Answer:
{2;-1;1}.
Step-by-step explanation:
it is possible to make up the system of three equations:
a) g(0)=1: c=1;
b) g(1)=2: a+b+c=2;
c) g(-1)=4: a-b+c=4;
2) the system has the only solution:
[tex]\left[\begin{array}{ccc}c=1\\a+b+c=2\\a-b+c=4\end{array} \ = > \ \left[\begin{array}{ccc}a= 2\\b=-1\\c=1\end{array}[/tex]
4) finally, a=2; b=-1 and c=1.
Beth currently brings in an annual salary of $37,000 and anticipates a raise of 5% every year. What will her salary be in 14 years? If necessary, round your answer to the nearest cent.
Beth salary in 14 years would be $62900.
What is the simple interest?Simple interest is the borrowing amount added only to the principal amount.
Given, Beth currently brings in an annual salary of $37,000 and anticipates a raise of 5% every year.
To find the interest rate:
The formula to calculate the simple interest is;
S.I. = P x T x R / 100 ,
Where S.I. is simple interest , P is principal amount, T is time period and R is interest rate in a year.
And according to the question,
P = 37000, T = 14 years and R = 5%
Substituting all the values to the formula,
S.I. = P x T x R / 100
S.I. = 37000 x 14 x 5 / 100
= 25900
Beth final salary = principal amount + interest rate
= 37000 + 25900
= 62900
Therefore, Beth salary after 14 years is $62900.
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3/5 of the students in Süd- class are in chorus. If there are 25 people in her class, how many are in the chorus?
Use the formula, I = PRT, to find the time if | = $387.50, P = $1,550, and R = 12.5%
Answer:
T = 2
Step-by-step explanation:
Take the given formulaer
I = PRT
And plug in the variables you know (I, P, R)
387.50 = 1,550(.125)T
(12.5% becomes .125 after you divide it by 100, because precents are really just fractions out of 100)
387.50 = 193.75T
T = 2
Round to the nearest thousandth, then subtract: 2.87349 1.54324
Answer:
1.33
Step-by-step explanation:
2.87349 rounded to the nearest thousandth is 2.873 because the number next to it (4) is less than 5.
1.54324 rounded to the nearest thousandth is 1.54324 is 1.543 because the number next to it (2) is less than 5.
Then you do 2.873 - 1.543 and that = 1.33. So 1.33 is your final answer :)
If it takes 3.6 minutes to fill a 3000ml container, how long will it take to fill a 1.5L container?
Answer:
1.8 min
Step-by-step explanation:
This question is easier to answer than it would be in general.
3000 mL = 3 L
1.5L is exactly half of that, so the time to fill the 1.5L container is half the time it takes to fill the 3L container.
Half of 3.6 minutes is 1.8 minutes
O is the center of the regular octagon below. Find its area. Round to the nearest tenth
if necessary.
Based on characteristics of regular polygons, the area of the regular octagon with an apothema of 17 units is approximately 239.415 square units. #SPJ1
How to find the area of a regular polygon
A polygon is regular when all sides and central angles have the same length.The area of a regular polygon (A) can be found in terms of the number of sides (n) and the apothema (a), whose length is 17, by using the following formula:
A = 0.25 · n · a² · tan (180/n) (1)
If we know that n = 8 and a = 17, then the area of the regular octagon is:
A ≈ 239.415
Based on characteristics of regular polygons, the area of the regular octagon with an apothema of 17 units is approximately 239.415 square units. #SPJ1
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What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
in²
The figure contains a triangle. One side is 13 inches. A second side is 7.5 inches. The angle between the given sides is 94 degrees.
Answer:
Area = 48.6 in²
Explanation:
The area of the triangle can be calculated using the side-angle-side method as follows:
Area = 0.5 * first side * second side * sin(angle included between the two sides)
This rule is illustrated in the attached image.
Now, we have:
first side = 13 in
second side = 7.5 in
The angle included between the two sides = 94 degrees
The given angle is included between the two given sides, therefore, we can apply the above rule to get the area.
Area of triangle = 0.5 * 13 * 7.5 * sin(94)
Area of triangle = 48.63 which is approximately 48.6 in²
Hope this helps :)
Describe a data set that has the same mean, median, and mode.
I not really understanding this question could somebody help
Answer: Okay, so you probably already know this but,
The mean - is the same as the average value of a data set and is found using a calculation. Add up all of the numbers and divide by the number of numbers in the data set.
Add up all of the numbers and divide by the number of numbers in the data set. The median is the central number of a data set. Arrange data points from smallest to largest and locate the central number.
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
Step-by-step explanation:
In a perfectly symmetrical distribution, the mean and the median are the same. This example has one mode (unimodal), and the mode is the same as the mean and median. In a symmetrical distribution that has two modes (bimodal), the two modes would be different from the mean and median.
hope this helps you!!
Answer:
One of the many examples is {0, 0, 0, 0, 0}
Step-by-step explanation:
The mean is the average of a data set.
The median is the number in the middle (or between the 2 middle numbers) of a data set that is placed from least to greatest.
The mode is the value that shows up the most times in the data set.
A few examples of a set with the same mean, median, and mode could be any number repeated in a data set:
{0, 0, 0, 0, 0}
This would work because the mean is 0, the median is 0, and the mode is 0.
The winners of a carnival game draw a ticket from a box to determine their prize. Each winner draws a ticket and places it back into the box before the next draw. Every winner has a 33% chance of getting cotton candy, a 46% chance of getting a shirt, and a 21% chance of getting a key chain.
The game operator wants to simulate what could happen for the next ten winners. So for each winner he generates a random whole number from 1 to 100. The range of values that the game operator can use to represent a winner is 1 to 3. What is the percentage of winners who got a shirt
Answer:
He generates a random whole number from 1 to 3.
Step-by-step explanation:
Each winner has 3 possibilities, gets cotton candy, gets a shirt, or gets a keychain. We can asign each of this possibiltiies a number, 1 for cotton candy, 2 for the shirt and 3 for a keychain. So, for a simulation, its enough to take one of this whole numbers for each winner.
Thomas works 12 days out of every month.
1. Does Thomas work the same percent of days each month? Explain.
Answer:
no (see below)
Step-by-step explanation:
Not all of the months have the same amount of days therefore Thomas does not work the same percentage of days each month.
How do you find total pension expense?
Answer:
Total periodic pension costs (TPPC) is equal to the contributions plus change in the pension liability during the year. Each period, the periodic pension cost is recognized in profit or loss (P&L) and/or in other comprehensive income (OCI).
Classify each number as rational or irrational. 3.31662479...
Answer:
3.31662479... is irrational
Step-by-step explanation:
The number 3.31662479... is written in a decimal form:
It is a nonterminating decimal (look at the three dots at the end)
and a nonrepeating decimal (no repeating pattern)
So it is irrational.
Answer:
IrrationalStep-by-step explanation:
The given number is :
3.31662479...The three dots at the end of the number indicates that it is non-terminating
Also you see that the digits do not repeat, hence it is also non-repeating
Definition of An Irrational Number
⇒ The decimal expansion of an irrational number is neither terminating nor recurring.
As it satisfies the criteria, the given number is irrational
What is the area of a circle with a diameter of 32?
Answer:
How much is 32 cm in diameter?
Centimeters to Inches table
centimeters inches
32cm 12.60
33cm 12.99
34cm 13.39
35cm 13.78
Step-by-step explanation:
Answer:
A
≈
804.25
I am sure just trust me ;)
In the accompanying diagram, angle ACD is an exterior angle of triangle ABC, angle A =3x, angle ACD is =5x, and angle B=50. What is the value of x ?
The value of x in the triangle ABC is 25.
How to find angles in a triangle?The interior angles of the triangle are given as m∠A = 3x and m∠B = 50°.
The exterior angle of the triangle is given as m∠ACD = 5x.
The sum of angle in a triangle is equals to 180 degrees. Therefore,
3x + 50 + (180 - 5x) = 180
3x + 50 - 5x + 180 = 180
3x - 5x + 50 + 180 = 180
-2x + 230 = 180
subtract 230 from both sides
-2x + 230 - 230 = 180 - 230
-2x = -50
divide both sidesby -2
-2x / -2 = -50 / -2
x = 25
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The red square is the image of the blue square after a SINGLE transformation. Use two or more complete sentences to describe each of the FOUR different transformations that could produce the image.
The transformations which can lead to the red square image of the blue Square are; Translation, Reflection, Rotation.
What transformations lead to the image?Translation is when we slide a figure in any direction. The translation of the shape can be by moving the blue leftward or rightward and the then downward.Reflection is when we flip a figure over a line. The reflection involves reflect the blue Square over the line; y = x.Rotation is when we rotate a figure a certain degree around a point. The rotation is by rotating the blue Square over 180⁰.Read more on transformations;
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Is 3,978×-32 positive or negative
Answer:
negative
Step-by-step explanation:
A positive times a negative is a negative
Which of the following represents a set of irrational numbers?
A: {√3, √16, √21, √25}
B: {3.1, 1.234..., √36, π}
C: {12π/4, √2/4, 1.121214…, √5 }
D {23.1, 1.234, √36, 4π }
Answer:
C
Step-by-step explanation:
[tex]\text{All other options contain rational numbers, such as} ~\sqrt{36} , \sqrt{25}, \sqrt{16}[/tex]
A teacher writes the name of each of her 25 students on a slip of paper and places the papers in a box. To call on a student,
she draws a slip of paper form the box. Each paper is equally likely to be drawn, and the papers are replaced in the box
after each draw.
What is the probability of calling on the same student twice in a row?
a. 0.0016
c.
0.56
b. 0.36
d.
0.04
Please select the best answer from the choices provided
the answer would be 0.56
Answer:
a: 0.0016
Step-by-step explanation:
Got it right on the test.
Hope this helps :)
This figure represents a platform on a stage. The stage crew needs to paint it black. One gallon of paint will cover 40 square yards.
How many full gallons of paint does the crew need to buy in order to paint the entire platform?
Enter your answer in the box.
gallons
Answer:
it is 4 or 3 i think 4 more tho
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
Handsome Jack is buying a pony made of Diamonds
Answer:
so what should we do?!?!?!?!¡!?!
fx) = X. What is g(x)?
f(x) = x
g(x)?
PLEASE HELP ASAP!!!!
Answer:
C
Step-by-step explanation:
vertex form:
[tex]y = {a(x - h)}^{2} + k[/tex]
the negative sign in front of x^2 is also -1, which is the "a". A controls if the parabola will opek up or down, and the width of the function. In this problem, the parabola opens down. the -3 corresponds to "k" in vertex form. K is the vertical shift or the y coordinate of the vertex. If k is positive it moves up, and if it is negative it moves down. Because of the -3, the vertex of the parabola will move down 3 units on the y-axis.
Which of the following gives an example of
an exponential function?
a. y = 3x^2
b. y = x^-5
c. y = 1.5^x
D. = x^2 - x
how to find the missing angle when given two sides of a right triangle?
Answer:
Step 1 The two sides we know are Opposite (300) and Adjacent (400).
Step 2 SOHCAHTOA tells us we must use Tangent.
Step 3 Calculate Opposite/Adjacent = 300/400 = 0.75.
Step 4 Find the angle from your calculator using tan-1
I need tho know the answer to 9/10 divided by 6/1
Answer: 3/20
Step-by-step explanation:
Inital Equation:
[tex]\frac{9}{10}[/tex] ÷ [tex]\frac{6}{1}[/tex]
Find the Recipricol of 6/1:
It's: 1/6
Multiply the Recipricol of 6/1 (1/6) by 9/10
9/10 x 1/6 = 9/60
Simplify
9/60 = 3/20
Answer: 3/20
Zachary has 10 9/16 cups of dough to make dumplings. If he uses 13/16 cup of dough for each dumpling, how many dumplings can Zachary make?
Answer:
Zachary can make 13 dumplings.
Step-by-step explanation:
We know the size of the groups (13/16 cups) and the total (10 9/16 cups of dough). We're trying to find the number of groups that would fit in our total (10 9/16 cups). To find that out, we need to compute:
13\16 x ? =10 9/16
10 9/16 divided by 13/16 = ?
10 9/16 x 16/13
Suppose that you are a member of the typical American household and your family carries a credit card debt of
$7942. Use the TVM (Time-Value-of-Money) Solver to model a few credit card scenarios. (Note: Use months
rounded to the nearest hundredths on all calculations.)
1. If the average annual interest rate is 17.11%, how many months will it take the average American family
to pay off their debt of $7,942 if they make a minimum payment of $175 each month and no additional
purchases are made?
2. How much interest did you pay during this time?
1. At an annual interest rate of 17.11%, an average family needs 74 months to settle $7,942 at a $175 monthly payment.
2. The total interest is $4,932.10.
What is a monthly payment?The monthly payment is the amount paid each month to settle the loan within its maturity period.
The monthly payment can be computed using an online finance calculator.
We can also determine the period of payment using the same online finance calculator as below.
Data and Calculations:I/Y (Interest per year) = 17.11%
PV (Present Value) = $7,942
PMT (Periodic Payment) = $-175
FV (Future Value) = $0
Results:
N = 73.566
Sum of all periodic payments = $12,874.10
Total Interest = $4,932.10
Thus, while it will take 74 months for the average American family to pay off the loan of $7,942 with a monthly payment of $175 at 17.11% interest, the total interest paid is $4,932.10.
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9) Center: (-2,9) Point on Circle: (-5, 18)
Answer:
[tex](x+2)^2+(y-9)^2=[/tex] 90
Step-by-step explanation:
The centre is (-2,9) so the first part of the equation will be (x+2)^2 + (y-9)^2 and to get the second half, you know the point on the circle which you can use to find the radius. So the triangle formed would be 3 long, 9 high and using Pythagoras you can do:
[tex]3^2+9^2=r^2[/tex]
9+81= [tex]r^2\\[/tex]
90 = [tex]r^2[/tex]
and this equation ends with r^2 so you can substitute that back into the equation so together it will be
[tex](x+2)^2+(y-9)^2=[/tex] 90
Let the vector v v have an initial point at ( 1 , − 7 ) (1,−7) and a terminal point at ( 3 , − 2 ) (3,−2). Determine the components of vector v . v.
Answer: The vector is < 2, 5 >
==========================================================
Explanation:
Label the initial point (1,-7) as point P and (3,-2) as point Q.
The x coordinate of P is 1The x coordinate of Q is 3This is a change of +2, meaning we move 2 units to the right.
Therefore, the x component of the vector is +2 or simply 2.
The y coordinate of P is -7The y coordinate of Q is -2This is a change of +5 when moving from P to Q. We have moved 5 units up. The y coordinate of the vector is +5 or simply 5.
Overall, the vector is < 2, 5 > which tells the reader "move 2 units to the right and 5 units up.
Refer to the diagram below.
Which of these is equal to sin 58°?
Answer:
C Cos32
Step-by-step explanation:
Law of Cosines
HELP!!!!!
Answer:
[tex]\displaystyle 21 \approx c[/tex]
Explanation:
Solving for Angles
[tex]\displaystyle \frac{a^2 + b^2 - c^2}{2ab} = cos\angle{C} \\ \frac{a^2 - b^2 + c^2}{2ac} = cos\angle{B} \\ \frac{-a^2 + b^2 + c^2}{2bc} = cos\angle{A}[/tex]
Do not forget to use [tex]\displaystyle arccos[/tex] or [tex]\displaystyle cos^{-1}[/tex]towards the end, or the result will be thrown off.
Solving for Edges
[tex]\displaystyle b^2 + a^2 - 2ba\:cos\angle{C} = c^2 \\ c^2 + a^2 - 2ca\:cos\angle{B} = b^2 \\ c^2 + b^2 - 2cb\:cos\angle{A} = a^2[/tex]
Take the square root of the result in the end, or you will throw yourself off.
Well, let us get to work:
[tex]\displaystyle 13^2 + 29^2 - 2[13][29]cos\:41 = c^2 \\ 169 + 841 - 754cos\:41 = c^2 \\ 1010 - 754cos\:41 = c^2 \\ \\ \sqrt{440,94897651...} = \sqrt{c^2} \\ 20,99878512... = c \\ \\ \boxed{21 \approx c}[/tex]
I am joyous to assist you at any time.