Answer:
cos 60° = 1/2 because the angles are complements.
Step-by-step explanation:
Which box holds more popcorn?
Answer:
Amanda's popcorn container holds more popcorn
Step-by-step explanation:
First we'll have to find the volume.
The Volume helps us determine which is bigger.
Step 1
We'll find Amanda's popcorn container
10cm*10cm*13.5cm=1350cm
Step 2
We'll find Mary's popcorn container
8cm*8cm*20cm=320cm
Step 3
Since Amanda's popcorn container has 1350cm (volume) and Mary's popcorn container has 320cm (volume) we'll have this. 1350cm>320cm. We can determine the Amanda's popcorn container has holds more,
Final Answer
Amanda's popcorn container holds more popcorn
A vat of milk has spilled on a tile floor. The milk flow can be expressed with the function r(t) = 4t, where t represents time in minutes and r represents how far the milk is spreading.
The spilled milk is creating a circular pattern on the tile. The area of the pattern can be expressed as A(r) = πr2.
Part A: Find the area of the circle of spilled milk as a function of time, or A[r(t)]. Show your work.
Part B: How large is the area of spilled milk after 4 minutes? You may use 3.14 to approximate π in this problem.
Answer:
For a) $A(r(t))=π(4t)^2.$
For b) 803.84
Step-by-step explanation:
For a) we can do a simple substitution on the variable r. Notice that $A=πr^2$ make $A$ a function of $r.$ Then, $A(r(t))=\pi (r(t))^2=\pi (4t)^2.$
For b) you only need to substitute the value $t=4$ on the expresión $A(r(t)).$
Fifteen chaperones went on a field trip with 225 students. Which fraction represents the number of chaperones to students on the field trip
Answer:
15/225
Step-by-step explanation:
The number of chaperones for the group of students can be represented with a ratio - 15:225 or 15/225.
Because there are 15 chaperones for the 225 students, you can state what the ratio does - for every 225 students, there are 15 chaperones.
However, 15/225 can be reduced to 1/15, so for every 15 students, there is 1 chaperone.
The sum of two polynomials is 10a^2b^2-8a^2b+6ab^2-4ab+2 if one addend is -5a^2b^2+12a^2b-5 what is the other addend
Answer:
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Step-by-step explanation:
The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]
[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]
[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]
The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].
Answer:
A
Step-by-step explanation:
find the range of the inequality 2e-3< 3e-1
Answer:
[tex]x = { - 1, 0,1 ,2 ...}[/tex]
Step-by-step explanation:
[tex]2e - 3 < 3e - 1 = 2e - 3e < - 1 + 3 = - 1e < 2 = e > - 2[/tex]
Hope this helps ;) ❤❤❤
5.
The width of a rectangle is one foot more than a third of the length. If the
perimeter is 42 feet, what is the width? What is the length?
1. Write a survey question for which you would expect to collect numerical
data.
2. Write a survey question for which you would expect to collect categorical
data.
Answer:
How many siblings do you have?
I hope this helps you out :)
Suppose that the Blood Alcohol Content (BAC) of students who drink five beers varies from student to student according to a Normal distribution with mean 0.07 ans standard deviation 0.01.
1. The middle 95% of students who drink five beers have a BAC between
a. 0.06 and 0.08 b. 0.05 and 0.09 c. 0.04 and 0.10 d. 0.03 and 0.11
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
Answer:
1. b. 0.05 and 0.09
2. d. 16%
3. a. 0.15%
Step-by-step explanation:
Given that :
mean = 0.07
standard deviation = 0.01
Confidence interval = 95%
The level of significance ∝= 1 - 0.95 = 0.05
At 0.05 level of significance,
critical value for [tex]z_{\alpha/2} = z_{0.05/2}[/tex]
critical value for [tex]z_{0.025}[/tex] = 1.96
Confidence interval = [tex]\mathtt{\mu \pm ( {z} \times{\sigma})}[/tex]
Lower limit = [tex]\mathtt{\mu -( {z} \times{\sigma})}[/tex]
Upper Limit = [tex]\mathtt{\mu +( {z} \times{\sigma})}[/tex]
Lower limit = [tex]\mathtt{0.07 - ({1.96} \times {0.01})}[/tex]
Upper limit = [tex]\mathtt{0.07 + ({1.96} \times {0.01})}[/tex]
Lower limit = 0.07 - 0.0196
Upper limit = 0.07 + 0.0196
Lower limit = 0.0504 [tex]\simeq[/tex] 0.05
Upper limit = 0.0896 [tex]\simeq[/tex] 0.09
The confidence interval of 95% is ( 0.05, 0.09)
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
[tex]P(X> 0.08) = P(\dfrac{0.08 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )[/tex]
[tex]P(X > 0.08) = P(z > \dfrac{0.08 - 0.07}{0.01} )[/tex]
[tex]P(X > 0.08) = P(z > \dfrac{0.01}{0.01} )[/tex]
[tex]P(X > 0.08) = P(z > 1 )[/tex]
[tex]P(X> 0.08) = 1- P(z < 1 )[/tex]
P(X > 0.08) = 1 - 0.8413
P(X > 0.08) = 0.1587
P(X > 0.08) [tex]\simeq[/tex] 16%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
[tex]P(X> 0.10) = P(\dfrac{0.10 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )[/tex]
[tex]P(X > 0.10) = P(z > \dfrac{0.10 - 0.07}{0.01} )[/tex]
[tex]P(X > 0.10) = P(z > \dfrac{0.03}{0.01} )[/tex]
[tex]P(X > 0.10) = P(z > 3)[/tex]
[tex]P(X> 0.10) = 1- P(z < 3 )[/tex]
P(X > 0.10) = 1 - 0.9987
P(X > 0.08) = 0.0013
P(X > 0.08) [tex]\simeq[/tex] 0.15% which is the closet value to 0.0013
A population has a mean and a standard deviation . Find the mean and standard deviation of a sampling distribution of sample means with sample size n. nothing (Simplify your answer.) nothing (Type an integer or decimal rounded to three decimal places as needed.)
Complete Question
A population has a mean mu μ equals = 77 and a standard deviation σ = 14. Find the mean and standard deviation of a sampling distribution of sample means with sample size n equals = 26
Answer:
The mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is [tex]\mu_{\= x } = 77[/tex]
The standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is
[tex]\sigma _{\= x} = 2.746[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 77[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
The sample size is [tex]n = 26[/tex]
Generally the standard deviation of sampling distribution of the sample mean ( [tex]\= x[/tex]) is mathematically represented as
[tex]\sigma _{\= x} = \frac{ \sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{ 14}{ \sqrt{26} }[/tex]
[tex]\sigma _{\= x} = 2.746[/tex]
Generally the mean of sampling distribution of the sample mean ( [tex]\= x[/tex]) is equivalent to the population mean i.e
[tex]\mu_{\= x } = \mu[/tex]
[tex]\mu_{\= x } = 77[/tex]
Describe and correct the error in determining the formula for the sequence below
Answer:An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
Step-by-step explanation:
Help with number 50 please. Thanks.
Answer:
[tex] d = 7 + 3\sqrt{3} [/tex] and
[tex] d = 7 - 3\sqrt{3} [/tex]
Step-by-step explanation:
To solve the equation, [tex] d^2 - 14d - 22 = 0 [/tex], using the quadratic formula,
Recall: quadratic formula = [tex] \frac{-b ± \sqrt{b^2 - 4ac}}{2a} [/tex]
Where,
a = 1
b = -14
c = 22
Plug in your values into the formula and solve:
[tex] \frac{-(-14) ± \sqrt{(-14)^2 - 4(1)(22)}}{2(1)} [/tex]
[tex] \frac{14 ± \sqrt{196 - 88}}{2} [/tex]
[tex] \frac{14 ± \sqrt{108}}{2} [/tex]
[tex] d = \frac{14 + \sqrt{108}}{2} [/tex]
[tex] d = \frac{14 + 6\sqrt{3}}{2} [/tex]
[tex] d = (\frac{2(7 + 3\sqrt{3})}{2} [/tex]
[tex] d = 7 + 3\sqrt{3} [/tex]
And
[tex] d = \frac{14 - \sqrt{108}}{2} [/tex]
[tex] d = \frac{14 - 6\sqrt{3}}{2} [/tex]
[tex] d = (\frac{2(7 - 3\sqrt{3})}{2} [/tex]
[tex] d = 7 - 3\sqrt{3} [/tex]
Write down the name of the shape for question D. Please help!
Step-by-step explanation:
thats shape is a delta
:)
Answer:
arrow head
Step-by-step explanation:
A hot air balloon descends 200 feet per
minute from an altitude of 1000 feet. Write a expression
An unfair coin is flipped. If a head turns up you win $1. The probability of a head is .54 and the probability of a tail is 0.46. What is the expected value of the game
Answer:
54 cents
Step-by-step explanation:
(.54 * 1)+(.46*0) = .54
The check_time function checks for the time format of a 12-hour clock, as follows: the hour is between 1 and 12, with no leading zero, followed by a colon, then minutes between 00 and 59, then an optional space, and then AM or PM, in upper or lower case. Fill in the regular expression to do that. How many of the concepts that you just learned can you use here
Answer:
Following are the correct code to this question:
import re#import package for regular expression
def check_time(text):#defining a method check_time that accepts string value
p = r'(1[012]|[1-9]):[0-5][0-9][ ]{0,1}?(am|pm|AM|PM)'#defining string variable p that stores values
val = re.search(p, text)#defining val variable that check serachs p and text variable values
return val!= None#use return keyword to return val value
print(check_time("12:45pm"))#defining print method that calls method by input value
print(check_time("9:59 AM")) #defining print method that calls method by input value
print(check_time("6:60 am")) #defining print method that calls method by input value
print(check_time("five o'clock"))#defining print method that calls method by input value
Output:
True
True
False
False
Step-by-step explanation:
In the above-given program, some data is missing that is code file so, the correct code can be defined as follows:
In the above-given method, that is "check time" it uses 12-hour time format validation, that is tested by coding the regex and all the value validates in the "val" variables, that can be defined as follows:
In the first step, its values should be in 1,2,3, ... 10,11,12 In the second step, it values in Between hour and minutes, and there will be a colon. In the third step, the minutes variable should take the double-digit, that will be like 00,01 .... 59. In the last step, one space becomes permitted after an hour: a minute or no space for am or pm value.Evaluate the expresión 6c-d when c=2 and d=10 I need help?
Answer:
the answer is 18
Step-by-step explanation:
8 is the answer
Which regular polygon has a rotation of 240 degree to carry the polygon onto itself?
Equilateral triangle
Octagon
Rectangle
Pentagon
The regular polygon that has a rotation of 240 degrees to carry the polygon onto itself is an B. Octagon.
What is an Octagon?This refers to an eight-sided polygon that has eight angles and is used in geometry.
Hence, we can see that an octagon, can be rotated to 240 degrees and when this is done, it is able to carry itself which cannot be done by others as other polygons would need 360 degrees to carry themselves.
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If xy = 1 what is the arithmetic mean of x and y in terms of y? Please show work as detailed as possible
Answer:
(1+y^2) /2y
Step-by-step explanation:
arithmetic mean is the average of x and y
(x+y)/2
Using the equation
xy = 1
and solving for x
x = 1/y
Replacing x in the first equation
(1/y + y) /2
Multiply by y/y
(1/y + y) /2 * y/y
(1/y + y)*y /2y
(1+y^2) /2y
A detective knows what time of day it is based on the angle at which the sun is hitting a man. Suppose a detective is looking at a photograph of a 6-foot tall man with a shadow that is 3.5 feet. Find the angle at which the sun is hitting the ground.
Answer:
The angle [tex]\theta[/tex] at which the sun is hitting the ground is:
[tex]\theta\approx 59.74^o[/tex]
Step-by-step explanation:
You can use right angle trigonometry to solve this, since the man (6 ft tall) and the shadow on the ground (3.5 ft long) form a right angle triangle as shown on the attached image.
The use the tangent function to find the angle that the sun's rays make with the ground:
[tex]tan(\theta)=\frac{opposite}{adjacent} \\tan(\theta)=\frac{6}{3.5} \\\theta=arctan(\frac{6}{3.5})\\\theta\approx 59.74^o[/tex]
I
Ifm DGF = 72, what equation can you use to find mZEGF?
Answer:
see explanation
Step-by-step explanation:
∠ DGE + ∠ EGF = ∠ DGF , that is
∠ EGF = ∠ DGF - ∠ DGE
∠ EGF = 72° - ∠ DGE
Multiply the following complex numbers:
(7+2i)(2+3i)
Please don’t guess
Answer:
14 + 25l + 6l^2
Step-by-step explanation:
(7 + 2i) (2 + 3i)
=> 14 + 4l + 21l + 6l^2
=> 14 + 25l + 6l^2
This is the correct answer
A normal distribution has a mean of 30 and a variance of 5.Find N such that the probability that the mean of N observations exceeds 30.5 is 1%.
Answer:
109
Step-by-step explanation:
Use a chart or calculator to find the z-score corresponding to a probability of 1%.
P(Z > z) = 0.01
P(Z < z) = 0.99
z = 2.33
Now find the sample standard deviation.
z = (x − μ) / s
2.33 = (30.5 − 30) / s
s = 0.215
Now find the sample size.
s = σ / √n
s² = σ² / n
0.215² = 5 / n
n = 109
What is the midpoint between A(-6,1) and B(0,2)?
Answer:
(-3, 3/2)
Step-by-step explanation:
To find the midpoint between two points you are going to add the X1 and X2, then divide by two. Then you are going to add the Y1 and Y2, and divide by two.
A(-6,1) B(0,2)
= (-6+0, 1+2)
= (-6, 3)
=(-6/2, 3/2)
=(-3, 3/2)
On a map 1 cm represents 4.5km. What is the actual distance between two towns which are 4cm apart on the map?
Answer:
18km
Step-by-step explanation:
1cm:4.5km/4cm then get the answer as 18km
1 cm represents [tex]4.5[/tex] km. To find the actual distance between two towns that are 4 cm apart on the map, we can use the scale ratio.
Since 1 cm represents [tex]4.5[/tex] km, we can calculate the actual distance by multiplying the map distance with the scale ratio. Map distance: 4 cm Scale ratio: 1 cm represents [tex]4.5[/tex] km Actual distance = Map distance × Scale ratio Actual distance[tex]= 4 cm × 4.5[/tex] km/cm Actual distance[tex]= 18 km[/tex]
Therefore, the actual distance between the two towns is18 [tex]18[/tex] km. Using the given scale, 1 cm on the map corresponds to[tex]4.5[/tex]km in reality. As the towns are represented as 4 cm apart on the map, the actual distance between them is [tex]18[/tex]km.
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Complete the table of values for y=-x^2+2x+1
X -3, -2, -1,0,1,2,3,4,5
Y -14,7, ,1, -2 -14
Answer:
see the attachment
Step-by-step explanation:
When you have a number of function evaluations to do, it is convenient to let a graphing calculator or spreadsheet do them. That avoids the tedium and the mistakes in arithmetic.
Here's your completed table.
Help please!! Simplify the following expression
*4 + 3x3 - 2x - 5x2 - X+ x2 + x +1+7x4
O A. 8x4 +5x2 + 4x2 + 0x+1
B. 8x4 +5x + 4x2 +1
C. 8x4 + x2 - 4x + 0x
D. 8x4 + x2 - 4x2 +1
━━━━━━━☆☆━━━━━━━
▹ Answer
D. 8x⁴ + x³ - 4x² + 1
▹ Step-by-Step Explanation
Remove the opposites:
x⁴ + 3x³ - 2x³ - 5x² + x² + 1 + 7x²
Collect like terms:
8x⁴ + 3x³ - 2x³ - 5x² + x² + 1
8x⁴ + x³ - 5x² + x² + 1
8x⁴ + x³ - 4x² + 1
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
25. After a horizontal reflection across the y-axis, f(x) is: options: f(–x) f(x – 1) –f(–x) –f(x)
Answer:
A, f(–x)
Step-by-step explanation:
Reflection about the y-axis is defined as:
f(x) = - f(-x)
So the correct answer is
A, f(–x)
Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Three coins are tossed; the result is at most one head. Which of the following sets of elements are included in the sample space
HHTHTTTTHTTTTHTHHHTHHHTH
List the elements of the given event. (Select all that apply.)
HHT
HTT
TTH
TTT
THT
HHH
THH
HTH
List the elements of the given event. (select all that apply)
HTT
TTH
HTH
THH
THT
HHH
TTT
HHT
Answer:
Even set = {HTT, THT, TTH, TTT}
Step-by-step explanation:
We are given that three coins are tossed; the result is at most one head.
And we have to find the sets of elements that are included in the sample space.
Firstly, as we know that when three coins are tossed, the total number of cases formed is 8.
Let Head on the coin be represented by 'H' and the Tail on the coin be represented by 'T'.
So, the sample space so formed is;
S = {HHH, HTH, HHT, THH, THT, TTH, HTT, TTT}
Now, our event is at most one head. So, the sample space for the favorable event is given by;
Even set = {HTT, THT, TTH, TTT}
In this, three cases are of head occurring only once and one case is of head not appearing in three tosses of a coin.
Find an equation of the circle whose diameter has endpoints (-6, -1) and (-2,3).
Step-by-step explanation:
Let find the distance of the diameter. using distance formula.
[tex](3 + 1) {}^{2} + ( - 2 + 6) {}^{2} = \sqrt{8} [/tex]
The diameter is sqr root of 8 units.
A circle equation is
[tex] {x}^{2} + {y}^{2} = {r}^{2} [/tex]
where r is the radius. The radius is half the diameter so
[tex]r = \frac{ \sqrt{8} }{2} = \frac{ \sqrt{8} }{ \sqrt{4} } = \sqrt{2} [/tex]
[tex] {r}^{2} = { \sqrt{2} }^{2} = 2[/tex]
So our radius is 2.
Now we need to find the midpoint or Center of the diameter.
[tex] \frac{ - 6 - 2}{2} = - 4[/tex]
[tex] \frac{3 - 1}{2} = 1[/tex]
So the center of the circle is (-4,1). So our equation of the Circle us
[tex](x + 4) {}^{2} + (y - 1) {}^{2} = ( \sqrt{2} ) {}^{2} [/tex]
Help plz! Jim is climbing a mountain that has a base 150 feet above sea level. If he climbs 233 feet then descends into a cave 64 feet, how far above sea level is Jim
Answer:
150+233-64=319
Jim is 319 ft above sea level.
Step-by-step explanation: