The sum and the difference in the amount saved in the accounts will be 180 + 50w and 20 + 30w respectively.
How to calculate the value?From the information, I have have $100 in a savings accoun and save an additional $40 each week.
Let the number of weeks be represented by w. The expression to represent this will be:
= 100 + 40w
My friend has $80 in a savings account and saves and addtional $10 each week. This will be:
= 80 + 10w
The sum will be:
= 100 + 40w + 80 + 10w
= 180 + 50w
The difference in the amount will be:
= 100 + 40w - (80 + 10w)
= 20 + 30w
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Dados los vectores: a = -2i + 2j -k ; b = 3i - j + 2k y c = (-2,3, -1) . a) Determine: (b x a). (a x c) b) Halle el angulo que forman los vectores a y c.
From the given vectors, we have that:
a) The vectorial products are given as follows:
(b x a) = -3i - j + 4z.(a x c) = a x c = 1i - 2z.b) The angle between vectors a and c is of 6.84º.
How to find a vectorial product?A vectorial product between two vectors A and B is found from the determinant of a matrix, in which:
The first line is composed by the coordinates i, j and k.The second line is composed by the elements of vector a.The third line is composed by the elements of vector b.Then for the vectorial product b x a, the matrix is:
[tex]\left[\begin{array}{ccc}i&j&k\\3&-1&2\\-2&2&1\end{array}\right][/tex]
Using a calculator, the determinant, which is the vectorial product, is given by:
b x a = -3i - j + 4z.
For the vectorial product a x c, the matrix is:
[tex]\left[\begin{array}{ccc}i&j&k\\-2&2&-1\\-2&3&-1\end{array}\right][/tex]
a x c = 1i - 2z.
The angle is found as follows:
sin(θ) = |a x c|/(|a| x |c|)
The norms are given as follows:
[tex]|a \times c| = \sqrt{1^2 + (-2)^2} = \sqrt{5}[/tex]. [tex]|a| = \sqrt{(-2)^2 + (2)^2 + (-1)^2} = 3[/tex]. [tex]|c| = \sqrt{(-2)^2 + (3)^2 + (-1)^2} = \sqrt{14}[/tex].Hence:
[tex]\sin{\theta} = \frac{\sqrt{5}}{3\sqrt{14}}[/tex]
[tex]\theta = \sin^{-1}{\left(\frac{\sqrt{5}}{3\sqrt{14}}\right)}[/tex]
θ = 6.84º.
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Use the ALEKS calculator to solve the following problems.
(a) Consider a t distribution with 5 degrees of freedom. Compute P (t≤ 1.05). Round your answer to at least three decimal
places.
P (t≤1.05)=
(b) Consider a t distribution with 26 degrees of freedom. Find the value of C such that P(-c
answer to at least three decimal places.
c=
1.Consider a 5-degree-of-freedom t distribution. P (t≤1.05)=0.829.
2. Think about a t distribution with 26 possible degree. P(t>c)=0.05 and c=1.7056
Given that,
We have 2 question
1. Consider a 5-degree-of-freedom t distribution.
We have to find P (t≤1.05) at least three decimal places, round your response.
From t- value cumulative distribution function
Given a t-value and the degrees of freedom, locate the area under the t-distribution from -t to t.
P(t≤1.05)=0.829.
Therefore, P(t≤1.05) is 0.829.
2. Think about a t distribution with 26 possible degree. P(t>c)=0.05.
We have to find c at least three decimal places.
From inverse t-value distribution function
t=invT(0.95,26)=1.7056
Therefore, c is 1.7056
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Find f(3) graph of function
Answer:Explanation:
(3)=5
In a graph, te value of f(x) is the cy-value for the given x-value.
Consider the graph below:
• When the x-value = 3
,• The corresponding y-value = 5.
[tex]f\mleft(3\mright)=5[/tex]Therefore, the value of f(3) is 5.
Per Share Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 60,000 shares of cumulative preferred 3% stock, $20 par and 405,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $30,000; second year, $75,000; third year, $90,000; fourth year, $120,000. Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00". 2nd Year 3rd Year Preferred stock (dividends per share). Common stock (dividends per share) 1st Year 0.50 X 4th Year
please help we are stuck on 2nd year and explanation.
The dividends per share on each class of stock for each of the four years are as follows:
Cumulative Preferred Common Stock
First-year, $0.50 $0
Second year, $0.70 $0.08
Third year, $0.60 $0.13
Fourth year, $0.60 $0.21
How are the dividends per share determined?The dividends per share for each class can be determined by dividing the allocated dividend by the number of shares in the issue.
The allocated dividend to each class depends on the amount of dividend declared. For cumulative preferred stock, when their fixed dividend cannot be sufficiently settled, the arrears are carried forward.
3% Cumulative Preferred Common Stock
Par value $20 $25
Issued shares 60,000 405,000
Stock Value $1,200,000 $10,125,000
Preferred Fixed Dividend = $36,000 ($1,200,000 x 3%)
Distributed Dividends: Cumulative Preferred Common Stock
First-year, $30,000 $30,000 $0.50 $0 $0
Second year, $75,000 $42,000 $0.70 $33,000 $0.08
Third year, $90,000 $36,000 $0.60 $54,000 $0.13
Fourth year, $120,000 $36,000 $0.60 $84,000 $0.21
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-3(3+ p) <-66=
A) p >1
B) p> -19
C) p< 19
D) p >19
Answer:
D
Step-by-step explanation:
[tex]-3(3+p)<-66 \\ \\ 3+p>22 \\ \\ p>19[/tex]
4. Leila just graduated from college and is comparing a few different cities to move to. Which of these factors is the LEAST important thing for her to consider right now?
The factor that is the least important thing for Lelia to consider right now is D. Average cost of Uber, Lyft, or taxi fare.
How to illustrate the information?It should be noted that Leila just graduated from college and is comparing a few different cities to move to.
It's important for her to consider the average rent for an apartment, food and grocery store options in the area, and employment opportunities.
In this case, the. oat of Uber isn't necessary. The correct option is D.
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Leila just graduated from college and is comparing a few different cities to move to. Which of these factors is the LEAST important thing for her to consider right now?
Average rent for an apartment
Food and grocery store options in the area
Employment opportunities
Average cost of Uber, Lyft, or taxi fare
Graph the function y= |x| +3 Use a table of values giving some values for x like -4,-3,-2,-1,0,1,2,3,4 . Then graph the points and complete the graph. Use arrowheads when applicable. Is it a function? Find domain and range.
The function y =|x|+3 has been plotted in the graph and
Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
Range = {7,6,5,4,3}
The function y =|x|+3
The some values of x = -4, -3, -2, -1, 0, 1, 2, 3 and 4
Substitute the values in the function
y=|-4|+3 =7
y=|-3|+3 = 6
y=|-2|+3 = 5
y=|-1|+3 = 4
y=|0|+3 = 3
y=|1|+3 = 4
y=|2|+3 =5
y=|3|+3 = 6
y=|4|+3 = 7
Using the values complete the graph
The domain is the set of all possible inputs of the function
Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
The range is the set of all possible outputs of the function
Range = {7,6,5,4,3}
Hence, the function y =|x|+3 has been plotted in the graph and, the Domain = {-4, -3, -2, -1, 0, 1, 2, 3, 4}
Range = {7,6,5,4,3}
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the membership for a local zoo is $135. Members do not pay admissions, but they are charged $3 to park. Non-member admission is $25 for the zoo and $5 for the parking. After how many visits have members and non-members paid the same amount?
The members and non-members who pay the equal cost after 5 visits for the local zoo.
What is defined as the term equations?When one variable is determined to be equal to the other, the equation formula method is used to calculate the value of the a second variable.This second variable's value is the value that the others have same value.For the given question;
The cost of membership of local zoo is $135 for members.
The parking cost is $3 for members.
Non-member admission cost is $25 for the zoo and $5 for the parking.
Let the number of number of visits paid the same amount be 'x'.
Then, the equation becomes.
Members: m = 135 + 3x
Non-Members: n = 25x + 5x
As, members and non-members are equal.
m = n
Put the values;
135 + 3x = 25x + 5x
135 + 3x = 30x
27x = 135
x = 5
Thus, members and non-members who pay the equal cost after 5 visits.
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2 3/16 divided by 3 3/4
The answer to your question is =
0.583333333
I believe the answer is 0.58333333333. I think it would be 0.583 if you rounded it up. Hope this helps:)
NEED THIS DONE ASAP!!
The ratios of y/x are the same for the graph of y = 3x
and the ratios of y/x are NOT the same for the graph of y = 3x + 4
In this question, we have been given the graphs of lines y = 3x and y = 3x + 4.
Consider the ratios of y/x for the graph y = 3x
6/2 = 3
3/1 = 3
(-6)/(-2) = 3
Consider the ratios of y/x for the graph y = 3x + 4.
7/1 = 7
(1)/(-1) = -1
(-2)/(-2) = 1
We can observe that the ratios of y/x are the same for the graph of y = 3x
and the ratios of y/x are different for the graph of y = 3x + 4.
Therefore, the ratios of y/x are the same for the graph of y = 3x
and the ratios of y/x are NOT the same for the graph of y = 3x + 4
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Luke is driving from Hillwood to Springfield, 926 miles apart from each other. If Luke drives at a constant speed of 57 miles per hour,what equation can we make to find out how much time will like take to get to Springfield? Represent the time in hours as the variable x.
The equation that calculates the time taken to get to Springfield is x = 926/57
What is rate?Rate is used to establish the relationship between two quantities of different units. one of the quantity is usually expressed to unity in order to estimate the change in the other quantity.
If Hillwood and Springfield are 926 mile apart, and the speed taken to get to Springfield is 57miles per hour.
Let the time taken to get to Spring field be x.
Then if 57 miles is covered in an hour and it takes x hours to get to the destination
It means total distance covered is 57 × x
This distance is equal to the distance from Hillwood to Springfield which is 926 miles.
Equating both equations.
57x = 926
In conclusion, 57x = 926 is the equation that can be used to find out the time taken.
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A die is a rolled. the set of equally likely outcomes is {1,2,3,4,5,6} find the probability of getting a 3
Answer:
1/6th chance
Step-by-step explanation:
Since there are 6 possible outcomes that will be the denominator, now count the number you want to roll, in this case 1 since you only want to find the probably of getting a 3. So the probably is 1/6
Which of the following numbers is written in scientific notation?
The numbers that are written in scientific notation are:
1.8 x [tex]10^{9}[/tex]
3.2 x [tex]10^{-9}[/tex]
5.99 x [tex]10^{-9}[/tex]
What are scientific notations?Scientific notation is a method used in mathematics to compress large numbers to smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example: 1 x 10² is equivalent to 100
The decimal point in scientific notation, must be between the first non zero digit number and the second non-zero digit number.
When writing numbers that are less than zero in scientific notation, the power would have a negative sign in front of it. For example, 1 x [tex]10^{-2}[/tex] is equal to 0.01.
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2 17/35+5 5/7 in simplest form.
PLS :(
Answer:
ur answer is 8 1/5
Step-by-step explanation:
Felipe is on his way home in his car his drive is 12 miles long he has finished one fourth of the drive so far how far is he driven
Answer: 3
Step-by-step explanation: We know that Felipe has driven 1/4 of the way, so 12 divided by 4 is 3.
A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of 3ft and a diameter of 8ft. The tank will be made from metal (including its top and bottom). If the metal costs $29 for each square foot, how much will the metal cost in total?
The total cost of the metal needed to cover the tank shaped like a metal is $5,099.36.
What is the total cost?In order to determine the total metal cost, we are to first calculate the total surface area of the tank. Since the tank is a closed cylinder, we are to determine the total surface area of a cylinder.
The total surface area of a closed cylinder can be determined by adding the area of all its faces.
Total surface area of the closed cylinder = 2πr(r + h)
Where:
r = radius = diameter / 2 = 8/2 = 4ft
h = height
π = pi = 3.14
(2 x 3.14 x 4)(4 + 3)
25.12 x 7 = 175.84 ft²
Total cost of the metal = $29 x 175.84 = $5,099.36
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Trigonometric functions using the ratio of two sides of a triangle can be used to solve ______ triangles.
A. acute
B.obtuse
C.oblique
D.right
Trigonometric functions using the ratio of two sides of a triangle can be used to solve D.right triangles.
How to solve right triangles?To solve for a missing side of a right angle, one can use trigonometric functions that will use the ratio of the other two known sides of the triangle in question.
For instance, using the trigonometric function of Sin can allow for the use of the opposite side and the hypotenuse to find the adjacent side. The Cos and Tan can also be used for the other sides.
This means that either of two sides (including the hypotenuse) can be used to find the other.
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Triangle side splitter theorem question
Applying the side splitter theorem
we have that
PT/TS=PQ/QR
so
substitute the given values
7/21=PQ/27
solve for PQ
PQ=27*7/21
PQ=9
Find the value of PR
PR=PQ+QR
PR=9+27
PR=36Q 2. Using a standard deck of cards (which has 26 red cards and 26 black cards, with 13 cards of
every suit), what is the probability of selecting a red card, and then after replacing the card, selecting a
heart card?
Answer:
1/8
Step-by-step explanation:
First Pick P(red card) = 26/52 = 1/2
Second Pick after replacement P(heart) = 13/52 = 1/4
P(red on first pick and heart on second pick
= 1/2 x 1/4 = 1/8
0.0001 in scientific notation
Answer:
1 × 10^-4
Step-by-step explanation:
This is because after the decimal point there are 4 numbers so u have to put -4, and the 1 is there because of the last number
Answer:
1 × 10^-4
Step-by-step explanation:
Which percent is larger 5 , 15 or 20?
A local hamburger shop sold a combined total of 449 hamburgers and cheeseburgers on Thursday. There were 51 fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Thursday?
Taking into account the definition of a system of linear equations, the local hamburger shop sold 199 hamburgers on Thursday.
System of linear equationsA system of linear equations is a set of equations in which every equation is linear., in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"c" is the number of cheeseburgers sold on Thursday."h" is the number of hamburgers sold on Thursday.You know:
A local hamburger shop sold a combined total of 449 hamburgers and cheeseburgers on Thursday. There were 51 fewer cheeseburgers sold than hamburgers.The system of equations to be solved is
h + c= 449
h= c - 51
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
c - 51 + c= 449
c+ c= 449 + 51
2c= 500
c= 500÷2
c= 250
Remembering that h= c - 51, you get:
h= 250 - 51
h= 199
Finally, 199 hamburgers were sold on Thursday.
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which point most closely approximates the difference of B and A, that is (B -A) ?
Point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).
What are mathematical operations?An operation, also known as an "operand" or "argument," is a function in mathematics that converts zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the operations that are most frequently studied. A constant is an operation of arity zero, also known as a nullary operation. An example of an operation of arity 3, also known as a ternary operation, is the mixed product.So, when we add up 2 numbers let's say A and B, the result is always a 3rd number which is C.
A + B = CSimilarly, when we subtract a number from another number (B - A), the result is always a third number C.
B - A = CSo, (C) C closely approximates the difference between B and A (B - A).
Therefore, point (C) C closely approximates the given mathematical operation that is the difference between B and A (B - A).
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Find the zeros of the function and state the multiplicities.
k(x)=15x³-48x²-48x
If there is more than one answer, separate them with commas. Select "None" if applicable.
Part: 0/2
Part 1 of 2
Zero(s) of k:
The zeroes of the function k(x)=15x³-48x²-48x are 0, 4 and -4/5.
The function provided is a cubic polynomial.
There will be three zeroes in total for the function k(x).
K(x) = 15x³-48x²-48x
If we put x = 0,
We can see that k(x) becomes zero,
So we can say that 0 is a solutions for this function,
Now,
K(x) = x(15x²-48x-48)
Solving 15x²-48x-48 seperately using quadratic formula,
a = 15
b = -48
c = -48
x = (-b+√D)/D and (-b-√D)/D
D = b²-4ac.
D = (-48)²-4(15)(-48)
D= 5184.
√D = 72
putting all the values to find x,
x = (-(-48)+72)/30 and (-(-48)+72)/30
x = 4 and -4/5.
our function becomes,
k(x) = x(x-4)(x+4/5)
so the zeroes are 0, 4, -4/5.
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Triangle PQT and Triangle RSU are similar right triangles. Which proportion can be used to show that the slope of QT is equal to the slope of RS?
AAS congruency is used to show the required proportion.
What is AAS congruency?Angle-Angle-Side is referred to as AAS. The triangles are said to be congruent if two of a triangle's angles and one of its non-included sides are equal to the equivalent angles and sides of another triangle.
In the given question ΔPQT ≅ ΔRSU
because ∠QPR= ∠RUS [ each 90°]
∠PQR= ∠URS [ since QP is parallel to UR so these two angles are corresponding angles]
PT= US
thus from AAS congruency ΔPQT ≅ ΔRSU
Thus QT = US from cpct
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Help find x-coordinate please
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+6}x\stackrel{\stackrel{c}{\downarrow }}{+3} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 6}{2(1)}~~~~ ,~~~~ 3-\cfrac{ (6)^2}{4(1)}\right) \implies \left( - \cfrac{ 6 }{ 2 }~~,~~3 - \cfrac{ 36 }{ 4 } \right)\implies (\stackrel{x}{-3}~~,~~-6)[/tex]
Please explain The polynomial passes through the point of (-4, -8) and has end behavior of down, down. The
intercepts of the graph are x = -2, 1, 2, and 4.
Answer:
The y-value of the point (4, 8) is (obviously) 8. Since the line has a slope of zero, everywhere on the line will have a y-value of 8. So the equation of the line is y = 8. The x-value can be any number, but the y-value will always be 8
The difference of three times a number and eight is two more than the number.
Answer:
The number is 5.
Step-by-step explanation:
Let x be the number.
[tex]3x - 8 = x + 2[/tex]
[tex]2x = 10[/tex]
[tex]x = 5[/tex]
Solve k over negative 1.6 is greater than negative 5.3 for k.
k > −8.48
k < −6.9
k > −6.9
k < 8.48
The required inequality is k > -8.48. Option A is correct.
Given that,
To determine the equivalent expression to the k / -1.6 > -5.3
What is inequality?
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
As per the given condition, we have to simplify the given expression to get the equivalent expression,
k / -1.6 > -5.3
k > -1.6 (-5.3)
k >- 8.48.
Thus, the required inequality is k > -8.48. Option A is correct.
PleSe help me solve this problem
Answer:
56
Step-by-step explanation:
[tex]\binom{8}{3}=\frac{8!}{5!3!}=56[/tex]