Answer:
The value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.
Step-by-step explanation:
We are given with the following polynomial function below;
[tex]\text{P}(x) = 2x^{5} +9x^{4} +9x^{3} +3x^{2}+7x-6[/tex]
Now, we have to calculate the value of P(x) at x = 1 and x = -2.
For this, we will substitute the value of x in the given polynomial and find it's value.
At x = 1;
[tex]\text{P}(1) = 2(1)^{5} +9(1)^{4} +9(1)^{3} +3(1)^{2}+7(1)-6[/tex]
[tex]\text{P}(1) = (2\times 1) +(9\times 1)+(9 \times 1)+(3\times 1)+(7\times 1)-6[/tex]
[tex]\text{P}(1) = 2 +9+9+3+7-6[/tex]
P(1) = 30 - 6
P(1) = 24
At x = -2;
[tex]\text{P}(-2) = 2(-2)^{5} +9(-2)^{4} +9(-2)^{3} +3(-2)^{2}+7(-2)-6[/tex]
[tex]\text{P}(-2) = (2\times -32) +(9\times 16)+(9 \times -8)+(3\times 4)+(7\times -2)-6[/tex]
[tex]\text{P}(-2) = -64 +144-72+12-14-6[/tex]
P(-2) = 156 - 156
P(-2) = 0
Hence, the value of the polynomial function at P(1) and P(-2) is 24 and 0 respectively.
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 .
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 basketball team plays half of its games during the day and half at night. Ten scores from day games and ten scores from night
games were randomly selected by the team's statistician. The following statistical information was calculated from the final game
scores.
Day Night
Mean 58 72
Median 46 63
Mode 50. 70
Range 21 33
Based on these samples, what generalization can be made?
A. The basketball team scored the same number of points in day games as night games.
OB. The basketball team scored more points in night games than in day games.
OC. The basketball team scored more points in day games than in night games.
OD. Not enough information is provided to draw any of these conclusions,
Option B
Because the average points scored in the night is more than that of the day
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 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]
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
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
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.
If 4 bushels of oats weigh 58 kg, how much do 6.5 bushels of oats weigh?
Answer:
94.25 kg I think
Step-by-step explanation:
58/4 =14.5 kg per bushel
6.5 x 14.5=94.25 kg
Answer:
94.25
Step-by-step explanation:
First you need to find the unit rate which is 58/4 which equals to 14.5 then you multiply by 6.5 to find 94.25
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
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!
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
write an expression: A number squared
added to 16
Answer:
16+x²
Step-by-step explanation:
Choose the correct answer.
1/1,000 liter
A: 1 milliliter
B: 1 deciliter
C: 1 centiliter
Answer:
A. 1 milliliter
Step-by-step explanation:
1000 milliliters = 1 liter
0.001 liters = 1 milliliter
Consider a normal distribution with mean 21 and standard deviation 4. What is the probability a value selected at random from this distribution is greater than 21
Answer:
P [ Z > 21 ] = 0,5 or P [ Z > 21 ] = 50 %
Step-by-step explanation:
Normal Distribution N(21;4)
The question here is what is the area of the bell shape curve. As 21 is a mean for this distribution is in the middle of the bell, so values bigger than 21 will have a probability of 0,5, and values smaller than 21 will have the same probability 0,5. We must remember that the whole area under the curve has an area of 1 ( or 100% )
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............
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $112 with a standard deviation of $16. Use a 0.05 level of significance and determine whether or not the average room price is significantly different from $108.50.
Which form of the hypotheses should be used to test whether or not the average room price is significantly different from $108.50?
H0:
a. mu is greater than or equal to $108.50
b. mu is greater than $108.50
c. mu is less than $108.50mu is less than or equal to $108.50
d. mu is equal to $108.50mu is not equal to $108.50
Ha:
a. mu is greater than or equal to $108.50
b. mu is greater than $108.50mu is less than $108.50
c. mu is less than or equal to $108.50
d. mu is equal to $108.50mu is not equal to $108.50
Answer:
H0 :
a. mu is greater than or equal to $108.50
Ha:
c. mu is less than or equal to $108.50
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence
In the given scenario the test is to identify whether the average room price significantly different from $108.50. We take null hypothesis as mu is greater or equal to $108.50.
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
solve for the variable x^2 - 8 = -1 Show all work please
Answer:
x = ±sqrt(7)
Step-by-step explanation:
x^2 - 8 = -1
Add 8 to each side
x^2 - 8+8 = -1+8
x^2 = 7
Take the square root of each side
sqrt(x^2) = ±sqrt(7)
x = ±sqrt(7)
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.
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.
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.
Which steps can be used in order to determine the solution to Negative 1.3 + 4.6 x = 0.3 + 4 x?
Answer:
x=8/3 OR 2.7
Step-by-step explanation:
-1.3+4.6x=0.3+4x
4.6x-4x=0.3+1.3
0.6x=1.6
x=1.6/0.6=8/3
x=8/3 OR 2.7
Hope this helps!
Answer:
[tex]\boxed{x = 2\frac{2}{3} }[/tex]
Step-by-step explanation:
[tex]-1.3+4.6x = 0.3 +4x[/tex]
Collecting like terms
[tex]4.6 x -4x = 0.3+1.3[/tex]
[tex]0.6x = 1.6[/tex]
Dividing both sides by 0.6
x = 1.6 / 0.6
x = 2 2/3
Holly wants to save money for an emergency. Holly invests $500 in an account that pays an interest rate of 6.75% How many years will it take for the account to
reach $14,300? Round your answer to the
nearest hundredth.
Answer:
51.339
Step-by-step explanation:
Hello,
At the beginning Holly has $500
After one year
he will get 500*(1+6.75%)=500*1.0675
After n year (n being real)
he will get
[tex]500\cdot1.0675^n[/tex]
and we are looking for n so that
[tex]500\cdot1.0675^n=14,300\\<=> ln (500\cdot1.0675^n)=ln(14,300)\\<=>ln(500)+n\cdot ln(1.0675)=ln(14,300)\\<=> n= \dfrac{ln(14,300)-ln(500)}{ln(1.0675)}=51.338550...\\[/tex]
so we need 51.339 years
Hope this helps
Use the given categorical data to construct the relative frequency distribution. Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 53, 63, 68, 58, 61, 43, 54. Does it appear that such births occur on the days of the week with equal frequency?
Answer: Yes
Step-by-step explanation:
See explanations in the attached document
Need answers please !!!!
inital height is 2 meters
Step-by-step explanation:
Identify which equations have one solution, infinitely many solutions, or no solution. No
Answer: all of them have one solutions
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]
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:
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