Answer:
b. y=0.6x+6
Step-by-step explanation:
First, find the slope using the slope formula, [tex]\frac{0-6}{-10-0}[/tex]. This is 6/10, which simplifies to 3/5 or 0.6. Then you need to find the y-intercept, however, this is already given to you. Remember that the y-intercept is when x=0, so (0,6) must be the y-intercept. Therefore the equation is y=0.6+6.
Which set of mixed numbers has a difference less than 1?
Lucas opened a savings account 20 years ago with a deposit of $3,815.24. The account has an interest rate of 3.3% compounded
quarterly. How much interest has Lucas earned?
a. $3,488.21
b. $3,546.50
c. $3,815.24
d. $3,941.14
Answer:
Interest earned = $3546.50
Option B is correct option.
Step-by-step explanation:
Time t = 20 years
Principal Amount P =$3815.24
Interest r = 3.3% or 0.033
Compounded quarterly n = 4
We need to find How much interest has Lucas earned?
First we need to find the future value in the account after 20 years
The formula used to find future value A is: [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Putting values of t, r , n and P to find A i.e future value
[tex]A=P(1+\frac{r}{n})^{nt}\\A=3815.24(1+\frac{0.033}{4})^{20*4} \\Simplifying:\\A=3815.24(1+0.00825)^{20*4} \\A=3815.24(1.00825)^{80}\\A=3815.24(1.929)\\A= 7361.74[/tex]
Now finding interest amount by subtracting the initial deposit from the future value
Interest earned = Future Value (A)- Initial Deposit (P)
Interest earned = 7,361.74 - 3815.24
Interest earned = 3546.50
So, Lucas have earned interest = $3546.50
Option B is correct option.
Hamburger-R-Us offers 8 toppings on its made to order burgers. you can order plain or any combination of toppings. How many types of burgers are possible?
Step-by-step explanation:
For every topping, you can either "take-it or leave-it" for your burger. This means there are 2 options for every topping.
Hence number of possible burgers = 2⁸ = 256.
Is it true that m || n?
Your response should be at least 3 complete sentences. Be sure to include information about the slopes of the line and calculations. NO PLAGIARISM!!
Answer:
False
Step-by-step explanation:
Lines m and n are not parallel
See attached that shows vertical segment of 6 units, its longer than the distance between the lines on the right and its shorter on the left
Parallel lines should have same distance at any point between them
Look at this graph:
What is the slope?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Which is the distance between the points M ( -21, -7)and N ( -5, -7)
Answer:
16
Step-by-step explanation:
becasue from -21 to -5 it's 16 units (-21 - -5= 16).
(a) Complete the table of values for y = 6 - 4x.
Please help ❤️
Answer:
[tex]\boxed{\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}}[/tex]
Step-by-step explanation:
Given equation to us is :-
[tex]\implies y = 6 - 4x [/tex]
So , here we can put different values of x in order to get different values of y .
Initial table given to us is ,
[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & & & 2&&-6 \\\cline{1-6}\end{tabular}[/tex]
Put x = (-1) :-
[tex]\implies y = 6 - 4x \\\\\implies y = 6 -4(-1) \\\\\implies y = 6 + 4 \\\\\red{\bf\implies y = 10} [/tex]
Put x = 0 :-
[tex]\implies y = 6 - 4x \\\\\implies y = 6-4(0) \\\\\implies y = 6 - 0 \\\\\pink{\bf\implies y = 6 }[/tex]
Put x = 2 :-
[tex]\implies y = 6-4x \\\\\implies y = 6 - 4(2) \\\\\implies y = 6 - 8 \\\\\blue{\bf\implies y = (-2)} [/tex]
Hence the final table would be :-
[tex]\begin{tabular}{|c|c|c|c|c|c|}\cline{1-6} \bf x & -1 & 0&1&2&3\\\cline{1-6} \bf y & 10& 6& 2&(-2)&-6 \\\cline{1-6}\end{tabular}[/tex]
Joanna is building 2 square planter boxes in her garden . Each box is 2 yard wide . What is the total perimeter of the boxes ?
Answer:
16 yards
Step-by-step explanation:
Square: all sides are equalSquare: 4 sides totalPerimeter of square: 2 + 2 + 2 + 22 + 2 + 2 + 2 = 8 yardsPerimeter of second box: 2 + 2 + 2 + 2 = 8 yardsPerimeters in total: 8 + 8 = 16 yardsI hope this helps!
use repeated subtraction to divide 93÷10
Answer:
9r3
Step-by-step explanation:
93-10=83-10=73-10=63-10=53-10=43-10=33-10=23-10=13-10=3
so 93÷10=9 remainder of 3
If f(x) = (4784), what is 13)?
Answer:
f(x)=4784
f(13)= 0 because there is x value on the right hand side
The daily output at a plant manufacturing chairs is
approximated by the function
f(L,K) = 453KL 3/5 chairs
where L is the size of the labor force measured in hundreds
of worker-hours and K is the daily capital investment in
thousands of dollars. If the plant manager has a daily budget
of $13,000 and the average wage of an employee is $9.00
per hour, what combination of worker-hours (to the nearest
hundred) and capital expenditures (to the nearest thousand)
will yield maximum daily production?
Complete Question
The daily output at a plant manufacturing chairs is approximated by the function
[tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] chairs
where L is the size of the labor force measured in hundreds
of worker-hours and K is the daily capital investment in thousands of dollars. If the plant manager has a daily budget of $13,000 and the average wage of an employee is $9.00 per hour, what combination of worker-hours (to the nearest hundred) and capital expenditures (to the nearest thousand) will yield maximum daily production?
a)200 worker-hours and $9000 in capital expenditure
b)1100 worker-hours and $3000 in capital expenditure
c)500 worker-hours and $8000 in capital expenditure
d)900 worker-hours and $5000 in capital expenditure
e)600 worker-hours and $6000 in capital expenditure
f)300 worker-hours and $10,000 in capital expenditure
Answer:
d)900 worker-hours and $5000 in capital expenditure
Step-by-step explanation:
From the question we are told that
Daily output at a plant manufacturing chairs is approximated by the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex]
Daily budget of $13,000
Average wage of an employee is $9.00 per hour
a) Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to for (a)
Mathematically solving with L=200 K=9000
[tex]f(L=200,K=9000) = (45\sqrt[3]{9000})200^3^/^5[/tex]
[tex]f(L=200,K=9000) = 45*20.8*24[/tex]
[tex]f(L=200,K=9000) = 22464[/tex]
b)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to for (b)
Mathematically solving with L=1100 K=3000
[tex]f(L=1100,K=3000) = (45\sqrt[3]{3000})1100^3^/^5[/tex]
[tex]f(L=1100,K=3000) = 45*14.4*66.8[/tex]
[tex]f(L=1100,K=3000) = 43286.4[/tex]
c)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (c)
Mathematically solving with L=500 K=8000
[tex]f(L=500,K=8000) = (45*\sqrt[3]{8000})*500^3^/^5[/tex]
[tex]f(L=500,K=8000) = 45*20*41.63[/tex]
[tex]f(L=500,K=8000) =37467[/tex]
d)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (d)
Mathematically solving with L=900 K=5000
[tex]f(L=900,K=5000) = (45*\sqrt[3]{5000})*900^3^/^5[/tex]
[tex]f(L=900,K=5000) = 45*17.09*59.2[/tex]
[tex]f(L=900,K=5000) =45577.88[/tex]
e)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (e)
Mathematically solving with L=600 K=6000
[tex]f(L=600,K=6000) = (45\sqrt[3]{6000})600^3^/^5[/tex]
[tex]f(L=600,K=6000) = 45*18.17*46.4[/tex]
[tex]f(L=600,K=6000) =37974[/tex]
f)Generally the function [tex]f(L,K) = 45\sqrt[3]{K}L^3^/^5[/tex] can be use to find (e)
Mathematically solving with L=600 K=6000
[tex]f(L=300,K=10,000) = (45*\sqrt[3]{10,000})*300^3^/^5[/tex]
[tex]f(L=300,K=10,000) = 45*21.5*30.6[/tex]
[tex]f(L=300,K=10,000) = 29704.2[/tex]
Therefore the function f shows maximum at L=900 K=5000
Giving the correct answer to be
d)900 worker-hours and $5000 in capital expenditure
A hexagon ABCDEF is shown.
С-115
D
B
145
Angle CDE is twice the size of angle DEF.
Work out the size of angle CDE.
You must show all your working.
E
160°
+
F
Answer:
140
Step-by-step explanation:
115+165+140+90=510
180*4=720 (sum of interior angles of hexagon)
115+165+140+90+x+2x=720
why 2x because i kept ANGLE DEF as x and ANGLE CDE is twice so 2x
510+2x+x=720
3x=210
x=210/3
x=70
ANGLE DEF IS 70
so because ANGLE CDE IS TWICE ANGLE DEF thus 70*2=140
ANGLE CDE =140
The angle CDE is 140°.
What is a hexagon?
A hexagon can be defined as a closed two-dimensional polygon with six sides. Hexagon has 6 vertices and 6 angles.
According to the given problem,
We know,
Sum of the interior angles of a polygon is,
Sum = 180° (n - 2) where n is the number of sides,
Here n = 6 , then
Sum = 180° × 4 = 720°
Let ∠ DEF be x
Therefore ∠ CDE = 2x,
Sum the interior angles,
⇒ 160 + 90 + 145 + 115 + 2x + x = 720
⇒ 510 + 3x = 720 ( subtracting 510 from both sides )
⇒ 3x = 210 ( dividing both sides by 3 )
⇒ x = 70
∠ CDE = 2x
= 2 × 70
= 140°
Hence, we can conclude, in the hexagon, the angle CDE is 140°.
Learn more about hexagon here:
https://brainly.com/question/2001860
#SPJ2
A ball is drawn from a bag of 26 red and 12 yellow balls. The process is repeated 50 times, replacing each ball that is drawn. Which of the following statements about the distributions of counts and proportions is true?A. The count of drawing a yellow ball is not a binomial distribution.B. The count of drawing a red ball is a binomial distribution.C. The distribution of the count of drawing a red ball cannot be approximated with a normal distribution D. The distribution of the count of drawing a yellow ball from a sample size of 10 can be approacimated with a normal distribution.
Answer:
B. The count of drawing a red ball is a binomial distribution.
Step-by-step explanation:
The count of drawing a red ball can be gotten by binomial distribution because:
the chance of success; p = 26/50 and chance of no failure; q = 24/50
For example, If we want to find probability of getting 5 red balls out of 20 selections, we will use the binomial probability distribution formula;
P(X = 5) = C(20, 5) × p^(5) × q^(20 - 5)
This same procedure also applies if we want to get the probability of getting a number of yellow balls out of a number of selections from the bag.
Looking at the options, the best option that explains how it's binomial probability that works is option B
Answer:b
Step-by-step explanation:
What is the surface area of an orange with a 3inch radius
Orange = sphere
S.A of sphere
= 4πr²
= 4 × π × r × r
[tex] = 4 \times \pi\times 3 \times 3[/tex]
[tex] = 36\pi[/tex]
Answer:
Step-by-step explanation:
the surface area of a sphere ( orange)
SA=4*3.14*r^2
radius=3
SA=4*3.14*3*3=113.04
What is the value of n in the equation below? a^n/a^3=a^9
3
6
12
27
O A. (-2, 1)
O B. (-2,-1)
O c. (-1,-2)
O D. (1.-2)
Answer:
the answer is C -1-2 to the equation
please awnser asap asap
Answer:
d) 280
Step-by-step explanation:
40320/3=6720
8720/24=280
Choose the rule to describe the transformation:
D(-3, -4), C(-3, -1), B(0, -4)
to
D '(3, -4), C '(3, -1), B '(0, -4)
a. reflection across the y-axis
b. reflection across y = -x
c. translation: (x,y)LaTeX: \longrightarrow⟶(x + 4, y)
d. reflection across y = x
Answer:
a. reflection across the y-axis
What is the total cost or sale price to the nearest cent?
$65 Jacket; 35% Discount
the area of square Garden is 625 metre square find its length its perimeter and find the cost of fencing it with 5 round at Rs 25 per metre
Answer:
Length=25m
Parameter=100m
5 round cost RS 12500
Step-by-step explanation:
The area of a square
=x²
According to the question the equation is
x²=625
x=√625
x=25
The parameter is
25×4
100 meter
So
1 meter costs 25
100 " " 25×100
2500
1 round = 100 meter
So
5 round cost 2500×5
12500
Baseball hat for
$22.90 at 5% sales tax
Answer:I got $21.76
Step-by-step explanation:
;-;
please help me i dont understand this
Answer:
Step-by-step explanation:
the range is the out put of the function.. what can y be.. in other words
so it's all real numbers... :)
Which of the following represents A U B?
(There's a venn diagram with a box around it
-in the box outside the diagram- 5, 11, 1, and 7
- in the circle labelled "A"- 3 and 9
-in the circle labelled "B"- 2, 4, 8, and 10
-in the middle portion where the circles overlap- 6 and 12)
Answer Choices
{6, 12}
{2, 3, 4, 6, 8, 9, 10, 12}
{1, 5, 7, 11}
{2, 3, 4, 8, 9, 10}
Answer:
Step-by-step explanation:
If Sin theta=3/4,find the value of cos theta
Answer:
[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Step-by-step explanation:
Given;
Sin θ = 3/4
To calculated Cos θ;
make a sketch of right-angled triangle with following sides;
opposite side = 3
hypotenuse side = 4
then, the adjacent side will be calculated from Pythagoras theorem;
let the adjacent side = b
b² = 4² - 3²
b² = 16 - 9
b² = 7
b = √7
Therefore, Cos θ is now calculated as;
Cos θ = adjacent / hypotenuse
Cos θ = √7/4
[tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Therefore, [tex]Cos \ \theta = \frac{\sqrt{7} }{4}[/tex]
Mofor bought 12 Avocados for $18. How many avocados can Stefan buy if he has $6
Answer:
4
Step-by-step explanation
Stefan can buy 4 apple with $6 because the apples are $1.50 each
Find the value of 3(5. 10 + 2).
Answer:
the value is
Step-by-step explanation:
=3(5.10+2)
=3(7.1)
=21.3
Answer:
3(5. 10+2)
Step-by-step explanation:
3(5.12)
3(60)
180
what is the answer for 5/8 ÷ 1/3
Answer:
15/8
5/8 ÷ 1/3
[Reciprocate the second fraction] =>
5/8 × 3/1
=>15/8
Answer:
1.875
as a fraction 15/8
Or
1 and 7/8
Siri told me.
Let V(t) represent the values of a bank account, in thousands dollars, t years after the account is opened at the bank. Determine whether each statement below is true
Complete question is;
Let V(t) represent the value of a bank account, in thousands of dollars, t years after the account is opened at the bank. Determine whether each statement below is true. Select True or False for each statement.
V(0) = 2 means that the value of the bank account when it is opened is $2000
V(5) = 2.2 means that 2.2 years after the bank account is opened, its value is $5000
V(10) – V(5) = 0.4 means that the bank account grows by $400 between 5 and 10 years after its opening
Answer:
Statement 1: True
Statement 2: False
Statement 3: False
Step-by-step explanation:
We are told that the function V(t) represents the value of a bank account, in thousands of dollars, t years after the account is opened at the bank.
This means that if V(10) = 50, it means that the bank account is valued after 10 years is $50,000
From this little explanation, it's clear that only statement 1 is correct.
Factor completely 3x^2+ 2x -1.
O (3x + 1)(x - 1)
O (3x + 1)(x + 1)
O (3x - 1)(x + 1)
O (3x - 1)(x - 1)
Answer:
option C
Step-by-step explanation:
[tex]3x^2+2x-1\\\\=(3x+a)(x+b)\\\\(3b+a)=2\\\\ab=-1[/tex]
and here we think of b=1 and a=-1
so we have
[tex](3x-1)(x+1)[/tex]
Describe the error in the simplification below.
2^4x2^5 = (2 • 2)4+5
= 49
Answer:
You need to multiply the exponents, then you can multiply the two factors.
Correct answer of the equation:
2^4 x 2^5, multiply exponents
16 x 32, multiply
= 512