Answer:
D is correct
Step-by-step explanation:
Since you have 2 parallel lines cut by a transversal, <BAC and <BDE are corresponding angels. Corresponding angles are congruent. You are able to prove that 2 pairs of angles are congruent so the triangles are similar. All of the answers show that the 2 triangles share angle B as the first part of the answer.
use the diagram to answer the question. what is the value of x
Answer:
2√(133)
Step-by-step explanation:
Triangle 1 = 8, 12, ?
triangle 2 = 18, x, ?
we have to find value of x which is a hypotenuse
a² + b² = c²
8² + 12² = 64 + 144 = √208 = 14.4222051019
x = 14.4222051019² + 18²
= 208 + 324
= 532
x = √532 = 2√(133)
A computer store decides to increase the prices of all the items it sells by 15%. the store manager uses matrices to prepare the new price list. matrix a contains the unit price of each product in each category. matrix b contains the revised price of each item in each category. how can the manager obtain the entries for matrix b? a. by adding 15 to each entry of matrix a b. by multiplying each entry of matrix a by 15 c. by multiplying each entry of matrix a by 1.15 d. by multiplying each entry of matrix a by 0.15
The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The manager could achieve scalar multiplication on Matrix A, utilizing the scalar 1.15.
What is the matrix?The matrix exists as a set of numbers placed in rows and columns to create a rectangular array. The numbers exist named the elements, or entries, of the matrix. Matrices contain wide applications in engineering, physics, economics, and statistics as well as in different branches of mathematics.
Increasing the price by 15% would mean we exist taking 100% of the value + another 15%
100 + 15 = 115%
115% = 115/100 = 1.15.
Multiplying every value in Matrix A by 1.15 will give the price raised by 15%.
Therefore, the correct answer is option c. by multiplying each entry of matrix a by 1.15.
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Answer:
C - by multiplying each entry by 1.15
Step-by-step explanation:
Edmentum.
What value of z* should be used to construct an 88% confidence interval of a population mean?
Z = 1.555 should be used
If we seek an 88% confidence interval, that means we only want a 12% chance that our interval does not contain the true value.
Assuming a two-sided test, that means we want a 6% chance attributed to each tail of the Z-distribution.
the zα/2 value of z0.06.
This z value at α/2=0.06 is the coordinate of the Z-curve that has 6% of the distribution's area to its right, and thus 94% of the area to its left. We find this z-value by reverse-lookup in a z-table.
What is Z-distribution?The standard normal distribution, also called the z-distribution, is a special normal distribution where the mean is 0 and the standard deviation is 1.
Any normal distribution can be standardized by converting its values into z-scores. Z-scores tell you how many standard deviations from the mean each value lies.
Why is z-score used?The standard score (more commonly referred to as a z-score) is a very useful statistic because it
(a) allows us to calculate the probability of a score occurring within our normal distribution and
(b) enables us to compare two scores that are from different normal distributions.
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The purpose of statistical inference is to make estimates or draw conclusions about a.
The purpose of statistical inference population based upon information obtained from the sample.
What is statistical inference?statistical inference uses sample data to make estimates of or draw conclusions about one or more characteristics of a population.
The purpose of statistical inference is to estimate this sample to sample variation or uncertainty. Understanding how much our results may differ if we did the study again, or how uncertain our findings are, allows us to take this uncertainty into account when drawing conclusions. It allows us to provide a plausible range of values for the true value of something in the population, such as the mean, or size of an effect, and it allows us to make statements about whether our study provides evidence to reject a hypothesis.
We have four ideas for using the statistical inference.
1. Estimating uncertainty.
2. Confidence intervals.
3. Hypothesis tests.
4. Connections with other material.
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The given question is not complete.
The purpose of statistical inference is to make estimates or draw conclusions about a population based upon information obtained from the sample.
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WILL GIVE BRAINLEST!!!
Kerry wants to know whether or not people will be voting in the upcoming presidential election. She posts signs giving the website for her survey. Which sampling method is described?
A. Unbiased Systematic Random Sample
B. Biased Convenience Sample
C. Unbiased Simple Random Sample
D. Biased Voluntary Response Sample
pls help me solve these
The conversion of 9.204 to a mixed number will be 9 51/250.
How to illustrate the information?It should be noted that converting decimal to mixed numbers simply means changing them to whole numbers and fractions.
Therefore, 9.204 will be:
= 9 204/1000
= 9 51/250
The percentage equivalent of 3 7/8 will be:
= (3 × 100) + (7/8 × 100)
= 300 + 87.5
= 387.5%
Dividing 72 in the ratio 2:3:4 will be:
= 2/9 × 72 = 16
= 3/9 × 72 = 24
= 4/9 × 72 = 32
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Simplify.
√75
OA. 3√5
OB. 15√5
OC. 25√3
OD. 5√3
Answer:
Option D
Step-by-step explanation:
Using the surd law :
[tex]\sqrt{ab} = \sqrt{a}\sqrt{b}[/tex]
We can find the largest square number that goes into 75 :
Let's write the multiples of 75 :
1 , 75
3 , 25
5 , 15
The only square number is 25
So using the law mentioned above we split √75 into :
√25√3
The square root of 25 is 5
Now we have our final answer of 5√3
Hope this helped and have a good day
The simplified form of expression √75 is 5√3.
Option D is the correct answer.
We have,
To simplify √75, we can factor it into its prime factors and then take the square root:
√75 = √(3 * 5 * 5)
= √(3 x 5²)
Take out the perfect square factor from under the square root:
= √3 x √5²
= √3 x 5
= 5√3
Thus,
The simplified form of expression √75 is 5√3 which is option D.
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Are the two triangles similar?
Answer:
Yes
Step-by-step explanation:
The missing angle in triangle DER is 42 (as angles in a triangle add up to 180) and the missing angle in TVA (LOKI lol ) is 110 (as angles in a triangle add up to 180) .
Since all angles are equal the triangles must be similar .
Hope this helped and have a good day
During the season, the Rangers played 25 games. They won 14 of the games.
What fraction and percent of the games did they lose? Show your work in the
space below. Remember to check your solution.
Answer:
See below
Step-by-step explanation:
Out of 25 games, they won 14
Fraction won = won / total = 14 / 25
Percent won = won /total * 100 % = 14/25 * 100 = .56 * 100 % = 56 %
To find the number of games lost
25-14 = 11
Fraction won = won / total = 11 / 25
Percent won = won /total * 100 % = 11/25 * 100 = .44 * 100 % = 44 %
To check your work, the percent total should be 100
56+44 = 100
Liam says -() is equivalent to 2. Explain if Liam is correct by completing the
statements below.
Click the arrows to choose an answer from each menu.
The fraction - (2) can be described as the opposite of a positive number divided by a positive
number. A positive number divided by a positive number results in a Choose...
quotient, and its opposite is always Choose...
The fraction can be described as a positive number divided by a negative number, which
-12
always results in a Choose...
quotient.
value, so Liam Choose...
The fractions have
Choose...
Y
correct.
Someone help I am on my big sisters phone
Answer:
I don't understand the format of the questions and choices. I simply made a few observation.
Step-by-step explanation:
The fraction - (2) can be described as the opposite of a positive number divided by a positive number.
-(2/1)?
A positive number divided by a positive number results in a Choose... Negative Number
quotient, and its opposite is always Choose... Opposite? Still a negative number.
I don't understand the following:
The fraction can be described as a positive number divided by a negative number, which
-12
always results in a Choose...
quotient.
value, so Liam Choose...
The fractions have
Choose...
Y
correct.
In step 2, the
property of equality was applied.
In step 4, the
property of equality was applied.
In step 2, the property of equality applied was addition property of equality.
In step 4, the property of equality applied was multiplication property of equality.
What is the Addition Property of Equality?The addition property of equality states that, to move a negative number over to the other side of an equation, add the number to both sides of the equation. For example, given the equation: a - c = b, to move c over to the other side of the equation, add c to both sides of the equation. we will have:
a - c + c = b + c
a = b + c.
What is the Multiplication Property of Equality?According to the multiplication property of equality, if we have, a/c = b, to isolate a, we would multiply both sides of the equation by c. Thus:
a/c × c = b × c
a = bc
In the table given, in step 2, 6 was added to both sides of the equation. This means the property of equality that was applied was: addition property of equality.
In step 4, both sides of the equation was multiplied by -2. Thus, the property of equality that was applied was: multiplication property of equality.
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Answer: step 2 - addition property
step 4 - multiplication property
Step-by-step explanation:
Solve the given differential equation by undetermined coefficients. y'' − y' − 12y = e4x
The general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]
For given question,
We have been given a differential equation y'' − y' − 12y = e^(4x)
We need to solve the given differential equation by undetermined coefficients.
We can write given differential equation as [tex](D^2-D-12)y=e^{4x}[/tex] where [tex]D=\frac{d}{dx}[/tex]
First solve the corresponding homogeneous differential equation:
y'' - y' - 12y = 0
The characteristic equation is:
m² - m - 12 =0
Let's find the roots of above quadratic equation by factorization.
⇒ m² - m - 12 = 0
⇒ (m - 4)(m + 3) = 0
⇒ m - 4 = 0 OR m + 3 = 0
⇒ m = 4 OR m = -3
Hence the complementary solution is,
[tex]y_c=C_1e^{4x}+C_2e^{-3x}[/tex]
Let the general solution of a second order homogeneous differential equation be [tex]y(x)=C_1(x)e^{4x}+C_2(x)e^{-3x}[/tex]
The unknown functions C1(x) and C2(x) can be determined from the system of two equations:
[tex]C'_1e^{4x}+C'_2e^{-3x}=0~~~~~~~............(1)\\\\C'_1(4e^{4x})+C'_2(-3e^{-3x})=e^{4x}~~~~~~~...................(2)[/tex]
from (1),
[tex]C'_2e^{-3x}=-C'_1e^{4x}[/tex]
Substitute this value in equation (2)
[tex]4C'_1e^{4x}+3C'_1e^{4x}=e^{4x}[/tex]
[tex]\Rightarrow C'_1=\frac{1}{7}[/tex] and [tex]C'_2=-\frac{1}{7}e^{7x}[/tex]
[tex]\Rightarrow C_1=\frac{1}{7} x+c_3[/tex] and [tex]C_2=\frac{1}{49}e^{7x}+c_2[/tex]
Therefore, the general solution of the given differential equation be [tex]y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}[/tex]
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4 pictures on 1/3 of a page
= ________pictures/page
Step-by-step explanation:
4 pictures correlate to 1/3 page.
how many 1/3 pages do we need to get 1 full page ?
3, as 3 × 1/3 = 3/3 = 1.
so, to keep the ratio, we need to multiply also the pictures by 3 and get
4×3 = 12 pictures per page
What are the values of sin a and tan a, if a is an acute angle in a right triangle:
cosa=15/17
Given that a is an acute angle in a right triangle, cos a = [tex]\frac{15}{17}[/tex]. The trigonometric ratio sin a = [tex]\frac{8}{17}[/tex] and tan a = [tex]\frac{8}{15}[/tex].
The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.
In any question,
cos a = [tex]\frac{base}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]
hypotenuse = side opposite of the right angle = 17
base = side adjacent to the acute angled marked = 15
[tex]hypotenuse^{2} = perpendicular ^2+base^2\\\\perpendicular = \sqrt{hypotenuse^2-base^2}[/tex]
perpendicular = [tex]\sqrt{17^2- 15^2} = 8[/tex]
sin a = [tex]\frac{perpendicular}{hypotenuse} = \frac{8}{17}[/tex]
tan a = [tex]\frac{perpendicular}{base} = \frac{8}{15}[/tex]
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Which line most accurately represents the line of best fit for the scatter plot?
A graph shows numbers from 0 to 14 on the x axis at increments of 2 and the numbers 0 to 28 on the y axis at increments of 4. Scatter plot shows ordered pairs 2, 5 and 5, 6 and 6, 8 and 8, 10 and 9, 12 and 10, 12 and 11, 14 and 12, 16 and 13, 20. A line labeled A joins ordered pair 0, 0 and 4, 28. A line labeled B joins the ordered pairs 0, 0 and 8, 28. A line labeled C joins the ordered pairs 0, 0 and 13, 28. A line labeled D joins the ordered pairs 0, 0 and 14, 18
Line A
Line B
Line C
Line D
Answer: Line D
Step-by-step explanation:
The points in the scatterplot are closest to line D.
Number
8.6134
5.5218
...to the nearest tenth ...to the nearest hundredth
..to the nearest thousandth
Concepts and Applicati
The following numbers are rounded up as follows:
8.6134
nearest tenth = 8.6nearest hundredth = 8.61nearest thousandth = 8.6135.5218
nearest tenth = 5.5nearest hundredth = 5.52nearest thousandth = 5.522How to round up?Rounding up a number means to round a number to the smallest integer that is not less than it, or to some other greater value.
Thousandth, hundredth and tenth are used after the decimal point.
nearest tenth means one number after the decimal pointnearest hundredth means two numbers after the decimal pointnearest thousandth means three numbers after the decimal point8.6134
nearest tenth = 8.6nearest hundredth = 8.61nearest thousandth = 8.6135.5218
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Kim has $10$ identical lamps and $3$ identical tables. How many ways are there for her to put all the lamps on the tables
There are 66 ways Kim can put the 10 identical lamps on the 3 identical tables
How to determine the number of ways?The given parameters are:
Identical lamps, n = 10Identical tables, r = 3The combination involving identical objects is calculated using:
(n + r - 1)C(r - 1)
So, we have:
n + r - 1 = 10 + 3 - 1
Evaluate the sum
n + r - 1 = 13 - 1
Evaluate the difference
n + r - 1 = 12
Also, we have:
r - 1 = 3 - 1
Evaluate the difference
r - 1 = 2
So, we have:
(n + r - 1)C(r - 1) = 12C2
Apply the following combination formula:
nCr = n!/((n - r)!r!)
So, we have:
12C2 = 12!/((12 - 2)! * 2!)
Evaluate the difference
12C2 = 12!/(10! * 2!)
Expand the numerator
12C2 = 12 * 11 * 10!/(10! * 2!)
Evaluate the quotient
12C2 = 12 * 11/2!
Expand the denominator
12C2 = 12 * 11/2 * 1
Evaluate the product
12C2 = 132/2
Evaluate the quotient
12C2 = 66
Hence, there are 66 ways Kim can put the 10 identical lamps on the 3 identical tables
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need some help with this
Answer:XDDXXDXD
DXDXXDXDDXDXDXDXXDDXDEDXXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-XDDXDXDXstep explanation:
seria tu cacá XDXDXDXDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Determine what type of model best fits the given situation: an internet phone company presently provides service to 5,000 customers at a monthly rate of $20 per month. after a market survey, it was determined that for each $1 decrease in the monthly rate an increase of 500 new customers would result.
The expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fit exists in the Linear model.
How to estimate the linear model?
Given: Monthly Rate = $20
Number of customers = 5000
If there exists a decrease of $1 in the monthly rate, the number of customers increases by 500.
Let us decrease the monthly rate by $1.
Monthly Rate = $20 - $1 = $19
Number of customers = 5000 + 500 = 5500
Let us decrease the monthly rate by $1 more.
Monthly Rate = $19 - $1 = $18
Number of customers = 5500 + 500 = 6000
Linear change in the number of customers whenever there exists a decrease in the monthly rate.
We have 2 pairs of values here,
x = 20, y = 5000
x = 19, y = 5500
The equation in slope-intercept form: y = mx + c
The slope of a function: [tex]$&m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\[/tex]
[tex]$&m=\frac{5500-5000}{19-20} \\[/tex]
[tex]$&\Rightarrow-500[/tex]
So, the equation is y = -500x + c
Putting x = 20, y = 5000:
[tex]$&5000=-500 \times 20+c \\[/tex]
[tex]$&\Rightarrow c=5000+10000=15000 \\[/tex]
[tex]$&\Rightarrow \mathbf{y}=-500 \mathbf{x}+15000[/tex]
Whether (18,6000) satisfies it.
Putting x = 18
[tex]$-500 \times 18+15000=-9000+15000=6000[/tex]
Therefore, the expression [tex]$-500 \times 18+15000=-9000+15000=6000[/tex] which best fits exist Linear model.
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Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?
Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.
What is a credit card?A credit card is a payment card that is issued to users (cardholders) to allow them to pay merchants for products and services based on the cardholder's incurred debt (i.e., promise to the card issuer to pay them for the amounts plus the other agreed charges). The card issuer (typically a bank or credit union) opens a revolving account and offers the cardholder a line of credit, from which the cardholder can borrow money to pay a merchant or for a cash advance.
The answer to why Lynn wants to wait would be:
The answer will be (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card. A and B don't make sense, because who cares about what happens to the store's money, and C can't be true because we don't know what kind of a person Lynn is. Most people don't forget to pay their bills.Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.
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The complete question is shown below:
Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?
a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.
b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.
c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.
d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.
Find the area of this triangle. Round to the nearest tenth.
The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
What is the area of the triangle?
Given the data in the diagram;
Angle B = 133°Side a = 7Side c = 13Side b = ?Angle C = ?First we find the dimension of side b.
From the rule of cosines.
b = √[ a² + c² - 2acCosB ]
We substitute into the formula.
b = √[ 7² + 13² - ( 2 × 7 × 13 × cos( 133° ) ]
b = √[ 49 + 169 - ( 182 × cos( 133° ) ) ]
b = √[ 218 - 182×cos( 133° ) ]
b = √[ 342.1237 ]
b = 18.5
Next, we find angle C.
From rule of cosines.
cosC = [ b² + a² - c² ] / 2ba
cosC = [ 18.5² + 7² - 13² ] / [ 2 × 18.5 × 7 ]
cosC = [ 342.25 + 49 - 169 ] / [ 259 ]
cosC = [ 222.25 ] / [ 259 ]
cosC = [ 0.8581 ]
C = cos⁻¹[ 0.8581 ]
C = 30.9°
Now, we can find the area of the triangle.
Area = [ ab × sinC ] / 2
Area = [ 7 × 18.5 × sin( 30.9 ) ] / 2
Area = [ 129.5 × 0.51354 ] / 2
Area = 66.5 / 2
Area = 33.3 in²
The area of the triangle rounded to the nearest tenth is 33.3 squared inches.
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Select the correct answer. the data manager for a state political party gathered data to determine how many citizens would support the party’s senate candidate. he polled citizens in 30 similarly sized senate districts and found a sample mean of 70,438 citizens. statewide data shows that the population standard deviation is 645.3. what is the approximate 90% confidence interval for this situation? a. 70,134 and 70,742 b. 70,207 and 70,669 c. 70,403 and 70,473 d. 70,244 and 70,632
Answer:
D. 70,244 and 70,632
Step-by-step explanation:
Got it right on PLATO/EDMENTUM
70,244 and 70,632 is the approximate 90% confidence interval for this situation.
A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
A confidence interval displays the probability that a parameter will fall between a pair of values around the mean.Confidence intervals measure the degree of uncertainty or certainty in a sampling method.They are most often constructed using confidence levels of 95% or 99%.Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. Confidence intervals are conducted using statistical methods.
Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample to see how it may represent the true value of the population variable. The resulting datasets are all different; some intervals include the true population parameter and others do not.
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Quadrilateral ABCD has vertices at A(0,0), B(0,3), C(5,3), and D(5,0). Find the vertices of the quadrilateral after a dilation with scale factor 2.5.
PLS ANSWER ASAP
The vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)
How to determine the vertices of the quadrilateral after a dilation with scale factor 2.5?The coordinates of the quadrilateral ABCD are given as:
A(0,0), B(0,3), C(5,3), and D(5,0)
When dilated by a scale factor of 2.5, we have the following equation
A' = A * 2.5
So, we have:
A' = (0,0) * 2.5
A' = (0, 0)
B' = (0,3) * 2.5
B' = (0, 7.5)
C' = (5,3) * 2.5
C' = (12.5, 7.5)
D' = (5,0) * 2.5
D' = (12.5, 0)
Hence, the vertices of the quadrilateral after a dilation with scale factor 2.5 are A' = (0, 0), B' = (0,7.5), C' = (12.5, 7.5) and D' = (12.5, 0)
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Use the drawing tools to form the correct answer on the graph.
Given the table of values, plot the corresponding points for the inverse of the function.
X
-1
0
1
2
f(x)
1
2
3
4
The inverse maps (x,y) onto (y,x).
If the probability of a new employee in a fast-food chain still being with the company at the end of the year is 0. 5, what is the probability that out of 8 newly hired people?
The probability that out of 8 newly hired people is 3.2.
According to the statement
we have given that the some conditions and based on these conditions we have to find the probability that out of 8 newly hired people.
So, For this purpose,
we have given that the
new employee in a fast-food chain still being with the company at the end of the year is 0.5
Now, we See that is probability of remaining with the company.
There is only one is 0.5.
According to the probability law
P + Q = 1
and this become
Q = 1 - 0.60.
And the probability of one people hired is Q.
Then
Q = 0.4
And probability that out of 8 newly hired people is
8Q = 0.4 * 8
it become 3.2.
So, The probability that out of 8 newly hired people is 3.2.
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Use the laplace transform to solve the given initial-value problem. y' − 2y = (t − 4), y(0) = 0
Using the Laplace transform, the value o y' − 2y = (t − 4), y(0) = 0 is⇒y(t) = 0 e^-t + u(t -1)e^1-t
Laplace rework is an critical rework approach that is in particular useful in fixing linear normal equations. It unearths very huge applications in regions of physics, electrical engineering, control optics, arithmetic and sign processing.
y' − 2y = (t − 4),
y(0) = 0
Taking the Laplace transformation of the differential equation
⇒sY(s) - y (0) + Y(s) = e-s
⇒(s + 1)Y(s) = (0+ e^-s)/s + 1
⇒y(t) = L^-1{0/s+1} + {e ^-s/s + 1}
⇒y(t) = 0 e^-t + u(t -1)e^1-t
The Laplace remodel method, the feature within the time area is transformed to a Laplace characteristic within the frequency domain. This Laplace feature will be inside the shape of an algebraic equation and it can be solved easily.
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HELP ASAP!!!! PLEASEEE!!!
Answer:
2
-2
Step-by-step explanation:
Use the second equation for x = -4.
f(-4) = 2
Use the third equation for x = 3.
f(x) = -x + 1 = -3 + 1 = -2
Give the equation for a circle with the given center and radius. center at (-1, 3), radius = 4
Answer:
(x + 1)² + (y - 3)² = 16
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (- 1, 3 ) and r = 4 , then
(x - (- 1) )² + (y - 3)² = 4² , that is
(x + 1)² + (y - 3)² = 16
Answer:
(x+1)^2 + (y-3)^2 = 16
Step-by-step explanation:
The standard form of an equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. Plugging in those values, we get (x-(-1))^2 + (y-3)^2= 4^2 = (x+1)^2 + (y-3)^2 = 16.
Identify tanX as a fraction and as a decimal rounded to the nearest hundredth.
The figure shows right triangle X Y Z with right angle Y. The length of leg Z Y is equal to 7 point 2 units. The length of leg Y X is equal to 6 point 4 units. The length of hypotenuse X Z is equal to 9 point 6 units.
The value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13
How to determine the tangent trigonometry ratio?The complete question is added as an attachment
From the question, the given parameters are as follows:
Hypotenuse = XZ
Hypotenuse XZ = 9.6
Leg ZY = 7.2
Leg YX = 6.4
The tangent of X is then calculated as:
tan(X) = ZY/YX
Substitute the known values in the above equation
tan(X) = 7.2/6.4
Evaluate the above quotient
tan(X) = 1.125
Approximate the above result
tan(X) = 1.13
Hence, the value of tan(X) in fraction is 7.2/6.4 and in decimal is 1.13
So, the complete parameters are:
Hypotenuse = XZ
Hypotenuse XZ = 9.6
Leg ZY = 7.2
Leg YX = 6.4
tan(X) = 7.2/6.4
tan(X) = 1.13
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Find the missing length indicated.
The value of the missing length in the image shown using the Pythagoras theorem is x = 65
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.
Let h represent the missing red line. Using Pythagoras:
x² = h² + 25²
h² = x² - 25²
Also:
r² = h² + 144²
r² = x² - 25² + 144²
And:
(144 + 25)² = r² + x²
(144 + 25)² = (x² - 25² + 144²) + x²
x = 65
The value of the missing length in the image shown using the Pythagoras theorem is x = 65
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