Answer:
[tex]{ \tt{simple \: interest = }} \\ { \tt principle \times rate \times period}\\ \\ = 7850 \times 6.55\% \times 18 \\ { \tt{interest = 925515 \: dollars}}[/tex]
Answer:
$925,515
Step-by-step explanation:
multiply 7850 by 131/ 20 because 6.55 as a fraction is 131/20 and then multiply it by 18 and divide it by 20 which is the denominator of 131/20
What is the probability that a randomly selected day in the summer will be rainy if it’s cloudy?
Answer:
0.872
Step-by-step explanation:
Given that :
P(cloudy) = P(C) = 0.94
P(cloudy and rainy) = P(C n R) = 0.82
Probability that a given day will be rainy if it is cloudy ; this is a conditional probability problem:
Recall ; P(A|B) = P(AnB) / P(B)
P(R|C) = P(C n R) / P(C) = 0.82 / 0.94 = 0.872
Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a spring 30 centimeters. How much work is done in stretching the spring from 30 centimeters to 60 centimeters?
Answer:
The work done is 202.50Nm
Step-by-step explanation:
Given
[tex]F =450N[/tex]
[tex]x_1 = 30cm[/tex]
[tex]x_2 = 60cm[/tex]
Required
The work done
First, we calculate the spring constant (k)
[tex]F = kx_1[/tex]
[tex]450N = k *30cm[/tex]
[tex]k = \frac{450N}{30cm}[/tex]
[tex]k =15N/cm[/tex]
So:
[tex]F = kx_1[/tex]
[tex]F(x) = 15x[/tex]
The work done using Hooke's law is:
[tex]W =\int\limits^a_b {F(x)} \, dx[/tex]
This gives:
[tex]W =\int\limits^{60}_{30} {15x} \, dx[/tex]
Rewrite as:
[tex]W =15\int\limits^{60}_{30} {x} \, dx[/tex]
Integrate
[tex]W =15 \frac{x^2}{2}|\limits^{60}_{30}[/tex]
This gives:
[tex]W =15 *\frac{60^2 - 30^2}{2}[/tex]
[tex]W =15 *\frac{2700}{2}[/tex]
[tex]W =15 *1350[/tex]
[tex]W =20250N-cm[/tex]
Convert to Nm
[tex]W =\frac{20250Nm}{100}[/tex]
[tex]W =202.50Nm[/tex]
What is the equivalent recursive definition for an = 12+ (n - 1)3?
A. a1 = 3, An = An-1 + 12
B. a1 = 12, An = 30n-1
C. a1 = 12, Un = On-1 +3
D. a1 = n, an= 1201-1+3
Answer:
[tex]A_1 = 12[/tex]
[tex]A_n = A_{n-1} + 3[/tex]
Step-by-step explanation:
Given
[tex]A_n =12+(n-1)3[/tex]
Required
Write as recursive
We have:
[tex]A_n =12+(n-1)3[/tex]
Open bracket
[tex]A_n =12+3n-3[/tex]
[tex]A_n =12-3+3n[/tex]
[tex]A_n =9+3n[/tex]
Calculate few terms
[tex]A_1 =9+3*1 = 9 + 3 = 12[/tex]
[tex]A_2 =9+3*2 = 9 + 6 = 15[/tex]
[tex]A_3 =9+3*3 = 9 + 9 = 18[/tex]
The above shows that the rule is to add 3.
So, we have:
[tex]A_1 = 12[/tex]
[tex]A_n = A_{n-1} + 3[/tex]
Answer the following.
A bag contains, 4, green balls 3 red balls, 6 yelow and 5 pink balls. A ball is
selected at random and not relased. The ball is green. What is the probably
of selecting another green be?
Express the answer as a frection |
Engress the answer as a decimal to three deomal places
ELess this answer as a percentage to the nearest Wacle number
Answer:
[tex]\frac{3}{17}, \\0.176, \\18\%[/tex]
Step-by-step explanation:
The area a total of 4+3+6+5=18 balls, consisting of:
4 green3 red6 yellow5 pinkAfter a green ball is selected (implied that it is not replaced or put back), there will be 17 balls total, consisting of:
3 green3 red6 yellow5 pinkTherefore, the probability of drawing another green one is:
[tex]\boxed{\frac{3}{17}=0.176=18\%}[/tex]
A stamp gets more expensive each year. It increases in value by 60 % each year. Wha
is the growth FACTOR?
9514 1404 393
Answer:
1.60
Step-by-step explanation:
The growth factor is 1 more than the growth rate:
1 + 60% = 1 + 0.60 = 1.60 = growth factor
Suppose a quadratic equation is given as follows:
(k – 1)x² + x + 1 = 0
Select all values of k for which the above equation has two real and unequal roots
0
.25
0.5
0.75
1
1.25
1.5
1.75
Answer:
k>1.25
Step-by-step explanation:
The given quadratic equation is :
(k – 1)x² + x + 1 = 0
We need to find all values of k for which the above equation has two real and unequal roots.
For a quadratic equation ax²+bx+c=0, for real and unequal roots,
b²-4ac>0
Here, a = (k-1), b = 1 and c = 1
Put all the values,
1²-4×(k-1)1>0
1-4k+4>0
5-4k>0
k>1.25
S, k can take values more than 1.25. Hence, it can take values 1.5, 1.75.
Alice has a total of 12 dimes and nickels.She h as 2 more nickels than dimes. Write an equation
Answer:
Step-by-step explanation: She has 2 more nickels then dimes not 2 times more therefore answers B and D are incorrect. C is incorrect because it has that there are 2 more dimes than nickels. A is correct because it says that there are c dimes, and then c +2 nickels.
3. The simple interest on $6,000 for 4 years is $1,680. *
A company that manufactures vehicle trailers estimates that the monthly profit for selling its midsize trailer is represented by function p, where t is the number of trailers sold. p(t)= -25t^3+625t^2-2500t Use the key features of function p to complete these statements. The company makes a profit when it sells _____trailers. The maximum profit of approximately $____ occurs when it sells approximately____ trailers.
Answer:
The answer is below
Step-by-step explanation:
The profit equation is given by:
p(t)= -25t³+625t²-2500t
The maximum profit is the maximum profit that can be gotten from selling t trailers. The maximum profit is at point p'(t) = 0. Hence:
p'(t) = -75t² + 1250t - 2500
-75t² + 1250t - 2500 = 0
t = 2.3 and t = 14.3
Therefore t = 3 trailers and t = 15 trailers
p(15) = -25(15³) + 625(15²) - 2500(15) = 18750
Therefore the company makes a maximum profit of approximately $18750 when it sells approximately 15 trailers.
Answer:
See below
Step-by-step explanation:
Since t is number of trailers, the domain includes only those values greater than 0.
On the relevant domain, the graph crosses the x-axis at the points (5,0) and (20,0). Between these points, the value of p(t) is positive. So the company makes a profit when it sells between 5 and 20 trailers.
On the positive interval between these points, the graph reaches a relative maximum when t roughly equals 14 and p(t) roughly equals $19,000.
So the maximum profit of approximately $19,000 occurs when it sells approximately 14 trailers.
find the derivative
f (x ) = (x-5)^2 (3-x)^2
Given:
The function is
[tex]f(x)=(x-5)^2(3-x)^2[/tex]
To find:
The derivative of the given function.
Solution:
Chain rule of differentiation:
[tex][f(g(x))]'=f'(g(x))g'(x)[/tex]
Product rule of differentiation:
[tex][f(x)g(x)]'=f(x)g'(x)+g(x)f'(x)[/tex]
We have,
[tex]f(x)=(x-5)^2(3-x)^2[/tex]
Differentiate with respect to x.
[tex]f'(x)=(x-5)^2\dfrac{d}{dx}(3-x)^2+(3-x)^2\dfrac{d}{dx}(x-5)^2[/tex]
[tex]f'(x)=(x-5)^2[2(3-x)(0-1)]+(3-x)^2[2(x-5)(1-0)][/tex]
[tex]f'(x)=(x^2-10x+25)(-6+2x)+(9-6x+x^2)(2x-10)[/tex]
[tex]f'(x)=(x^2)(-6)+(-10x)(-6)+(25)(-6)+(x^2)(2x)-10x(2x)+25(2x)+(9)(2x)+(-6x)(2x)+x^2(2x)+9(-10)+(-6x)(-10)+x^2(-10)[/tex]
On further simplification, we get
[tex]f'(x)=-6x^2+60x-150+2x^3-20x^2+50x+18x-12x^2+2x^3-90+60x-10x^2[/tex]
[tex]f'(x)=(2x^3+2x^3)+(-6x^2-20x^2-12x^2-10x^2)+(60x+50x+18x+60x)+(-90-150)[/tex]
[tex]f'(x)=4x^3-48x^2+188x-240[/tex]
Therefore, the derivative of the given function is [tex]f'(x)=4x^3-48x^2+188x-240[/tex].
Choose which two numbers the following will fall between: *
V156 PLEASE HELP ME FASTTTTT
[tex]\sf\purple{A.\:Between \:12\:and\:13.}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \sqrt{156} \\ = 12.4899 \\ = 12.49[/tex]
Therefore, [tex] \sqrt{156} [/tex] will fall in between 12 and 13.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
Find the area of the sector in
terms of pi.
90°
24
Area = [?]
Enter
Step-by-step explanation:
area of a circle is r x r x pi
so one quarter of it us r x r x pi /4
I need help with this pls help and write the Correct answer
what is the mean mark of 847 ÷ 30?
Answer:
Step-by-step explanation:
What is the remainder of 26 divided by 53.3
WILL GIVE BRAINLIEST
Answer:
0.48780487804
Use the following image to determine the measure of arc GH.
Answer:
Arc GH = 78°
Step-by-step explanation:
Inscribed angle = m<GIH = 39°
Measure of arc related to inscribed angle = arc GH = ?
Thus:
m<GIH = ½(arc GH) => Inscribed angles theorem
Substitute
39° = ½(arc GH)
Multiply both sides by 2
2*39° = arc GH
78° = arc GH
Arc GH = 78°
3p(2p - 9) - 2p(-9 + p)
Answer:
4p² - 9p
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
3p(2p - 9) - 2p(-9 + p)
Step 2: Simplify
[Distributive Property] Distribute 3p: 6p² - 27p - 2p(-9 + p)[Distributive Property] Distribute -2p: 6p² - 27p + 18p - 2p²[Subtraction] Combine like terms (p²): 4p² - 27p + 18p[Addition] Combine like terms (p): 4p² - 9p1 squared + 1= 2 sqaured - 2
2 sqaured + 2 = 3 squared - 3
3 squared + 3= 4 squared - 4
a) make a conjecture about this pattern. write your conjecture in words
b) generalise your conjecture for this pattern
c) prove that your conjecture is true
Answer:
It would be the letter B :)
Explain why in a drawer containing only two different colors of socks one must draw only three socks to find a matching pair
An item was marked down 64% from its original price, x. The amount discounted was $30. Which equation can be
used to find the original price?
0.64(x) = 30
0.64(30) = x
30 +0.64 = x
x + 0.064 = 30
Answer:
0.64(x) = 30
Step-by-step explanation:
Hope that's correct.
A circular sinkhole has a radius of 12 meters. A week later, it has a diameter of 48 meters. How much greater is the circumference of the sinkhole compared to the previous week?
Answer:
B
Step-by-step explanation:
1) initial circumference
radius * 2 * pi = 24 * pi = 75,398224
2) final circumference
diameter * pi = 48 * pi = 150,796447
150,796447 - 75,398224 = 75.36 m
Katy runs a day care center . So far this year , the enrollment has consisted of 2 toddlers and 8 children of other ages . Considering this data, how many of the next 20 children to enroll should you expect to be toddlers?
Answer:
You should expect 4 of the next 20 children to enroll to be toddlers.
Step-by-step explanation:
This question is solved by proportions.
So far:
We have that of 2 + 8 = 10 children, 2 are toddlers, so the proportion of toddlers is 2/10 = 0.2.
How many of the next 20 children to enroll should you expect to be toddlers?
0.2 out of 20, so: 0.2*20 = 4
You should expect 4 of the next 20 children to enroll to be toddlers.
Solve the solution as an ordered pair
X + 9 = y
X = 4y - 6
Answer:
-10, -1
Step-by-step explanation:
See Image below:)
HELP ME ON THIS I HAVE MORE.
Answer:
The answer is 5 units.
Step-by-step explanation:
I just counted the squares
Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.
Let n represent the interger l, the three consective intergers are represented by
[tex]n[/tex]
[tex]n + 2[/tex]
[tex]n + 4[/tex]
The second one represent
[tex](n + 2) {}^{2} + 76 =( n + 4) {}^{2} [/tex]
Simplify both sides
[tex]n {}^{2} + 4n + 4 + 76 = {n}^{2} + 8n + 16[/tex]
[tex] {n}^{2} + 4n + 4 = {n}^{2} + 8n - 60[/tex]
[tex]4n + 4 = 8n - 60[/tex]
[tex]4n + 64= 8n[/tex]
[tex]64= 4n[/tex]
[tex]n = 16[/tex]
The intergers are 16,18,20
the sumof 8pq and -17 pq is
Answer:
= -9pq
Step-by-step explanation:
=8pq + (-17pq)
=8pq-17pq
= -9pq
NO LINKS!!!
What is the volume of this solid?
220 cubic units.
Answer:
Solution given:
for small cylinder
r=1
and for large cylinder
R=5+1=6
height for both [h]=2
Now
Volume of solid=πR²h-πr²h=πh(R²-r²)
=3.14*2(6²-1²)=219.8 =220 units ³.
Small cylinder is r=1
Large cylinder is R= 5+1 =6
Height (h) =2
Volume of solid,
→ πR²h-πr²h
→ πh(R²-r²)
→ 3.14 × 2(6²-1²)
→ 219.8
→ 220 cubic units
Powers are repeated ___________________.
multiplications
mark me brainliesttt :))
wich one is the answer
A privately owned lake contains two types of game fish, bass and trout. The owner provides two types of food, A and B, for these fish. Bass require 2 units of food A and 4 units of food B,
and trout require 5 units of food A and 2 units of food B. If the owner has 400 units of each food, find the maximum number of fish the lake can support.
fish
Need Help?
Read
Watch it
Answer:
133 fishes
Step-by-step explanation:
Units of food A = 400 units
Units of food B = 400 units
Fish Bass required 2 units of A and 4 units of B.
Fish Trout requires 5 units of A and 2 units of B.
i. For food A,
total units of food A required = 2 + 5
= 7 units
number of bass and trout that would consume food A = 2 x [tex]\frac{400}{7}[/tex]
= 114.3
number of bass and trout that would consume food A = 114
ii. For food B,
total units of food B required = 4 + 2
= 6 units
number of bass and trout that would consume food B = 2 x [tex]\frac{400}{6}[/tex]
= 133.3
number of bass and trout that would consume food B = 133
Thus, the maximum number of fish that the lake can support is 133.
