Simplify the following expression: (4x2)2 • (3x3)3
Answer:
432x^13
Step-by-step explanation:
(4x^2)^2 • (3x^3)^3
We know that a^b^c = a^(b*c)
4^2 x^2^2 * 3^3 x^3^3
16 x^4 * 27 x^9
We know that a^b ^ a^c = a^(b+c)
16*27 x^(4+9)
432x^13
Answer:
432x¹³
Step-by-step explanation:
( 4x² ) ² • ( 3x³ ) ²
( 16x²)² • ( 27x³)²
[tex]16 x{}^{2 \times 2} \times 6 {}^{3 \times 3 } \\ 16x {}^{4} \times27 {}^{9} [/tex]
[tex](16 \times 27)x {}^{4 + 9} [/tex]
432x¹³
Find the exact values of the six trigonometric functions at “a” given cos(2a) = - 4/5 and a is
in the 2nd quadrant.
If a is in the second quadrant, then cos(a) < 0 and sin(a) > 0.
Recall the double angle identity for cosine:
cos(2a) = 2 cos²(a) - 1 = 1 - 2 sin²(a)
It follows that
2 cos²(a) - 1 = -4/5 ==> cos²(a) = 1/10 ==> cos(a) = -1/√10
1 - 2 sin²(a) = -4/5 ==> sin²(a) = 9/10 ==> sin(a) = 3/√10
Then we find
1/cos(a) = sec(a) = -√10
1/sin(a) = csc(a) = √10/3
sin(a)/cos(a) = tan(a) = -3
1/tan(a) = cot(a) = -1/3
help with numer 5 please. thank you
Answer:
See Below.
Step-by-step explanation:
We are given that:
[tex]\displaystyle I = I_0 e^{-kt}[/tex]
Where I₀ and k are constants.
And we want to prove that:
[tex]\displaystyle \frac{dI}{dt}+kI=0[/tex]
From the original equation, take the derivative of both sides with respect to t. Hence:
[tex]\displaystyle \frac{d}{dt}\left[I\right] = \frac{d}{dt}\left[I_0e^{-kt}\right][/tex]
Differentiate. Since I₀ is a constant:
[tex]\displaystyle \frac{dI}{dt} = I_0\left(\frac{d}{dt}\left[ e^{-kt}\right]\right)[/tex]
Using the chain rule:
[tex]\displaystyle \frac{dI}{dt} = I_0\left(-ke^{-kt}\right) = -kI_0e^{-kt}[/tex]
We have:
[tex]\displaystyle \frac{dI}{dt}+kI=0[/tex]
Substitute:
[tex]\displaystyle \left(-kI_0e^{-kt}\right) + k\left(I_0e^{-kt}\right) = 0[/tex]
Distribute and simplify:
[tex]\displaystyle -kI_0e^{-kt} + kI_0e^{-kt} = 0 \stackrel{\checkmark}{=}0[/tex]
Hence proven.
write your answer in simplest radical form
Answer:
s = 7√6.
Step-by-step explanation:
From the 30-60-90 triangle we know that cos 30 = √3/2.
cos 30 = s / 14√2
√3/2 = s / 14√2
2s = 14√2√3
s = 14√2√3 / 2
s = 7√6.
given a∥b and c∥d, m<4=35. find m<1, m<2, and m<3
its the rsm problem lesson 6 homework geometry
Answer:
<2 = 35degrees
<3 = 55degrees
Step-by-step explanation:
Find the diagram attached:
From the diagram:
<3 + <4 = 90
<3 + 35 = 90
<3 = 90 - 35
<3 = 55degrees
Also m<1 + m<2+ m<3 = 180 (sum of angles in a traingle)
90+<2+55=180
145+<2 = 180
<2 = 180 - 145
<2 = 35degrees
A county office gets an average of 10 calls in a 2 hour time period. What is the probability that the county office will get more than 0 calls in a 15 minute period? Round your answer to three decimal places.
Answer:
0.713 = 71.3% probability that the county office will get more than 0 calls in a 15 minute period.
Step-by-step explanation:
We have the mean during a time-period, which means that the Poisson distribution is used to solve this question.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
A county office gets an average of 10 calls in a 2 hour time period.
10 calls each 120 minutes, which means that the mean for n minutes is:
[tex]\mu = \frac{10n}{120} = \frac{n}{12}[/tex]
15 minute period:
This means that [tex]n = 15, \mu = \frac{15}{12} = 1.25[/tex]
What is the probability that the county office will get more than 0 calls in a 15 minute period?
This is:
[tex]P(X > 0) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-1.25}*1.25^{0}}{(0)!} = 0.287[/tex]
So
[tex]P(X > 0) = 1 - P(X = 0) = 1 - 0.287 = 0.713[/tex]
0.713 = 71.3% probability that the county office will get more than 0 calls in a 15 minute period.
An alarm clock is slow. It falls behind 4 minutes every 24 hours. If the clock was showing the correct time at 6:00 this morning, how many seconds ahead was the clock at 10:00 last night?
Answer:
80 Seconds
I dont really want to type the whole thing out, just think about it again, or go to a tutor website, you should be able to get it, you have to use these, multiplication of three numbers, and multiplication and division by factorization of numbers.
write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
VW = 4.9
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 46°
Hypothenus = VU = 7
Adjacent = VW =?
The value of VW can be obtained by using the cosine ratio as illustrated below:
Cos θ = Adjacent / Hypothenus
Cos 46 = VW / 7
Cross multiply
VW = 7 × Cos 46
VW = 4.9
Therefore, the value of VW is 4.9
2) If licorice cost $6.59 a pound, how much would it cost to buy a quarter pound of licoric
(Hint: Convert the mixed fraction to an improper fraction or decimal and multiply by th
quantity required)
Answer:
$1.65
Step-by-step explanation:
[tex]6.59*.25=1.65[/tex]or
[tex]6.59*\frac{1}{4} =1.65[/tex]Please please help me i can’t figure this out .. ernest's friend rolls a six-sided number cube and lands on square 8. She asks Ernest to guess what number she rolled. He guesses that she rolled a 3. She says he's wrong.
ernest wonders if she could have rolled a number other than 3. Use a mapping diagram to help guess what number she rolled.
If she would have rolled
Create a Mapping Diagram
When playing this game, the square you land on during the first turn depends on the number you roll. You can write this as a function: SQUARE(number), or S(n). For example, if you roll a 2, you end up on square 2 (when you land on 3 you move back a space). So S(2) = 2.
1. Describe the possible inputs of S(n) using words. (2 points: 1 point for the description, 1 point for the list of numbers)
2. Describe the possible outputs of S(n) using words. (1 point)
3. Draw a mapping diagram for S(n) that maps all the possible inputs and outputs for a player's first turn. Note that the player should begin on square 1. (6 points: 3 points for the inputs and outputs, and 3 points for the mapping)
4. In the mapping diagram you created, what numbers are in the domain of S(n)? Explain what this means. (2 points: 1 point for the domain, 1 point for the explanation)
5. What numbers are in the range of S(n)? Explain what this means. (2 points: 1 point for the range, 1 point for the explanation)
Evaluate the Conjecture
6. Based on the mapping diagram, is it possible that the player rolled a number other than 3 to land on square 8? If so, which number or numbers? Explain your answer. (2 points: 1 point for the answer, and 1 point for the explanation)
Defining Functions
7. Does the mapping diagram you created for S(n) for the first turn of the game represent a function? Why or why not? (2 points: 1 point for the answer, and 1 point for the explanation)
Step-by-step explanation:
1. The inputs are the dice values. Since the cube is six sided, the possible. values are (1,2,3,4,5,6).
2. The outputs values are points if we roll the number. If we land in a special space, we must respect that rule so our outputs are
(2,2,8,5,6,8).
3. I cant show a mapping diagram on brainly. Draw a mapping diagram and make sure to connect the x values and y values of the following.Also make sure to start on square 1.
1 corresponds with 22 corresponds with 23 corresponds with 84 corresponds with 55 corresponds with 66 corresponds with 84. The domain of the function is the same as the input. The dice values, 1,2,3,4,5,6
5.The range are the. values that occur if we roll the number about square 1.
2,2,8,5,6,8
6. No, the player could have rolled 3 and landed on 8. The player also could have rolled 6.
7. Yes, every one x value corresponds with one y value.
Ryan bought coco powder, sugar, and wheat flour. The cost of sugar is $3
lesser than 2 times the cost of coco powder, and the white flour is $2 more
than į of the cost of coco powder. The total cost is $22.56. Find the cost of
each item (Estimate to the nearest tenths place).
Answer:
A
Step-by-step explanation:
Because it’s correct, and explains the property correctly
Remember the dataset of alligators which was about the length and weight of several aligators in Florida. The variable X is the length of aligator and the Y variable is the weight of them. A researcher decided to use decision tree and designed two steps: X<4, X>4. What is the name of this method of splitting?A. Multi-way splitting.B. Entropy classification.C. Binary splitting.D. Gini index.
Answer:
A. multi-way split.
Step-by-step explanation:
Multi way split consists of internal at decision tree branches. Gini index measures probability of impurity in the random variables chosen. Entropy is measure of uncertainty in the sample selected. Binary splitting is used to speed up numerical evaluation.
Test for symmetry and then graph the polar equation.
r=3−5sinθ
Answer:
Symmetric with respect to the x-axis
Symmetric with respect to the y-axis
Symmetric with respect to the origin
A machine in a factory must be repaired if it produces more than 10% defectives in production. A random sample of 100 items from a day's production contains 15 defectives, and the foreman says that the machine must be repaired. Statistically, does the sample evidence support his decision to repair at the 0.01 significance level? Conduct a test by using both the critical region method and the p-value method.
From the test the person wants, and the sample data, we build the test hypothesis, find the test statistic, and use this to reach a conclusion both using the critical value and the p-value.
Doing this, the conclusions are:
The test statistic is [tex]z = 1.67 < z_c[/tex], meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.The p-value of the test is 0.0475 > 0.01, meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.---------------------------------------------------------
Hypothesis:
A machine in a factory must be repaired if it produces more than 10% defectives in production.
At the null hypothesis, we test if it does not have to be repaired, that is, the proportion is of at most 10%. So
[tex]H_0: p \leq 0.1[/tex]
At the alternative hypothesis, we test if it does have to be repaired, that is, the proportion is greater than 10%. So
[tex]H_1: p > 0.1[/tex]
------------------------------------------------------
Decision rule:
0.01 significance level, using a left-tailed test(testing if the mean is more than a value), which means that:
The critical value is Z with a p-value of 1 - 0.01 = 0.99, so [tex]Z_c = 2.327[/tex]. If the test statistic z is less than this, there is not enough evidence to reject the null hypothesis, that the proportion is of at most 10%, otherwise, there is.The p-value is the probability of finding a sample proportion above the one found. If it is more than 0.01, there is not enough evidence to reject the null hypothesis, otherwise, there is.----------------------------------------------------------
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, is the value tested at the null hypothesis, is the standard deviation and n is the size of the sample.
0.1 is tested at the null hypothesis:
This means that [tex]\mu = 0.1, \sigma = \sqrt{0.1*0.9}[/tex]
A random sample of 100 items from a day's production contains 15 defectives.
This means that [tex]n = 100, X = \frac{15}{100} = 0.15[/tex]
Value of the test-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.15 - 0.1}{\frac{\sqrt{0.1*0.9}}{\sqrt{100}}}[/tex]
[tex]z = 1.67[/tex]
----------------------------------------------
Decision: Critical region
The test statistic is [tex]z = 1.67 < z_c[/tex], meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.
Decision: p-value
The p-value of the test is the probability of finding a sample proportion above 0.15, which is 1 subtracted by the p-value of z = 1.67.
Looking at the z-table, z = 1.67 has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
The p-value of the test is 0.0475 > 0.01, meaning that there is not enough evidence to conclude that the proportion of defectives is above 10%, that is, it does not support his decision to repair at the 0.01 significance level.
A similar problem is found at https://brainly.com/question/24326664
Please help out would really appreciate it
Answer:
Step-by-step explanation:
1. Apply the Pythagoras theorem to determine the value of x, we have;
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]x^{2}[/tex] = [tex]15^{2}[/tex] + [tex]8^{2}[/tex]
= 289
x = [tex]\sqrt{289}[/tex]
x = 17
2. Trigonometric ratios of <D.
i. Sin <D = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{8}{17}[/tex]
ii. Cos <D = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
= [tex]\frac{15}{17}[/tex]
iii. Tan <D = [tex]\frac{Opposite}{Adjacent}[/tex]
= [tex]\frac{8}{15}[/tex]
3. Trigonometric ratios of <F.
i. Sin <F = [tex]\frac{opposite}{hypotenuse}[/tex]
= [tex]\frac{15}{17}[/tex]
ii. Cos <F = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
= [tex]\frac{8}{17}[/tex]
iii. Tan <F = [tex]\frac{Opposite}{Adjacent}[/tex]
= [tex]\frac{15}{8}[/tex]
Five friends each spent the same amount of money, x, on school supplies. They expected to spend a total of $130, but the actual
amount spent differed from the expected amount by $15.
Which equation represents the situation? What are the possible amounts that each friend spent?
O
13 - 130 = 15
The amount that each friend spent is $115 or $145.
O
151 - 130 = 15
The amount that each friend spent is $23 or $29.
O
151 + 15 = 130
The amount that each friend spent is $31 or $38.
O
(15.3 – 1300 = 5
The amount that each friend spent is $8 or $9.
Answer:
its the second option
Step-by-step explanation:
hope this helps
Answer: 5x-130=15
Step-by-step explanation:
edmentum
60 units needed, 14 units per case. What is the number of cases and the number of additional units?
Answer:
5 cases
10 additional units
Step-by-step explanation:
Given that :
Total number of units needed = 60 units
Total number of units per case = 14
Hence, the total number of cases required will be :
Number of units needed / number of units per case
Number of cases required = 60 / 14 = 4.285 (this means that 5 cases are required as 4 cases won't be up to 60 units)
With 5 cases, we have exceeded the required units needed :
Additional units will be : (14 * 5) - 60
Additional units = 70 - 60 = 10 units
The square pyramid shown below has a base with sides of 10 units. The slant height of the pyramid is 8 units. What is the vertical height, h?
Round your answer to the nearest tenth.
Answer:
h = 6.2 units
Step-by-step explanation:
Given triangle ABC is a right triangle with the measures of the two sides,
BC = [tex]\frac{10}{2}[/tex] = 5 units
AC = 8 units
By applying Pythagoras theorem in the given triangle,
AC² = AB² + BC²
8² = AB² + 5²
AB² = 64 - 25
AB = √39
AB = 6.24 units
AB ≈ 6.2 units
PLEASE HELP ME ASAP!!!
The answer is 4 because the frequency is the number of cycles completed in one interval. Typically, the interval given is 2π. Here, you can count the cycles and get 4.
If 6,000 dollars in aacount after 3 years after account earn 6% interest yearly how much do you deposit today.
I need the help for this quick app anyone can help
Please help! Thank you :)
Answer:
FE→
Step-by-step explanation:
You start with the endpoint and go in the direction of the arrow
FE
It will have an arrow on top with an endpoint on the left and an arrow going in the same direction to indicate it is a ray→
Suppose the amount of protein is at least 8.6 grams. What is the probability that it is more than 8.7 grams
This question is incomplete, the complete question is;
Many people grab a granola bar for breakfast or for a snack to make it through the afternoon slump at work. A Kashi GoLean Crisp Chocolate Caramel bar weighs 45 grams. The mean amount of protein in each bar is 8 grams. Suppose the amount of protein in the bars have a normal distribution with a standard deviation of 0.32 grams and a random Kashi bar is selected.
Suppose the amount of protein is at least 8.6 grams. What is the probability that it is more than 8.7 grams
Answer:
the required probability is 0.472
Step-by-step explanation:
Given the data in the question;
Let x represent the random variable that shows the protein in the bar.
{ normal distribution }
mean μ = 8
standard deviation σ = 0.32
Now, Suppose the amount of protein is at least 8.6 grams. What is the probability that it is more than 8.7 grams
first we get the z-score for x = 8.6
z = x - μ / σ
z = ( 8.6 - 8 ) / 0.32
z = 0.6 / 0.32
z = 1.875
so
P( x ≥ 8.6 ) = P( z ≥ 1.875 ) = 1 - 0.9696 = 0.0304
Also for, x = 8.7
z = x - μ / σ
z = ( 8.7 - 8 ) / 0.32
z = 0.7 / 0.32
z = 2.1875
so
P( x > 8.7 ∩ x ≥ 8.6 ) = P( x > 8.7 ) = P( z > 2.1875 ) = 1 - 0.98565 = 0.01435
Now, the required probability will be;
P( x > 8.7 | x ≥ 8.6 ) = [P( x > 8.7 ∩ x ≥ 8.6 )] / [ P( x ≥ 8.6 ) ]
= 0.01435 / 0.0304
= 0.472
Therefore, the required probability is 0.472
Which of the following is the vertical asymptote for the graph below?
Answer:
C
Step-by-step explanation:
Vertical asymptotes are always in the form x = ?
If you look at the dotted line, it lands on 2. Because it's a vertical line, the asymptote is going to be x = 2
Choose the function whose graph is given by:
OA.y= cos(2x)
OB.y= cos(1/2x)
OC.y= cos(4x)
D. y = cos(1/4x)
Using translation concepts, it is found that the function whose graph is given is:
A. y= cos(2x)
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The original cosine function has period of [tex]2\pi[/tex], and in this problem, the function has a period of [tex]\pi[/tex], hence the domain was multiplied by 2, which means that option A is correct.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
Question
Elvira and Aletheia live 3.2 miles apart on the same street. They are in a study group that meets at a coffee shop between their houses. It took Elvira 1/2 hour and Aletheia 2/3 hour to walk to the coffee shop. Find both women's walking speeds.
Missing from the question
Aletheia's speed is 0.6 miles per hour slower than Elvira's speed.
Answer:
[tex]s_E = 3.0[/tex]
[tex]s_A = 2.4[/tex]
Step-by-step explanation:
Given
[tex]d = 3.2m[/tex] -- distance
[tex]t_E = 1/2[/tex] --- Elvira time
[tex]t_A = 2/3[/tex] --- Aletheia time
[tex]s_E - s_A = 0.6[/tex] --- the relationship between their speeds
Required
Their walking speed
Distance (d) is calculated as:
[tex]d = speed * time[/tex]
For Elvira, we have:
[tex]d_E = s_E * 1/2[/tex]
For Aletheia, we have:
[tex]d_A = s_A * 2/3[/tex]
So, we have:
[tex]d_E + d_A = d[/tex] --- total distance
This gives:
[tex]s_E * 1/2 + s_A * 2/3 = 3.2[/tex]
Recall that:
[tex]s_E - s_A = 0.6[/tex]
Make sE the subject
[tex]s_E = 0.6+s_A[/tex]
Substitute [tex]s_E = 0.6+s_A[/tex] in [tex]s_E * 1/2 + s_A * 2/3 = 3.2[/tex]
[tex](0.6+s_A)* 1/2 + s_A * 2/3 = 3.2[/tex]
[tex]0.3+1/2s_A + 2/3s_A = 3.2[/tex]
Collect like terms
[tex]1/2s_A + 2/3s_A = 3.2-0.3[/tex]
[tex]1/2s_A + 2/3s_A = 2.9[/tex]
Express all as decimal
[tex]0.5s_A + 0.7s_A= 2.9[/tex]
[tex]1.2s_A= 2.9[/tex]
Divide both sides by 1.2
[tex]s_A = 2.4[/tex]
Recall that:
[tex]s_E = 0.6+s_A[/tex]
So, we have:
[tex]s_E = 0.6+2.4[/tex]
[tex]s_E = 3.0[/tex]
Help only 19 & 21 please thank you
Answer:
19) The square root of 35 with one digit decimal accuracy is 5.9.
21) The sqrt. of 61 to the nearest integer is 8!
Step-by-step explanation:
take the square roots around 61.
the square root of 8 is 64,
the square root of 7 is 49.
61 is closer to 64.
Integers cannot be fractions, so the answer of 7.8 is rounded up to 8! (This Is For Number 21)am not really that sure about number 19
An ecologist finds 220 yellow-flowered plants and 180 white-flowered plants. Use the normal distribution to find the Lower boundary of a 95% confidence interval for the proportion of yellow-flowered plants. Which of the following answers is correct to 2 decimal places?
a. Lower boundary = 0.30
b. Lower boundary = 0.60
c. Lower boundary = 0.50
d. Lower boundary = 0.40
Answer:
c. Lower boundary = 0.50
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
An ecologist finds 220 yellow-flowered plants and 180 white-flowered plants.
220 out of 220 + 180 = 400. So
[tex]n = 400, \pi = \frac{220}{400} = 0.55[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 1.96\sqrt{\frac{0.55*0.45}{400}} = 0.5[/tex]
Thus the correct answer is given by option c.
what's the radius of 16x^2+16y^2=1 With a center of (0,0) ?
Answer:
The center is (0,0) and the radius is 1/4
Step-by-step explanation:
The formula for a circle is
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
16x^2+16y^2=1
Divide by 16
x^2+y^2=1/16
x^2 + y^2 = (1/4) ^2
(x-0)^2 + (y-0)^2 = (1/4) ^2
The center is (0,0) and the radius is 1/4
F(4) =
If g(x) = 2, x=
An
Step-by-step explon:
A person who is 5 feet tall standing 120 feet from the base of a tree, and the tree casts a 132 foot shadow. The person’s shadow 12 feet in length what is he height of the tree
