After each guess, your opponent has to tell you if your number is too high or too low. each guess is considered fifth attempt the last guess.
Let's dive deeper into the game and understand it from a mathematical perspective. You are given five chances to guess the number your opponent has written down. In each turn, you can guess a number, and your opponent will tell you if the number you guessed is too high or too low. This information is crucial because it helps you to narrow down the possibilities of what the actual number could be.
Now, let's consider the game in mathematical terms. Suppose the number your opponent has written down is called "X." Your goal is to guess X in five attempts. Let's call these attempts "A1, A2, A3, A4, and A5." After each attempt, your opponent will give you a clue that the number you guessed is either too high or too low. Based on this feedback, you can eliminate some possibilities of what the number X could be.
As you can see, with each guess, you are narrowing down the possibilities of what the number X could be. The game is all about using logical reasoning and deduction to guess the number X correctly in five attempts. If you guess the number correctly before your fifth attempt, you win the game.
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Jane moved from a house with 78 square feet of closet space to an apartment with 47.58 square feet of closet space. what is the percentage decrease of jane's closet space?
Jane's closet space decreased by approximately 38.97%.
To find the percentage decrease of Jane's closet space, we need to first calculate the amount of decrease and then express it as a percentage of the original value.
The amount of decrease is the difference between the original closet space and the new closet space:
Decrease = Original closet space - New closet space
Decrease = 78 - 47.58
Decrease = 30.42
So Jane's closet space decreased by 30.42 square feet.
To express this decrease as a percentage of the original value, we use the following formula:
Percentage decrease = (Decrease / Original value) x 100%
Substituting the values, we get:
Percentage decrease = (30.42 / 78) x 100%
Percentage decrease ≈ 38.97%
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On the same coordinate plane, mark all points (x,y) such that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2
The marked point under (x, y) are (-4,-6), (-3,-5), (-2,-4), (-1,-3), (0,-2), (1,-3), (2,-4), (3,-5) and (4,-6), under the condition that (A) y=x-2, (B) y=-x-2, (C) y=|x|-2.
Point A
where y=x-2.
This projects that for every x value, y will be 2 less than that x value. So if we place in x=0, we get y=-2. If we plug in x=1, we get y=-1 and so on. So we could plot these points on the coordinate plane as (0,-2), (1,-1), (2,0), (3,1) .
Then, similarly point B
where y=-x-2.
This projects that for every x value, y should be 2 less than the negative of that x value. So if we place in x=0, we get y=-2. If we place in x=1, we get y=-3 and .
Then, we can place these points on the coordinate plane as (0,-2), (1,-3), (-1,-1), (2,-4) .
Finally let's proceed on to point C where y=|x|-2. This projects that for every positive x value, y will be 2 less than that x value and for every negative x value, y will be 2 less than the negative of that x value. So if we plug in x=0, we get y=-2. If we plug in x=1, we get y=-1 and so on.
So we can place these points on the coordinate plane as (0,-2), (1,-1), (-1,-1), (2,0), (-2,0) and so on.
So all the evaluated points are (-4,-6), (-3,-5), (-2,-4), (-1,-3), (0,-2), (1,-3), (2,-4), (3,-5) and (4,-6).
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Determine the length of the leg of 45* -45*-90* triangle with a hypotenuse length of 26
The length of leg of given triangle is s 13√(2) units.
A 45-45-90 triangle is a special right triangle in which the two legs are congruent and the angles opposite the legs are both 45 degrees. The hypotenuse is the longest side of the triangle and is located opposite the right angle.
In this problem, we are given that the hypotenuse length of a 45-45-90 triangle is 26 units. Our goal is to find the length of one of the legs of the triangle. Let us denote the length of one of the legs as x.
By the Pythagorean theorem, we know that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In a 45-45-90 triangle, the two legs are congruent, so we can set up the following equation:
x² + x² = 26²
Simplifying the left-hand side of the equation, we get:
2x² = 676
Dividing both sides by 2, we get:
x² = 338
Taking the square root of both sides, we get:
x = √(338)
Since we are asked to give the answer in simplified radical form, we can write:
x = √(2 × 169) = √(2) × √(169) = 13√(2)
Therefore, the length of one of the legs of the 45-45-90 triangle with a hypotenuse length of 26 units is 13√(2) units.
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use the confidence level and sample data to find a confidence interval for estimating the population μ. round your answer to one decimal place.
a group of 64 randomly selected students have a mean score of 38.6 with a standard deviation of 4.9 on a placement test. what is the 90% confidence interval for the mean score, μ, of all students taking the test?
The 90% confidence interval for the mean score, μ, of all students taking the test is (37.6, 39.6).
To find the confidence interval for estimating the population mean score, we can use the following formula:
CI = x ± z*(σ/√n)
Where:
x = sample mean score = 38.6
σ = population standard deviation (unknown)
n = sample size = 64
z = z-score for the desired confidence level, which is 1.645 for 90% confidence interval
First, we need to estimate the population standard deviation using the sample standard deviation:
s = 4.9
Next, we can plug in the values into the formula:
CI = 38.6 ± 1.645*(4.9/√64)
= 38.6 ± 1.645*(0.6125)
= 38.6 ± 1.008
= (37.6, 39.6)
Therefore, the 90% confidence interval for the mean score, μ, of all students taking the test is (37.6, 39.6).
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Anita plans to take $2600 loan for one year at an annual interest rate of 14% compounded monthly. She plans to pay off the loan in one payment at the end of the year. Multiplying 2600 by 0. 14, she determines she will pay $364 in interest on the loan. Describe the error and calculate how much interest she will pay
The actual interest paid by Anita is $2949.44 - $2600 = $349.44 (rounded to the nearest cent).
In this case, we have:
P = $2600
r = 0.14 (14%)
n = 12 (compounded monthly)
t = 1 (one year)
Plugging in the values, we get:
A = $2600(1 + 0.14/12)^(12*1)
= $2600(1.0116667)^12
= $2949.44
Interest refers to the amount of money charged by a lender to a borrower for the use of borrowed funds. It is typically expressed as a percentage of the amount borrowed and is usually charged over a specified period of time, such as a month or a year.
Interest can be either simple or compound. Simple interest is calculated only on the principal amount borrowed, while compound interest is calculated on the principal amount as well as any accumulated interest. This means that with compound interest, the borrower ends up paying more in interest over time. Interest rates can vary depending on a range of factors, such as the borrower's credit score, the length of the loan, and prevailing market conditions. In general, higher-risk borrowers are charged higher interest rates, while lower-risk borrowers are charged lower rates.
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U = {all triangles}
E = {x|x ∈ U and x is equilateral}
I = {x|x ∈ U and x is isosceles}
S = {x|x ∈ U and x is scalene}
A = {x|x ∈ U and x is acute}
O = {x|x ∈ U and x is obtuse}
R = {x|x ∈ U and x is right}
Which is a subset of I?
E
S
A
R
The set R is not a subset of I. the only subset of I from the given options is A
How we find the subset of I?The set I represents all isosceles triangles.
The set E represents all equilateral triangles, and an equilateral triangle is a special case of an isosceles triangle where all sides are equal. Therefore, the set E is a subset of I.
The set S represents all scalene triangles, and a scalene triangle is not isosceles since it does not have any equal sides. Therefore, the set S is not a subset of I.
The set A represents all acute triangles, and an acute isosceles triangle is a triangle where all angles are less than 90 degrees and two sides are equal in length. Therefore, the set A is a subset of I.
The set O represents all obtuse triangles, and an obtuse isosceles triangle is a triangle where one angle is greater than 90 degrees and two sides are equal in length. Therefore, the set O is not a subset of I.
The set R represents all right triangles, and a right isosceles triangle is a triangle where one angle is equal to 90 degrees and two sides are equal in length. the only subset of I from the given options is A.
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Use substitution to find the indefinite integral. szve ? 2 zV9z+ - 5 dz [21922-5 Zy9z 9z- 5 dz = =]
To solve this problem, we can use substitution. Let u = 9z - 5, then du/dz = 9 and dz = du/9.
Using this substitution, we can rewrite the integral as:
∫(2/(u+5))(1/9)du
Simplifying this expression:
(2/9) ∫(1/(u+5))du
We can then solve this integral by using the formula for the natural logarithm:
(2/9) ln|u+5| + C
Substituting back in for u:
(2/9) ln|9z| + C
2 zV9z+ - 5 dz is (2/9) ln|9z| + C.
Consider the integral:
∫2z√(9z² - 5) dz
We can use the substitution method. Let's choose the substitution:
u = 9z² - 5
Now, differentiate u with respect to z:
du/dz = 18z
Solve for dz:
dz = du/(18z)
Now, substitute u and dz back into the integral and simplify:
∫(2z√u) * (du/(18z)) = (1/9)∫√u du
Now, integrate with respect to u:
(1/9)(2/3)(u^(3/2))/(3/2) + C = (2/27)u^(3/2) + C
Finally, substitute back the original expression for u:
(2/27)(9z² - 5)^(3/2) + C
So, the indefinite integral is:
(2/27)(9z² - 5)^(3/2) + C
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(a) Find an equation of the tangent plane to the surface at the given point. z = x2 - y2, (5, 4, 9) X-5 (b) Find a set of symmetric equations for the normal line to the surface at the given point. Х y z 10 -8 -1 y - 4 Z - 9 10 -8 -1 Ox - 5 = y - 4 = Z - 9 X + 5 y + 4 Z +9 10 -8 -1 Ox + 5 = y + 4 = 2 + 9 =
z - 9 = 10(x - 5) - 8(y - 4) this is the equation of the tangent plane at the point (5, 4, 9). (x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1). These are the symmetric equations for the normal line to the surface at the given point.
(a) To find the equation of the tangent plane to the surface z = x^2 - y^2 at the point (5, 4, 9), we first need to find the partial derivatives with respect to x and y:
∂z/∂x = 2x
∂z/∂y = -2y
Now, we evaluate these at the given points (5, 4, 9):
∂z/∂x(5, 4) = 2(5) = 10
∂z/∂y(5, 4) = -2(4) = -8
Using the tangent plane equation:
z - z₀ = ∂z/∂x (x - x₀) + ∂z/∂y (y - y₀)
Plugging in the values:
z - 9 = 10(x - 5) - 8(y - 4)
This is the equation of the tangent plane at the point (5, 4, 9).
(b) The normal vector to the surface at the given point is given by the gradient vector (∂z/∂x, ∂z/∂y, -1) = (10, -8, -1). To find the symmetric equations for the normal line, we use the point-normal form:
(x - x₀)/a = (y - y₀)/b = (z - z₀)/c
Plugging in the point (5, 4, 9) and the normal vector components (10, -8, -1):
(x - 5)/10 = (y - 4)/(-8) = (z - 9)/(-1)
These are the symmetric equations for the normal line to the surface at the given point.
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CAN SOMEONE HELP ME PLEASEEEEEEEEEEEEEE I NEED HELP :(
Answer:
for the first three, divide the number by 2
for the second three, multiply by 2
9 and 11. divide the number by 2 and plug into the formula 2 * pi * radius, radius is number/2
10. plug 7 into formula 2 * pi * radius, radius = 7
Step-by-step explanation:
radius is half the length of the circle, diameter is the full length, circumference is 2 * pi * radius
PLEASEEEEEEEEEEEEEEE HEEEEEEEEEEEELP
If a force of 1500 N is applied on a cart with a mass of 500 Kg, calculate the
acceleration of the cart
Answer:
3 m/s²
Step-by-step explanation:
We can use Newton's Second Law of Motion. The Second Law of Motion states that acceleration is calculated by dividing the force by the mass.
[tex]A=\frac{F}{m}[/tex] with f being the force and m being the mass
We know that the force is 1,500 N and the mass is 500 kg.
So, let's substitute:
[tex]A=\frac{1500}{500}\\A=3[/tex]
So the acceleration of the cart is 3 m/s²
Hope this helps :)
An environmentalist is studying a certain microorganism in a sample of city lake water. The function h(x) = 146(1.16)ˣ gives the number of the microorganisms present in the water sample at the end of x weeks. Which statement is the best interpretation of one of the values of the function?
F. After 1 week, there will be 146 microorganisms in the water sample.
G. The initial number of microorganisms in the water sample was 16.
H. The number of microorganisms decreases by 84% each week.
J. The number of microorganisms increases by 16% each week.
The best interpretation of one of the values of the function is The number of microorganisms increases by 16% each week.
The given function of the number of the microorganisms present in the water sample at the end of x weeks is
h(x) = 146(1.16)ˣ
To find the number of microorganisms present in the water sample after one week, we substitute x = 1 in the above equation
h(1) = 146(1.16)¹
h(1) = 169.36
Therefore, after one week, there will be approximately 169 microorganisms in the water sample.
Thus, the correct interpretation of one of the values of the function is F.
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solve for b
18, b, 27, 22
(round your answer to the nearest tenth
b=[?]
The length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
Using the sine rule;
18/sin22° = b/sin27°
b = (18 × sin27°)/sin22° {cross multiplication}
b = 21.8144
Therefore, the length of side b for the triangle is equal to 21.8 to the nearest tenth using the sine rule.
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Find the area of the shaded sector.
round to the nearest tenth.
167°
17.8 yd
area = [ ? ]yd?
The area of the shaded sector is 461.7 [tex]yd ^ {2}[/tex]
The shaded region in the given question is a sector. So, we will calculate the area of the sector. The area of a sector is nothing but a fraction of the area of the whole circle. So, we will use the given formula to find the area of a sector of the circle.
area of sector = [tex]\frac{angle of sector}{360} * \pi r^{2}[/tex]
We know that the angle of the sector is 167 degrees and the radius of the circle is given to be 17.8 yd. We will substitute these values in the formula to calculate the area.
area of sector = [tex]\frac{167}{360} * \pi * (17.8)^{2}[/tex]
area of sector = 461.7 [tex]yd^{2}[/tex]
Therefore the area of the shaded region to the nearest tenth is 461.7 square yards.
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The complete question is "Find the area of the shaded sector.
round to the nearest tenth.
167°
17.8 yd
area = [ ? ]yd?
The image is shown below."
Several scientists decided to travel to South America each year beginning in 2001 and record the number of insect species they encountered on each trip. The table shows the values coding 2001 as 1, 2002 as 2, and so on. Find the model that best fits the data and identify its corresponding R2 value. 1 2 3 Year 4 5 6 7 9 8 10 53 38 49 35 42 Species 47 60 67 82
The result of the regression analysis will provide you with the best-fitting model and its R² value.
To find the model that best fits the data, we will perform a regression analysis using the given data. The dependent variable is the number of insect species, and the independent variable is the year coded as 1, 2, 3, and so on. The table can be rewritten as:
Year (X): 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
Species (Y): 53, 38, 49, 35, 42, 47, 60, 67, 82
A linear regression can be performed to determine the model that best fits the data. After analyzing the data, we will identify the corresponding R² value, which represents the proportion of the variance in the dependent variable (insect species) that is predictable from the independent variable (year).
The result of the regression analysis will provide you with the best-fitting model and its R² value. Keep in mind that higher R² values (closer to 1) indicate a better fit of the model to the data.
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Complete the interest table below.
The second-period interest is approximately $13.61, and the second-period amount is approximately $927.11.
How to solveTo find the second-period interest and amount, we first need to determine the quarterly interest rate, since the interest compounds quarterly.
Quarterly interest rate =[tex](1 + Annual interest rate)^(1/4) - 1[/tex]
= [tex](1 + 0.06)^(1/4) - 1[/tex]
≈ 0.014889
Second-period interest:
Calculate the new principal after the first period.
Principal_after_1st_period = Principal + First period interest
= $900 + $13.50
= $913.50
Calculate the second-period interest.
Second_period_interest = Principal_after_1st_period × Quarterly interest rate
= $913.50 × 0.014889
≈ $13.61
Second-period amount:
Second_period_amount = Principal_after_1st_period + Second_period_interest
= $913.50 + $13.61
≈ $927.11
The second-period interest is approximately $13.61, and the second-period amount is approximately $927.11.
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What needs to be corrected in the following construction for copying ABC with point D as the vertex?
-The second arc should be drawn centered at K through A.
-The second arc should be drawn centered at J through A.
-The third arc should cross the second arc.
-The third arc should pass through D.
Answer:
(c) The third arc should cross the second arc.
Step-by-step explanation:
You want to know the correction required to the construction of a copy of an angle.
Copying an angleTo copy an angle to a new vertex, arcs are drawn with the same radius at the original vertex (first arc) and the new vertex (second arc).
Then the compass is set to the length JK, and a third arc is drawn with L as the center, marking off the distance JK on the second arc.
In order do that, the third arc should cross the second arc.
__
Additional comment
This allows you to create ∆DLM congruent to ∆BKJ. Hence angle D will be congruent to angle B.
It helps to actually do these constructions on paper using compass and straightedge. That gives you better intuition about how they work, and about geometric relations in general.
Answer:
Step-by-step explanation:
A particle, initially at rest, moves along the x-axis such that the acceleration at time t > 0 is given by a(t)= —sin(t) . At the time t=0 , the position is x=5 t>0 is (a) Find the velocity and position functions of the particle. b) For what values of time t is the particle at rest?
(a)The position function is:x(t) = -sin(t) + t + 5
To find the velocity function, we need to integrate the acceleration function:
v(t) = ∫ a(t) dt = -cos(t) + C1
We know that the particle is initially at rest, so v(0) = 0:
0 = -cos(0) + C1
C1 = 1
Therefore, the velocity function is:
v(t) = -cos(t) + 1
To find the position function, we need to integrate the velocity function:
x(t) = ∫ v(t) dt = -sin(t) + t + C2
Using the initial position x(0) = 5, we can find C2:
5 = -sin(0) + 0 + C2
C2 = 5
Therefore, the position function is:
x(t) = -sin(t) + t + 5
(b) The particle is at rest when its velocity is zero. So we need to solve for t when v(t) = 0:
0 = -cos(t) + 1
cos(t) = 1
t = 2πn, where n is an integer.
Therefore, the particle is at rest at times t = 2πn, where n is an integer.
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help I am not sure of the answer it asks for the domain and the range thank you
Answer:
480 - 96x = 0, so x = 5.
Domain: [0, 5]
Range: [0, 480]
given a standard deck of cards, what is the probability of choosing a diamond, then a heart, then a black card if no replacement is made
Answer:The probability of both is 1/4*13/51.
Step-by-step explanation:
There are 52 cards in the deck, 13 hearts and 13 spades. The probability of getting a heart is 13/52 or 1/4. Given an initial heart there are 51 cards remaining; the probability of a spade is now 13/51
please help, I don't understand how to solve these Geometry questions.
The segment lengths are given as follows:
6. AB = 15.
7. RS = 47.
How to obtain the length of segment TU?The length of segment TU is obtained applying the trapezoid midsegment theorem, which states that the length of the midsegment of the trapezoid is equals to the mean of the length of the bases of the trapezoid.
For item 6, we have that the mean of AB = x and 29 is of 22, hence:
(x + 29)/2 = 22
x + 29 = 44
x = AB = 15.
The value of x in item 7 is obtained as follows:
3x + 5 = (2x + 15 + 6x - 37)/2
8x - 22 = 6x + 10
2x = 32
x = 16.
Hence the length of RS is given as follows:
RS = 2 x 16 + 15
RS = 47.
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Do couples get engaged or not? If they are engaged, how long did they date before becoming engaged? A poll of 1000 couples conducted by Bruskin and Goldring Research for Korbel Champagne Cellars gave Time Never Engaged Number of Couples 200 the following information: Time Number of Couples Never Engaged 200 Less than 1 year 240 1 to 2 years 210 More than 2 years 350 What is the sample space in this problem?
The sample space in this problem is the total number of couples surveyed, which is 1000.
The sample space in probability refers to the set of all possible outcomes of an experiment. In this case, the experiment is the survey conducted by Bruskin and Goldring Research, and the possible outcomes are the different categories of time taken by couples before getting engaged.
The given information provides the number of couples in each category, which can be added to find the total number of couples surveyed:
Sample space = Number of couples never engaged + Number of couples engaged for less than 1 year + Number of couples engaged for 1 to 2 years + Number of couples engaged for more than 2 years
Sample space = 200 + 240 + 210 + 350
Sample space = 1000
Therefore, the sample space in this problem is 1000, which represents the total number of couples surveyed by the research firm.
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There's a roughly linear relationship between the length of someone's femur (the long leg-bone in your thigh) and their expected height. Within a certain population, this relationship can be expressed using the formula h=62. 6+2. 35fh=62. 6+2. 35f, where hh represents the expected height in centimeters and ff represents the length of the femur in centimeters. What is the meaning of the hh-value when f=49f=49?
For an individual with a femur length of 49 centimeters, we can expect their height to be approximately 177.15 centimeters.
When f=49, plugging it into the formula h=62.6+2.35f, we get h=62.6+2.35(49)=177.15.
This means that for an individual with a femur length of 49 centimeters, we would expect their height to be approximately 177.15 centimeters.
This provides an estimate of the individual's height based on the relationship between femur length and height indicated by the formula. It's important to note that this is an estimate and individual variation may exist.
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Peter had to solve a puzzle.which mathematical symbol can be placed between 5 and 9, to get a numbergreater than 5, but less than 9?
To get a number greater than 5,but less than 0, Peter can use the mathematical symbol of a decimal point (.) to solve this puzzle.
If Peter places decimal point between 5 and 9, he can get a number like 5.1, 5.2, 5.3... up to 8.9, which meets the conditions of being greater than 5 but less than 9.
A decimal point (.) is a mathematical symbol. When this decimal point is placed in between two numbers, suppose x and y, then x.y means x.y is greater than x and less than y.
So to solve the puzzle, Peter can use decimal point.
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You get a part time job earning $12.50/hr. Tips are $4.60/hr average. Deductions are FICA (7.65%) and Federal Tax Withholding (10%). You work for 18 hours. What is your gross base pay?
If you are earning $12.50/hr in a part-time job, then your gross "base-pay" after deductions is $253.48.
Your base pay is $12.50/hr and you worked for 18 hours, so the base pay would be:
⇒ $12.50/hr × 18 hrs = $225;
The tips are $4.60/hr on average, so the "total-tips" earned would be:
⇒ $4.60/hr × 18 hrs = $82.80;
To calculate the "total-deductions", we first find the total percentage deducted, which is the sum of FICA and Federal Tax Withholding:
⇒ 7.65% + 10% = 17.65%,
To find the total amount deducted, we multiply the total percentage deducted by the "base-pay" + "tips";
⇒ 17.65% x ($225 + $82.80) = $54.32,
So the pay, before any deductions, is the sum of "base-pay" and "tips";
⇒ $225 + $82.80 = $307.80;
To find the "net-pay", we subtract "total-deductions" from pay;
We have,
⇒ $307.80 - $54.82 = $253.48,
Therefore, your gross base pay is $253.48.
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Answer:
add the tips and pay together , this equals 17.10
then multiply by the 18 hours and you’ll get 307.80
Step-by-step explanation:
A new plane can travel 1200000 m in 120 minutes. Find its speed in km/h.
Answer:
Step-by-step explanation:
We can start by converting the distance and time to the appropriate units.
1200000 meters = 1200 kilometers (since 1 kilometer = 1000 meters)
120 minutes = 2 hours (since 1 hour = 60 minutes)
Now we can use the formula:
speed = distance / time
speed = 1200 km / 2 hours
speed = 600 km/h
Therefore, the speed of the new plane is 600 km/h.
Answer: 600km/
First step:
1200000m=1200Km * 1m=0,001km
Second step:
120min=2h *1h=60min
Last step:
1200km÷2h= 600km/
SOLUTION
600km/
Step-by-step explanation:
A 40 -degree angle is translated 5 inches along a vector. What is the angle measurement, in degrees, of the image?
The angle measurement would remain as 40 degrees
Does angle change when translated?No, when a geometric figure, such as a line or an angle, is translated (moved) to a new position without being rotated, reflected, or scaled, its shape and size do not change, and therefore its angle measure remains the same.
This property is a fundamental concept in geometry and is known as the "invariance of angle measure under translation". It means that if two angles are congruent (have the same measure) in their original position, they will remain congruent after being translated to a new position.
Hence The angle measurement would remain as 40 degrees
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Samuel buys 3 bottles of juice that each have an original price of $2.80. He uses a coupon for 35% off. How much does Samuel pay for 3 bottles of juice? Show your work.
________________________________
= $2.80 × 3 Bottles= $8.04= 35% × $8.04= $2.94= $8.04 - $2.94= $5.46Samuel Pays $5.46 For The 3 Bottles of Juice.________________________________
two players simultaneously toss (independently) a coin each. both coins have a chance of heads p. they keep on performing simultaneous tosses till they end up with different. what is the expected number of trials (simultaneous tosses) before they stop?
The expected number of tosses until two players get different results when simultaneously tossing a coin each with a chance of heads p is (1-2p)/(2p-2p²).
The probability that both players get the same result (either both heads or both tails) on any given toss is p² + (1-p)² = 2p² - 2p + 1. The probability that they get different results (one head and one tail) is therefore 1 - (2p² - 2p + 1) = 2p - 2p².
Let E be the expected number of tosses until they end up with different results. If they get different results on the first toss, the game ends after 1 toss.
Otherwise, they have to repeat the process again, and the expected number of tosses is increased by 1. Therefore, we can express E in terms of the probabilities of getting different or same results on the first toss
E = (2p - 2p²)1 + (1 - 2p + 2p²)(1 + E)
Simplifying, we get
E = 1 + 2pE - 2p + 2p²
Rearranging and solving for E, we get
E = (1 - 2p) / (2p - 2p²)
Therefore, the expected number of tosses before the players end up with different results is (1 - 2p) / (2p - 2p²).
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Jesus works at a computer outlet. He receives a bi-weekly salary of
$300 plus 5. 5% commission on his sales. In the last two weeks, he sold
$16,200 of computer equipment. He pays 8% for State Income Tax,
12. 3% for Federal Income Tax, 6. 3% for Social Security, and 1. 45%
for Medicare. What steps did I take to find Jesus' net bi-weekly
pay? (Show your work)
Jesus' net bi-weekly pay is $856.69 after paying his taxes and deductions.
To find Jesus' net bi-weekly pay, I followed these steps:
Calculate Jesus' commission: Jesus sold $16,200 of computer equipment, so his commission is 5.5% of $16,200, which is $891.
Calculate Jesus' gross bi-weekly pay: Jesus receives a bi-weekly salary of $300 plus his commission of $891, so his gross bi-weekly pay is $1,191.
Calculate Jesus' deductions: Jesus pays 8% for State Income Tax, 12.3% for Federal Income Tax, 6.3% for Social Security, and 1.45% for Medicare. To calculate the deductions, I multiplied his gross bi-weekly pay by each percentage rate:
State Income Tax: 8% of $1,191 = $95.28
Federal Income Tax: 12.3% of $1,191 = $146.67
Social Security: 6.3% of $1,191 = $75.09
Medicare: 1.45% of $1,191 = $17.27
Subtract the deductions from the gross bi-weekly pay: To find Jesus' net bi-weekly pay, I subtracted the total deductions of $334.31 from his gross bi-weekly pay of $1,191:
Net bi-weekly pay = $1,191 - $334.31 = $856.69
Therefore, Jesus' net bi-weekly pay is $856.69 after paying his taxes and deductions.
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Under her cell phone plan Yaritza pays a flat cost of $41 and 50 Cent per month and five dollars per gigabyte she wants to keep her bill under $60 per month which inequality can be used to determine ask the minimum number of gigabytes Yahritza can use while staying within her budget
Answer:3 gigabytes of storage.
Step-by-step explanation: Because you start at $41.50 and add 5 is $46.60 and then add 5 again and you get $51.50 then add 5 more you get $56.50.
