=medium
x+3x+2x=12
6x=12
x=2
so smallest is 2
largest is 6 (3x)
medium is 4 (2x)
2+6+4=12
One integer is
5 less than another. The sum of their squares is
157. Find the integers.
Answer:
[tex]\large \boxed{\sf \ \ 6 \ and \ 11 \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's note a and b the two numbers.
a = b - 5
[tex]a^2+b^2=157[/tex]
We replace a in the second equation and we solve it
[tex](b-5)^2+b^2=157 \\ \\ \text{*** develop the expression ***} \\ \\b^2-10b+25+b^2=157 \\ \\ \text{*** subtract 157 from both sides ***} \\ \\2b^2-10b+25-157=2b^2-10b-132=0 \\ \\ \text{*** divide by 2 both sides ***} \\ \\b^2-5b-66=0[/tex]
It means that the sum of the two roots is 5 and the product is -66.
because
[tex](x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta \\ \\ \text{ where } \alpha \text{ and } \beta \text{ are the roots }[/tex]
And we can notice that 66 = 6 * 11 and 11 - 6 = 5
So let's factorise it !
[tex]b^2-5b-66=0 \\ \\b^2+6b-11b-66=0 \\ \\b(b+6)-11(b+6)=0 \\ \\(b-11)(b+6) =0 \\ \\ b=11 \ or \ b=-6[/tex]
It means that the solutions are
(6,11) and (-6,-11)
I guess we are after positive numbers though.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the minimum sample size necessary to be 99% confident that the population mean is within 3 units of the sample mean given that the population standard deviation is 29. (a) What is the critical value that corresponds to the given level of confidence? Round your answer to two decimals, and remember that critical values are always positive.
Answer:
623
Step-by-step explanation:
Given that margin of error (E) = 3 unit, standard deviation (σ) = 29, sample size (n) = ?
a) The confidence (C) = 99% = 0.99
α = 1 - C = 1 - 0.99 = 0.01
α/2 = 0.01 / 2 = 0.005
From the normal distribution table, The z score of α/2 (0.005) is the critical value and it corresponds to the z score 0.495 (0.5 - 0.005) which is 2.58.
[tex]critical\ value = z_{\frac{\alpha}{2} }=z_{0.005}=2.58\\[/tex]
b) The margin of error (E) is given as:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\\\\sqrt{n}= z_{\frac{\alpha}{2} }*\frac{\sigma}{E }\\ \\n=( z_{\frac{\alpha}{2} }*\frac{\sigma}{E })^2\\\\Substituting:\\\\n=(2.58*\frac{29}{3} )^2=622.0036\\\\\\n=623(to\ the \ next\ whole\ number)[/tex]The minimum sample size (n) is 623
The length of a rectangle is four times its width. If the perimeter of the rectangle is 50 yd, find its area
Answer:
100yd²
Step-by-step explanation:
length=4x
width=x
perimeter=2(l+w)
50=2(4x+x)
50=2(5x)=10x
50=10x
x=5yd
width=5yd
length=20yd
area=length×width
=20×5
=100yd²
Answer:
[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]
Step-by-step explanation:
width = x
length = 4x
so,
perimeter of a rectangle
[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]
So, in this rectangle,
width = 5 yd
length = 4x
= 4*5
= 20yd
Now, let's find the area of this rectangle
[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]
The ratio of the legs of a trapezoid is 1:2, and the sum of the angles adjacent to the bigger base is 120°. Find the angle measures of the given trapezoid.
Answer:
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Step-by-step explanation:
A trapezoid is a quadrilateral that is symmetrical and whose bases are of different length and in every quadrilateral the sum of internal angles is equal to 360º. The bigger base has the pair of adjacent angles of least measure, whereas the smaller base has the pair of adjancent angles of greatest measure.
Since the sum of the angles adjacent to bigger base is 120º, the value of each adjacent angle ([tex]\alpha[/tex]) is obtained under the consideration of symmetry:
[tex]2\cdot \alpha = 120^{\circ}[/tex]
[tex]\alpha = 60^{\circ}[/tex]
The sum of the angles adjacent to smaller base is: ([tex]\alpha = 60^{\circ}[/tex])
[tex]2\cdot \alpha + 2\cdot \beta = 360^{\circ}[/tex]
[tex]2\cdot \beta = 360^{\circ} - 2\cdot \alpha[/tex]
[tex]\beta = 180^{\circ}-\alpha[/tex]
[tex]\beta = 180^{\circ} - 60^{\circ}[/tex]
[tex]\beta = 120^{\circ}[/tex]
The angle measures of the trapezoid consists of two angles of 60º adjacent to the bigger base and two angles of 120º adjacent to the smaller base.
Which graph shows a line with a slope of 0?
The graph D shows a line with slope zero.
Zero slope:Zero slope is perfectly flat as horizontal line.Since it is perfectly a horizontal line, it is also known as horizontal line.Here the x value and the y value both are independent.It is neither increasing nor decreasing.Formula used in zero slope/ horizontal line is given by y=c; where c is constant.Since graph A, B and C doesn't make horizontal line, it is not a zero slope/ horizontal line.
Graph D is a horizontal line. It doesn't depend on any y value. It is neither increasing nor decreasing.
Therefore, graph D shows a line with a slope of zero.
Learn more about slope here:
https://brainly.com/question/3493733
#SPJ2
Since "a line has a slope of zero when it does not have any vertical rise. It will be a straight horizontal line." the answer is D
A statistical program is recommended.
The following observations are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.
32.1 30.9 31.6 30.4 31.0 31.9
The report states that under these conditions, the maximum allowable stopping distance is 30. A normal probability plot validates the assumption that stopping distance is normally distributed.
Required:
a. Does the data suggest that true average stopping distance exceeds this maximum value? Test the appropriate hypotheses using α= 0.01.
b. Calculate the test statistic and determine the P-value.
c. What can you conclude?
Answer:
We conclude that the true average stopping distance exceeds this maximum value.
Step-by-step explanation:
We are given the following observations that are on stopping distance (ft) of a particular truck at 20 mph under specified experimental conditions.;
X = 32.1, 30.9, 31.6, 30.4, 31.0, 31.9.
Let [tex]\mu[/tex] = true average stopping distance
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 30 {means that the true average stopping distance exceeds this maximum value}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 {means that the true average stopping distance exceeds this maximum value}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean stopping distance = [tex]\frac{\sum X}{n}[/tex] = 31.32 ft
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 0.66 ft
n = sample size = 6
So, the test statistics = [tex]\frac{31.32-30}{\frac{0.66}{\sqrt{6} } }[/tex] ~ [tex]t_5[/tex]
= 4.898
The value of t-test statistics is 4.898.
Now, at 0.01 level of significance, the t table gives a critical value of 3.365 at 5 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.898 > 3.365, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average stopping distance exceeds this maximum value.
how yo calculate step by step 0.082×100
Answer:
8.2
Step-by-step explanation:
When you calculate it by 100, there are two zeros, so you move two decimals to the right.
This makes 8.2, and 8.2 will be the answer.
Another example could be... 0.082✖️10.
In this case, there is 1 zero, so you move the decimal to the right once, making it 0.82.
Hope this helps!!!
Answer:
8.2
Step-by-step explanation:
When you calculate it by 100, there are two zeros, so you move two decimals to the right.
so you will get 8.2
hope it helps you
Which presents a quadratic function
Answer:
The answer is option 2.
Step-by-step explanation:
Quadratic function is always written in the form of ax² + bx + c where the highest power of x is 2.
In the options above :
Option 1 is Cubic function.
Option 2 is Quadratic function.
Option 3 and 4 are Linear function.
Answer:
I guess....
Step-by-step explanation:
option 2............
You are hiking and are trying to determine how far away the nearest cabin is, which happens to be due north from your current position. Your friend walks 245 yards due west from your position and takes a bearing on the cabin of N 22.6°E. How far are you from the cabin? answer asap and ill give you a pat on the back
Answer:
101.98 yards.
Step-by-step explanation:
Please refer to the diagram that I drew (sorry for the messiness; I do not own a stylus and so I was using my mouse to try to draw it).
Since the triangle is a right triangle, you can use SOH CAH TOA. In this case, you are trying to figure out the opposite length, but you are given the adjacent. So, we will use tangent to solve this (TOA = Tangent, Opposite over Adjacent).
The angle is 22.6 degrees, and the tangent of the angle is equivalent to the opposite length, x, divided by the adjacent length, 245 yards.
tan(22.6) = x / 245
x / 245 = tan(22.6)
x = tan(22.6) * 245
x = 0.4162598242 * 245
x = 101.9836569
So, you are about 101.98 yards from the cabin.
Hope this helps!
write an expression: A number squared
added to 16
Answer:
16+x²
Step-by-step explanation:
What is the five-number summary for this data set?
12, 15, 17, 20, 22, 25, 27, 30, 33, 37
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.
Answer: min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .
Step-by-step explanation:
The five-number summary for this data set consists of min, Q1,
median, Q3, max.
Given data: 12, 15, 17, 20, 22, 25, 27, 30, 33, 37, which is already arranged in a order.
Minimum value = 12
Maximum value = 37
since , number of observations = 10 (even)
So , Median = Mean of middle most terms
Middle most terms = 22, 25
Median =[tex]\dfrac{22+25}{2}=23.5[/tex]
First quartile ([tex]Q_1[/tex])= Median of first half ( 12, 15, 17, 20, 22)
= middle most term
= 17
Third quartile ([tex]Q_3[/tex]) = Median of second half (25, 27, 30, 33, 37)
= middle most term
= 30
Hence, five-number summary for this data set :
min = 12, Q1 =17, median =23.5 , Q3 = 30, max = 37 .
evaluate the following when x=3
[tex]y = - 3 \times 4^{x} [/tex]
evaluate the following when x=-2
[tex]f(x) = 6 \times ( \frac{1}{3} )^{x} [/tex]
evaluate the following when x=4
[tex]f(x) = \frac{1}{4}\times {2}^{x} [/tex]
(help me with this please)
Answer:
y=-192
Step-by-step explanation:
What is the density of a brownie the shape of a cube weighing 15 grams measuring 5 cm on a side?
Answer:
0.12 g/cm³
Step-by-step explanation:
Density is the ratio of mass to volume. The volume of the brownie is the cube of its side dimension:
V = s³ = (5 cm)³ = 125 cm³
Then the density is ...
ρ = M/V = (15 g)/(125 cm³) = 0.12 g/cm³
The density of the brownie is 0.12 g/cm³.
What is the value of x in the equation 5 (4 x minus 10) + 10 x = 4 (2 x minus 3) + 2 (x minus 4)?
Answer:
x = 1.5
Step-by-step explanation:
5(4x-10)+10x=4(2x-3)+2(x-4)
Distribute(5)
20x-50+10x=4(2x-3)+2(x-4)
Distribute(4)
20x-50+10x=8x-12+2(x-4)
Distribute(2)
20x-50+10x=8x-12+2x-8
Combine like terms
30x-50=10x-20
Subtract(10x)
20x-50=-20
Add(50)
20x=30
Divide(20)
x = 1.5
Hope it helps <3
Answer:
x = 3/2Step-by-step explanation:
5 ( 4x - 10) + 10x = 4(2x - 3) + 2(x - 4)
Expand the terms
That's
20x - 50 + 10x = 8x - 12 + 2x - 8
Simplify
30x - 50 = 10x - 20
Group the constants at the right side of the equation
That's
30x - 10x = - 20 + 50
20x = 30
Divide both sides by 20
x = 3/2
Hope this helps you
A bus company has contracted with a local high school to carry 450 students on a field trip. The company has 18 large buses which can carry up to 30 students and 19 small buses which can carry up to 15 students. There are only 20 drivers available on the day of the field trip.
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
Answer:
The answer is below
Step-by-step explanation:
Let x represent the big buses and y represent small buses. The large buses can carry 30 students and the small buses can carry 15 students. The total number of students are 450, this can be represented by the inequality:
30x + 15y ≤ 450
They are only 20 drivers, therefore only 20 buses can be used. It is represented by:
x + y ≤ 20
They are only 19 small buses and 18 large buses:
x ≤ 18
y ≤ 19
After plotting the graph, the minimum solution to the graph are at:
A (15,0), B(18,0), C(10, 10), D(18, 2).
The cost function is given as:
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
F(x, y) = 225x + 100y
At point A:
F(x, y) = 225(15) + 100(0) = $3375
At point B:
F(x, y) = 225(18) + 100(0) = $4050
At point C:
F(x, y) = 225(10) + 100(10) = $3250
At point D:
F(x, y) = 225(18) + 100(2) = $4250
The minimum cost is at point C(10, 10) which is $3250
For what value of k are the roots of the quadratic equation kx (x-2)+6=0 equal?
Answer:
[tex]\boxed{\sf k=6}[/tex]
Step-by-step explanation:
[tex]\sf kx (x-2)+6=0[/tex]
Expand brackets.
[tex]\sf kx^2 -2kx+6=0[/tex]
This is in quadratic form.
[tex]\sf ax^2 +bx+c=0[/tex]
Since this is for equal roots:
[tex]\sf b^2 -4ac=0[/tex]
[tex]\sf a=k\\b=-2k\\c=6[/tex]
[tex]\sf (-2k)^2 -4(k)(6)=0[/tex]
[tex]\sf 4k^2-24k=0[/tex]
[tex]\sf 4k(k-6)=0[/tex]
[tex]\sf 4k=0\\k=0[/tex]
[tex]\sf k-6=0\\k=6[/tex]
Plug k as 0 to check.
[tex]\sf \sf 0x^2 -2(0)x+6=0\\6=0[/tex]
False.
So that means k must equal 6.
2 x - 3 + 3x equals -28 what is the value of x
Answer:
[tex]x = -5[/tex]
Step-by-step explanation:
We can simplify this equation down until x is isolated.
[tex]2x - 3 + 3x = -28[/tex]
We can combine the like terms of x.
[tex]5x - 3 = -28[/tex]
Add 3 to both sides.
[tex]5x = -25[/tex]
Now we can divide both sides by 5.
[tex]x = -5[/tex].
So x = -5.
Hope this helped!
Answer:
x=-5
Step-by-step explanation:
first combine like terms
5x-3=-28
add on both sides
5x=-25
divide
x==-5
An equation is shown below: 4x + 2(x – 3) = 4x + 2x – 11 Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points) Part B: Name one property you used to solve this equation. (4 points)
Answer:
Part A: no solution
Part B: Distributive property of multiplication over addition.
Step-by-step explanation:
Part A:
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 6x - 11
6x - 6 = 6x - 11
-6 = -11
Since -6 = -11 is a false statement, there is no solution.
Number of solutions: 0
Part B:
Property used: Distributive property of multiplication over addition.
Part A: Here are the steps I used to solve this equation-
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 6x - 11
6x - 6 = 6x - 11
-6 = -11
Since -6 = -11 is a false statement, there is no solution.
The final number of solutions: 0
Part B: I used the distributive property of multiplication over addition.
Fake Question: Should Ujalakhan01 be a moderator? (If you could answer I'd appreciate it haha.)
Real Question: Simplify [tex](a^5*a^4)+(b^2*b^3)-(c^7*c^6)[/tex]
Answer:
[tex]a^9 + b^ 5 + c^{13}[/tex]
Step-by-step explanation:
[tex](a^5 \times a^4)+(b^2 \times b^3) + (c^7 \times c^6)[/tex]
When bases are same and it is multiplication, then add the exponents.
[tex](a^{5+4})+(b^{2+3})+(c^{7+6})[/tex]
[tex](a^9)+(b^ 5) + (c^{13})[/tex]
Apply rule : [tex](a^b)=a^b[/tex]
[tex]a^9 + b^ 5 + c^{13}[/tex]
Answer:
[tex]a^9+b^5-c^{13[/tex]
Step-by-step explanation:
[tex](a^5*a^4) + (b^2*b^3)-(c^7*c^6)[/tex]
When bases are same, powers are to be added.
=> [tex](a^{5+4})+(b^{2+3})-(c^{7+6})[/tex]
=> [tex]a^9+b^5-c^{13[/tex]
What is the measure of x?
Answer:
9 in.
Step-by-step explanation:
Given that the line 10 in. and line 4 in. are parallel, then the two triangles are similar.
As such, the ratio of the sides would give the same results.
Hence,
4/6 = 10/(6 + x)
cross multiplying
4(6 + x) = 60
Dividing both sides by 4
6 + x = 15
collecting like terms
x = 15 - 6
= 9
Rounded to the nearest tenth what is the perimeter of the triangle
Answer:
D. 11.8 cm.
Step-by-step explanation:
This is a 30-60-90 triangle, which means that the hypotenuse is 2x, the short leg is x, and the long leg is x[tex]\sqrt{3}[/tex].
In this case, the hypotenuse is 5.
5 / 2 = 2.5. That is the short leg.
The long leg is 2.5 * [tex]\sqrt{3}[/tex] = 4.330127019.
5 + 2.5 + 4.330127019 = 7.5 + 4.330127019 = 11.83012702, which is about D. 11.8 cm.
Hope this helps!
3. Use the Counting Principle to find the probability.
rolling a 1 on each of 4 number cubes
329
324
1
24
1
1, 296
Step-by-step explanation:
Each number cube has 6 possible values, so there are 6⁴ = 1296 possible permutations. Only 1 of those permutations is all ones. Therefore, the probability is 1/1296.
Duane is making cookies. The recipe calls for two times as many cups of sugar as butter, two times as many cups of oats as sugar, and two times as many cups of flour as oats. If Duane puts in one cup of butter, how many cups of flour does he need to add? (also this is from MobyMax)
Answer:
Step-by-step explanation:
Let b represent the number of cups of butter needed.
Let s represent the number of cups of sugar needed.
Let o represent the number of cups of oat needed.
Let f represent the number of cups of flour needed.
The recipe calls for two times as many cups of sugar as butter. It means that
s = 2b
Two times as many cups of oats as sugar. It means that
o = 2s
Two times as many cups of flour as oats. It means that
f = 2o
If Duane puts in one cup of butter, it means that b = 1
Therefore,
s = 2 × 1 = 2 cups
o = 2s = 2 × 2 = 4 cups
f = 2o = 2 × 4 = 8 cups
Therefore, he needs to add 8 cups of flour
Answer: Let b represent the number of cups of butter needed. Let s represent the number of cups of sugar needed. Let o represent the number of cups of oat needed. Let f represent the number of cups of flour needed. The recipe calls for two times as many cups of sugar as butter. It means that s = 2bTwo times as many cups of oats as sugar. It means that o = 2sTwo times as many cups of flour as oats. It means that f = 2oIf Duane puts in one cup of butter, it means that b = 1Therefore, s = 2 × 1 = 2 cupso = 2s = 2 × 2 = 4 cupsf = 2o = 2 × 4 = 8 cups Therefore, he needs to add 8 cups of flour
Step-by-step explanation:
magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. What values do , , n, E, and p represent? If the confidence level is %, what is the value of ?
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do [tex]\r p , \ \r q[/tex], n, E, and p represent? If the confidence level is 90%, what is the value of [tex]\alpha[/tex] ?
Answer:
a
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e [tex]\r q = 1- \r p[/tex]
b
[tex]\alpha = 10\%[/tex]
Step-by-step explanation:
Here
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e
[tex]\r q = 1- \r p[/tex]
[tex]\r q = 1- 0.12[/tex]
[tex]\r q = 0.88[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as
[tex]\alpha = ( 100 - C )\%[/tex]
Where [tex]C[/tex] is the confidence level which is given in this question as [tex]C = 90 \%[/tex]
So
[tex]\alpha = ( 100 - 90 )\%[/tex]
[tex]\alpha = 10\%[/tex]
Find the indicated limit, if it exists. (2 points) limit of f of x as x approaches negative 1 where f of x equals 4 minus x when x is less than negative 1, 5 when x equals negative 1, and x plus 6 when x is greater than negative 1
Answer:
5
Step-by-step explanation:
The limit of f(x) at x=-1 is 5 when approached from the left or right. Since those limits are the same, the limit exists and is ...
[tex]\boxed{\lim\limits_{x\to-1}f(x)=5}[/tex]
Match each pair of points A and B to point C such that ∠ABC = 90°. A(3, 3) and B(12, 6) C(6, 52) A(-10, 5) and B(12, 16) C(16, -6) A(-8, 3) and B(12, 8) C(18, 4) A(12, -14) and B(-16, 21) C(-11, 25) A(-12, -19) and B(20, 45) A(30, 20) and B(-20, -15) arrowBoth arrowBoth arrowBoth arrowBoth
Answer:
i) A = (3, 3), B = (12, 6), C = (6, 52) : Not orthogonal, ii) A = (-10, 5), B = (12, 16), C = (6, 52) : Not orthogonal, iii) A = (-8, 3), B = (12, 8), C = (18, 4) : Not orthogonal, iv) A = (12, -14), B = (-16, 21), C = (-11, 25) : Orthogonal, v) A = (-12, -19), B = (20, 45) : Impossible orthogonality, vi) A = (30, 20), B = (-20, -15) : Impossible orthogonality.
Step-by-step explanation:
The statement indicates that segments AB and BC must be orthogonal. Vectorially speaking, this can be expressed by using the following expression from Linear Algebra:
[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = 0[/tex]
[tex](AB_{x}, AB_{y})\bullet (BC_{x},BC_{y}) = 0[/tex]
[tex]AB_{x}\cdot BC_{x} + AB_{y}\cdot BC_{y} = 0[/tex]
Now, let is evaluate each choice:
i) A = (3, 3), B = (12, 6), C = (6, 52)
[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]
[tex]\overrightarrow {AB} = (12, 6) - (3, 3)[/tex]
[tex]\overrightarrow {AB} = (12-3, 6-3)[/tex]
[tex]\overrightarrow {AB} = (9, 3)[/tex]
[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]
[tex]\overrightarrow {BC} = (6, 52) - (12, 6)[/tex]
[tex]\overrightarrow {BC} = (6 - 12, 52 - 6)[/tex]
[tex]\overrightarrow {BC} = (-6, 46)[/tex]
[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (9, 3)\bullet (-6, 46)[/tex]
[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (9)\cdot (-6) + (3) \cdot (46)[/tex]
[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 84[/tex]
AB and BC are not orthogonal.
ii) A = (-10, 5), B = (12, 16), C = (6, 52)
[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]
[tex]\overrightarrow {AB} = (12, 16) - (-10, 5)[/tex]
[tex]\overrightarrow {AB} = (12+10, 16-5)[/tex]
[tex]\overrightarrow {AB} = (22, 11)[/tex]
[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]
[tex]\overrightarrow {BC} = (6, 52) - (12, 16)[/tex]
[tex]\overrightarrow {BC} = (6 - 12, 52 - 16)[/tex]
[tex]\overrightarrow {BC} = (-6, 36)[/tex]
[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (22, 11)\bullet (-6, 36)[/tex]
[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (22)\cdot (-6) + (11) \cdot (36)[/tex]
[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 264[/tex]
AB and BC are not orthogonal.
iii) A = (-8, 3), B = (12, 8), C = (18, 4)
[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]
[tex]\overrightarrow {AB} = (12, 8) - (-8, 3)[/tex]
[tex]\overrightarrow {AB} = (12+8, 8-3)[/tex]
[tex]\overrightarrow {AB} = (20, 5)[/tex]
[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]
[tex]\overrightarrow {BC} = (18, 4) - (12, 8)[/tex]
[tex]\overrightarrow {BC} = (18 - 12, 4 - 8)[/tex]
[tex]\overrightarrow {BC} = (6, -4)[/tex]
[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (20, 5)\bullet (-6, -4)[/tex]
[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (20)\cdot (-6) + (5) \cdot (-4)[/tex]
[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = -140[/tex]
AB and BC are not orthogonal.
iv) A = (12, -14), B = (-16, 21), C = (-11, 25)
[tex]\overrightarrow {AB} = \vec B - \vec A[/tex]
[tex]\overrightarrow {AB} = (-16,21) - (12, -14)[/tex]
[tex]\overrightarrow {AB} = (-16-12, 21+14)[/tex]
[tex]\overrightarrow {AB} = (-28, 35)[/tex]
[tex]\overrightarrow {BC} = \vec C - \vec B[/tex]
[tex]\overrightarrow {BC} = (-11,25) - (-16, 21)[/tex]
[tex]\overrightarrow {BC} = (-11+16, 25-21)[/tex]
[tex]\overrightarrow {BC} = (5, 4)[/tex]
[tex]\overrightarrow {AB} \bullet \overrightarrow {BC} = (-28,35)\bullet (5, 4)[/tex]
[tex]\overrightarrow{AB} \bullet \overrightarrow {BC} = (-28)\cdot (5) + (35) \cdot (4)[/tex]
[tex]\overrightarrow{AB}\bullet \overrightarrow {BC} = 0[/tex]
AB and BC are orthogonal.
v) A = (-12, -19), B = (20, 45)
It is not possible to determine the orthogonality of this solution, since point C is unknown.
vi) A = (30, 20), B = (-20, -15)
It is not possible to determine the orthogonality of this solution, since point C is unknown.