Answers
M = $6,400
C = $3,600
CD interest = $180
Money market interest = $256
Here, we want to start by completing the chart
We proceed as follows;
Let us take it line by line
a) The rate for the CD account is 5%
Writing this as decimal is 5/100 = 0.05
b) The time for the CD account is 1 year
Next line;
a) Principal invested in money market is $M
b) The time is also 1 year
Next line;
The interest earned on investment is the sum of both
That will be;
0.05c + 0.04m
So, let us write the equations to solve simultaneously;
\(\begin{gathered} c\text{ + m = 10,000} \\ 0.05c\text{ + 0.04m = 436} \\ \text{second equation multiplied through by 100;} \\ 5c\text{ + 4m = 43,600} \\ \text{From i;} \\ c\text{ = 10,000-m} \\ \text{put this into the multiplied equation} \\ 5(10,000-m)\text{ + 4m = 43600} \\ 50,000\text{ - 5m + 4m = 43600} \\ m\text{ = 50,000-43600} \\ m\text{ = 6400} \\ c\text{ = 10,000-6400} \\ c\text{ = 3,600} \end{gathered}\)So, let us fill the last parts;
a) $3,600 + $6,400 = Total $10,000 invested
b) CD interest is 0.05 c = 0.05 (3,600) = $180
Money market interest = 0.04M = 0.04 (6,400) =$256
$180 + $256 = $436 total interest
Related Questions
2(x+5)-4x=3(x-2)-5x+16 true or false
Answers
Answer:
True
Step-by-step explanation:
sorry need the pointes
Answer:
true
Step-by-step explanation:
What is x if the volume of
the box is 70 in^3 ?
Answers
Answer:
12.25.
Step-by-step explanation:
1) the formula of the volume given in the condition is:
V=2*2/7*10x.
2) If V=70, then
2*2/7*10x=70, where x=12.25.
Answer:
(10x)(7/4)(2)=70
=10x=70/7/4/2
=10x=20
x=2
Answer: 2
Step-by-step explanation:
pls help me not doing well wit it
Answers
Answer:
I think its 40 because you can multiply the first number in the other 3 ratios by 4 to get the second nummber.
Step-by-step explanation:
Hope this helps!
Two angel's of a triangle measure 12* and 40* what is the measure
of the third angle
Answers
Choose all lengths that are equal to 3 yards 16 inches.
A. 124 in.
B. 4 yd 4 in.
C. 3 yd 1 1/2 ft ( this is a fraction number 1 and 1 half)
D. 2 yd 52 in.
E. 10 ft 4 in.
Answers
Answer:
a,d, and e
Step-by-step explanation:
because 3 yards is equal to 108 inches
A circle with center C(4,-2) passes through the point A(1,3). Does the point B (8,-2) lie inside the circle? Prove your answer
Answers
Answer:
\(\begin{gathered} (A)\Rightarrow\text{ Point B lies inside the circle Because:} \\ CA=\sqrt[]{34} \\ CB=4 \end{gathered}\)Explanation: The general form of the equation of the circle is as follows:
\(\begin{gathered} (x-x_o)^2+(y-y_o)^2=k^2 \\ (x_o,y_o)\rightarrow\text{ Center of the circle}\rightarrow(4,-2) \\ \therefore\Rightarrow \\ (x-4)^2+(y+2_{})^2=k^2\Rightarrow(1) \end{gathered}\)(1) is the equation of the circle. since it passes through the point (1,3), therefore substituting the (x,y) values of it in (1) gives the value complete equation (1) as follows:
\(\begin{gathered} (1-4)^2+(3+2_{})^2=k^2 \\ 9+25=k^2 \\ k^2=34 \\ \therefore\Rightarrow \\ (x-4)^2+(y+2_{})^2=k^2\Rightarrow(2) \end{gathered}\)(2) is the complete equation for the circle, the following graph shows if point B is inside or outside the circle.
Given m ∥ n, find the value of x.
Answers
given that m is parallel to n,
the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.
using the corresponding angle rule we know that:
2x + 16 = 96
2x = 80
so x = 40
1
A red die is tossed and then a green. die is tossed.
What is the probability that the red die shows a
number larger than 4 or the green die shows a
number less than 2?
The two events are not mutually exclusive. So to find the
probability of the union, use:
P(A or B) = P(A) + P(B) - P(A and B)
[?]
P(A or B)
=
8
P(B)
Green die
What is the probability of the red die rolling a
P(A)
Red die
+
-
8)
P(B)
P(A)
Red die Green die
number greater than 4?
Enter your answer in simplest form.
Enter
Answers
On solving the provided question, we can say that the probability of the red die rolling is 16.67% probability = 0.1667
What is probability?A branch of mathematics called probability theory determines the chance that an event will occur or that a statement is true. A probability is a number between 0 and 1, where 1 denotes certainty and about 0 denotes how probable an event is to occur. The possibility or likelihood that a specific event will occur is expressed numerically as a probability. Probabilities can also be expressed as percentages from 0% to 100% or as numbers between 0 and 1. the proportion of occurrences among all equally likely alternatives that lead to a certain event relative to all possible outcomes.
red die, there are 3 numbers greater than 3 out of 6 numbers
Probability (A) = 3/6 = 1/2.
green die, there are 2 numbers less than 3 out of 6 numbers
Probability (B) = 2/6 = 1/3.
events are independent
P(A and B) = \(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667\)\(P(A)P(B) = 1/2 X 1/3 = 1/6 = 0.1667.\)
16.67% probability = 0.1667
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
9. Use the graph of the function f(x) = x³ – 7x² + 10x to
x`
identify its relative maximum and minimum.
da
-4
8
8
2
K
T
2
da
y
8
+w
8
maximum = 4.1, minimum = -8.2
maximum = 0.9, minimum = 3.8
Answers
The extremas of the function f(x) = x³ - 7x² + 10x are given as follows:
Relative maximum: (0.88, 4.061).Relative minimum: (3.786, -8.209).What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing, that is, where the function curves down.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing, that is, where the function curves up.More can be learned about extremas of a function at https://brainly.com/question/9839310
#SPJ1
Parte de Cálculo: En cada una de las siguientes proporciones, utilizar regla de tres para determinar el valor desconocido
x/5 = 8/10
8/12 = 2/x
15/3 = x/2
x/6 = 6/12
x/8 = 4/2
10/2 = x/7
Answers
Answer:
x = 4
x = 3
x = 10
x = 3
x = 16
x = 35
Step-by-step explanation:
\(\frac{x}{5} :\frac{8}{10}\)
x · 10 = 5 · 8
10x = 40
10x ÷ 10 = 40 ÷ 10
x = 4
\(\frac{8}{12} :\frac{2}{x}\)
x · 8 = 12 · 2
8x = 24
8x ÷ 8 = 24 ÷ 8
x = 3
\(\frac{15}{3} :\frac{x}{2}\)
x · 3 = 15 · 2
3x = 30
3x ÷ 3 = 30 ÷ 3
x = 10
\(\frac{x}{6}:\frac{6}{12}\)
x · 12 = 6 · 6
12x = 36
12x ÷ 12 = 36 ÷ 12
x = 3
\(\frac{x}{8} :\frac{4}{2}\)
x · 2 = 8 · 4
2x = 32
2x ÷ 2 = 32 ÷ 2
x = 16
\(\frac{10}{2} :\frac{x}{7}\)
x · 2 = 10 · 7
2x = 70
2x ÷ 2 = 70 ÷ 2
x = 35
Evaluate the expression for s = 10, t = –2, and u = 9.
t2u + s = ?
Answers
Answer:
46
Step-by-step explanation:
You want to evaluate the expression t²u+s for t=-2, u=9, s=10.
Evaluating an expressionPut the numbers in the places of the corresponding variables, and do the arithmetic.
(-2)²·9 +10 = 4·9 +10 = 36 +10 = 46
The value of the expression is 46.
The graph of g(x), shown below, is a vertical shift of the graph of f(x) = 2x.
Write the equation for g(x).
10
9
8
8 9 10
O A. g(x) = 2x+1
OB. g(x) = 2x-1
OC. g(x) = 2x + 1
OD. g(x) = 2x - 1
op
7
ob
10 +3
10
GN
2 3
4
FOF
5
8
7
Answers
The equation which represents the given graph g(x) is 2ˣ-1.
What is Equation?
Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.
Here, given graph passes through origin.
Put x = 0 in all the given equation and verify which equations gives result as zero.
Put x = 0 in option A
g(0) = 2⁰⁺¹ = 2 ≠ 0
in option B
g(0) = 2⁰-1 = 1 - 1 = 0
Thus, option B g(x) = 2ˣ-1 is the correct expression for the given graph.
Learn more about Equations from:
https://brainly.com/question/10413253
#SPJ1
The gasoline tax is a ______ tax
Answers
Answer:
Excise tax
Step-by-step explanation:
Correct me if I'm wrong <3
the candle was 1 inches long when new.Each half hour 3/4 inch of the candle burned away.After 4 hours,how long was the candle
Answers
After 2 hours, the candle would have burned away another 1.5 inches (4 half-hour periods * 3/4 inch burned in each period), leaving it with a length of 0 inches. At this point, the candle has completely burned down.
Therefore, after 4 hours, the length of the candle would be 0 inches.
James is a welder who earns $12.50 per hour. he works 8 hours per day, Monday through Friday. How much does James earn in one Week?
Answers
Answer:
$500 per week
Step-by-step explanation:
$12.50 × 8 × 5 = $500
A salesman normally makes a sale (closes) on % of his presentations. Assuming the presentations are independent, find the probability of the following. a) He fails to close for the first time on his attempt. b) He closes his first presentation on his attempt. c) The first presentation he closes will be on his second attempt. d) The first presentation he closes will be on one of his first three attempts.
Answers
Answer:
\((a)\ 0.0864\)
\((b)\ 0.096\)
\((c)\ 0.24\)
\((d)\ 0.936\)
Step-by-step explanation:
Given
\(p \to\) close
\(q \to\) fail to close
\(p = 60\%\)
\(p = 0.60\)
First, calculate the value of q
Using complement rule
\(q = 1 - p\)
\(q = 1 - 0.60\)
\(q = 0.40\)
So, we have:
\(p = 0.60\) and \(q = 0.40\)
Solving (a): Fails to close on the 4th attempt
This means that he closes the first three attempts. The event is represented as: p p p q
So, we have:
\(Pr = p*p*p*q\)
\(Pr = p^3*q\)
\(Pr = 0.60^3*0.40\)
\(Pr = 0.0864\)
Solving (b): He closes for the first time on the 3rd attempt
This means that he fails to close the first two attempts. The event is represented as: q q p
So, we have:
\(Pr = q * q * p\)
\(Pr = q^2 * p\)
\(Pr = 0.40^2 * 0.60\)
\(Pr = 0.096\)
Solving (c): First he closes is his 2nd attempt
This means that he fails to close the first. The event is represented as: q p
So, we have:
\(Pr = q * p\)
\(Pr = 0.40 * 0.60\)
\(Pr = 0.24\)
Solving (d): The first he close is one of his 3 attempts
To do this, we make use of complement rule
The event that he does not close any of his first three attempts is: q q q
The probability is:
\(Pr = q*q*q\)
\(Pr = q^3\)
The opposite is that the first he closes is one of the first three
So, we have:
\(Pr' = 1- Pr\) --- complement rule
\(Pr' = 1- q^3\)
\(Pr' = 1- 0.40^3\)
\(Pr' = 1- 0.064\)
\(Pr' = 0.936\)
5th grade math. correct answer will be marked brainliest
Answers
Answer:
7/12 teaspoons
fraction
Step-by-step explanation:
Amount of salt that would be used = 1\(\frac{3}{4}\) x \(\frac{1}{3}\)
Convert \(1\frac{3}{4}\) to an improper fraction
to convert to improper fraction, take the following steps :
1. Multiply the whole number by the denominator
2. Add the numerator to the answer gotten in the previous step
3. divide the number gotten in the previous step by the denominator
(1 x 4) + 3 = \(\frac{7}{4}\)
7/4 x 1/3 = 7/12
NEED ANSWER FAST PLEASE
!! Marty keiths annual salary is 56,000 as a computer- aided designer. If the state tax is 4% what does he pay yearly in state taxes?
Answers
Answer:
$3240.Step-by-step explanation:
there is no way to explain it on computer but hope this helps
Convert the 4% to a decimal by dividing by 100 = 0.04
56,000 x 0.04 = 2,240
-3/-11 + 5/9 find the sum
Answers
How do you do these two questions?
Answers
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
Melissa started to run on treadmill after setting his timer for 73 minutes the display says that she has finished 69% of a run how many minutes have gone by round your answer to the nearest tenth
Answers
Answer:
The answer is 50 minutes to the nearest tenth
Step-by-step explanation:
Total time to complete =73 minutes
69% of Total time is completed=?
\( = \frac{69}{100} \times 73\)
=50 minutes to the nearest tenth
Answer:
50.4 minutes
Step-by-step explanation:
To calculate how many minutes have gone by, we can multiply the total time (73 minutes) by the percentage of the run that has been completed (69%).
73 × 69% = 50.37 minutes.Rounding to the nearest tenth:
50.4 minutes.Therefore, Melissa has been running for approximately 50.4 minutes.
16)
15 km
K
H
8 km
85
P
A) 43.5 km
C) 62.3 km
B) 58.4 km
D) 53.4 km
Answers
Sorry if it’s wrong
the sine of the angle at a is equal to side bc divided by side ab. the sine of angle a is therefore equal to:
Answers
sin(a) = bc/ab. is the angle of a is therefore the sine of angle at a is equal to side bc divided by side ab.
this is explained as below as :
The sine of an angle in a right triangle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse. In this case, the angle at "a" is opposite side "bc" and the hypotenuse is side "ab". Therefore, the sine of angle "a" is equal to the ratio of side "bc" divided by side "ab", or sin(a) = bc/ab.
The sine of an angle in a triangle is a trigonometric function that is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. The hypotenuse is the side of a right triangle that is opposite the right angle.
In this particular case, the statement "the sine of the angle at a is equal to side bc divided by side ab" is referring to a right triangle where angle "a" is one of the angles, side "bc" is the side opposite angle "a" and side "ab" is the hypotenuse.
This is known as the sine ratio and it is used in trigonometry to calculate the sine of an angle in a right triangle. It is important to note that the sine ratio is only valid for right triangles, and the measure of the angle must be in radians.
It's also worth mentioning that this relationship holds true for any angle in a triangle, not only in right triangles, but in non-right triangles sine, cosine and tangent ratios are defined differently.
So, the sine of angle "a" is calculated as the ratio of side "bc" to side "ab" (bc/ab).
To know more about sine click here:
brainly.com/question/30162646
#SPJ4
If the Math Olympiad Club consists of 11 students, how many different teams of 3 students can be formed for competitions?
Answers
Answer:
165 different teams of 3 students can be formed for competitions
Step-by-step explanation:
Combinations of m elements taken from n in n (m≥n) are called all possible groupings that can be made with the m elements so that:
Not all items fitNo matter the order Elements are not repeatedThat is, a combination is an arrangement of elements where the place or position they occupy within the arrangement does not matter. In a combination it is interesting to form groups and their content.
To calculate the number of combinations, the following expression is applied:
\(C=\frac{m!}{n!*(m-n)!}\)
It indicates the combinations of m objects taken from among n objects, where the term "n!" is called "factorial of n" and is the multiplication of all the numbers that go from "n" to 1.
In this case:
n: 3m: 11Replacing:
\(C=\frac{11!}{3!*(11-3)!}\)
Solving:
\(C=\frac{11!}{3!*8!}\)
being:
3!=3*2*1=68!=8*7*6*5*4*3*2*1=40,32011!=39,916,800So:
\(C=\frac{39,916,800}{6*40,320}\)
C= 165
165 different teams of 3 students can be formed for competitions
Answer:
There will be 3 teams of 3 students, and one team of 2 students, so there will be 4 teams with one team one student short, but only 3 teams that can hold 3 students
riangle NMO is drawn with vertices N(−5, 2), M(−2, 1), O(−3 , 3). Determine the image vertices of N′M′O′ if the preimage is reflected over x = −2.
N′(5, −2), M′(2, 1), O′(3, 3)
N′(−2, 2), M′(1, 1), O′(0, 3)
N′(1, 2), M′(−2, 1), O′(−1, 3)
N′(−5, −2), M′(−2, −1), O′(−3, −3)
Answers
The vertices after transformation are N′(1, 2), M′(−2, 1), O′(−1, 3).
We have,
N(−5, 2), M(−2, 1), O(−3 , 3).
We know the rule to reflect over a vertical line x =a is
(x, y) --> (-x-2a, y)
So, for x=2 the rule will be
(x, y) --> (-x-4, y)
Now, the vertices after transformation are
M(-2, 1) -> M'(-2, 1)
N(-5, 2) -> N'(1, 2)
O(-3, 3) -> O'(-1, 3)
Learn more about Transformation here:
https://brainly.com/question/29184180
#SPJ1
fv=100000, pmt=4000, i/y=5%, n=10, what is pv?
Answers
The Present value is $6,139.132.
We have,
FV=100000, pmt = 4000, I =5%, n=10
So, The present value formula is
PV=FV / (1 + \(i)^n\)
So, PV = 100, 000 / (1+ 5/100\()^{10\\\)
PV = 100,000 / (1+ 0.05\()^{10\\\)
PV = 100, 000/ (1.05\()^{10\\\)
PV = 100,000 / 1.6288946
PV= $6,139.132
Learn more about Future Value here:
https://brainly.com/question/14860893
#SPJ1
let d be diagonal, with repeated diagonal entries grouped contiguously. show that if a commutes with d, then it must be block diagonal.
Answers
As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So, if a commutes with d, then it must be block diagonal.
Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,
d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),
where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.
Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.
Then, for any \(i \in {1, 2, \dots, k}\), we have
\(ad_{ii} = da_{ii}\)
Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and
hence
\(ad_{ij} = da_{ij} = 0\)
for all \(i \neq j\).
Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have
\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)
Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.
Therefore, if a commutes with d, then it must be block diagonal.
For similar question block diagonal,
https://brainly.com/question/10635277
#SPJ4
what are the terms, coefficients, and constants of the following expression?
21x+9y-7z-5
Answers
Answer:
coefficent=21,9,7
constant=x,y,z
coefficient: 21 , 9 , 7
constant: 5
sorry if i’m wrong:(
For each value of w, determine whether it is a solution to -13=
W
9
27
Answers
\( - 13 = \frac{w}{9} - 6 \\ - 13 + 6 = \frac{w}{9} \\ - 7 = \frac{w}{9} \\ w = - 63\)
so only -63 is the solution, the rest three are NOT solution for this equation.
Sarah used properties of operations to write the following three equivalent expressions to .
A. There are no errors. All of the expressions are equivalent.
B. Expression 1. Sarah can’t apply the Distributive Property if there are three addends.
C. Expression 2. Sarah can’t combine -4 and -6. She must combine -4 with 8.
D. Expression 3. Sarah applied the Distributive Property but incorrectly multiplied 1/2 (-6) .
Answers
Answer:
The answer is d
Step-by-step explanation:
The step expression 3 is incorrect, there should be -3 in place of +3.
What is expression?An expression in maths, a statement involving at least two different numbers (known or unknown) and at least one operation.
Given is an expression, 1/2{-4+8+(-6)}
On solving, we get,
1/2{-4+8+(-6)}
= 1/2(-4) + 1/2(8) +1/2(-6)
= 1/2{-4+(-6)} + 4
= -2+4-3
When we will divide, -6 by 2, we will get -3 and Sarah used +3 which made her expression 3 incorrect.
Hence, The step expression 3 is incorrect, there should be -3 in place of +3.
For more references on expression, click;
https://brainly.com/question/14083225
#SPJ2