Answer:
The sum of money deposited is approximately $22,021.74
Step-by-step explanation:
The given interest and amounts of the deposit are outlined as follows;
The simple interest per annum, R = 0.325%
The number of years the money is deposited, T = 4 years
The total amount received (Interest + Initial deposit), A = $50,650
We have;
I = P × R × T
Where;
P = The principal (initial amount deposited)
R = The (annual) interest rate = 0.325%
T = The time = 4 years
Therefore;
The total amount received, A = P + I
P + I = P + P × R × T = P × (1 + R × T)
∴ A = P + I = P × (1 + R × T)
P = A/(1 + R × T)
Plugging in the values, gives;
P = 50,650/(1 + 0.325 × 4) = 506,500/23 ≈ 22,021.74
The sum of money deposited, P = $22,021.74
Assume that AABC= APQR. Which of the following congruence statements
are correct? Check all that apply.
U
A. ACS PQ
B. ZREZC
C. BC = PQ
D. ZB=
U
E. BC = QR
O F. ZA= 20
Answer:
Options B, D, E
Step-by-step explanation:
If triangle ABC and triangle PQR are congruent,
∠A ≅ ∠P
∠B ≅ ∠Q
∠C ≅ ∠R
AB ≅ PQ
BC ≅ QR
AC ≅ PR
Therefore, Options B, D, E are the correct options.
Bryon is solving the equation 22 - 6x = 15. He gets to 7 = 62. Is this a valid way to solve the equation?
Answer:
No
Step-by-step explanation:
22 - 6x = 15
subtract 22 from both sides
-6x = -7
divide both sides by -6
x = 7/6 or 1 1/6
The quantity of an element is decaying over time such that the amount of material at
any time is given by the function S(t) = 1000(0.9)3t. Write an equivalent function
of the form S(t) = abt.
Answer:
S(t) = 1000(0.729)^t
Step-by-step explanation:
S(t) = 1000(0.9)^(3t)
S(t) = 1000((.09)^(3))^t
S(t) = 1000(0.729)^t
For the pair of similar triangles, find the value of x.
Answer: The value of x is 184.
Step-by-step explanation:
According to the similar right angled triangle properties, the product of same side of triangles is equal to the another side product.
Now calculating the value of x for the given pair of similar triangles.
According to the given figure:
24 × (2x - 8) = 45 × (x + 8)
(24 × 2x) - (24 × 8) = (45 × x) + (45 × 8)
48x - 192 = 45x + 360
48x - 45x = 360 + 192
3x = 552
x = 184
Thus, the value of x is 184.
Rotate triangle P 90° clockwise about the point (2, -1).
Answer:
Step-by-step explanation:
If we are rotating about the point (2,-1) , then we first need to translate the triangle two points to the left so that point P is at location (2,-1). Once we have that we rotate everything 90 degrees clockwise, while maintaining the same distance and angles between each point in the triangle. After doing this we will get the triangle seen in the attached picture below. Which is fully rotated 90 degrees clockwise about the point (2,-1)
what is the area of the figure below?
Answer:
61
Step-by-step explanation:
n3=8/125 for n n= ???
Answer:
2/25
Step-by-step explanation:
[tex]n^3 = \frac{8}{125}[/tex]
[tex]n^3 = (\frac{2}{5})^3[/tex]
[tex]n = \sqrt[3]{n^3} = \sqrt[3]{(\frac{2}{25})^3}[/tex]
[tex]n = \sqrt[3]{(\frac{2}{25})^3}[/tex]
[tex]n = \frac{2}{25}[/tex]
PLEASEEEEEEEE HELPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
1.009, 1.09, 1.7, 1.7082
Step-by-step explanation:
hope this helped.
if 5x-26=x+50, then what is the value of x
Answer:
x = 19
Step-by-step explanation:
5x - 26 = x + 50
Subtract x on both sides of the equation.
4x - 26 = 50
Add 26 on both sides.
4x = 76
Now, divide by 4 on both sides.
x = 19
Answer:
x = 19
Step-by-step explanation:
5x-26=x+50
5x = 76 +x
4x = 76
x = 19
Find csc 0, sin 0, and cot 0, where is the angle shown in the figure.
Give exact values, not decimal approximations.
PLZ HELP I BEEN STUCK FOR AN HOUR I WILL MARK BRAINLIEST!!!
Answers:
[tex]\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
=============================================
Explanation:
Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem
[tex]a^2+b^2 = c^2\\\\4^2+b^2 = 7^2\\\\16+b^2 = 49\\\\b^2 = 49-16\\\\b^2 = 33\\\\b = \sqrt{33}[/tex]
The vertical side is [tex]\sqrt{33}[/tex] units long.
------------------------------------
The side we just found is the opposite side to angle [tex]\theta[/tex] (greek letter theta)
The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.
Divide the hypotenuse over opposite to get the cosecant.
[tex]\csc(\theta) = \frac{\text{hypotenuse}}{\text{opposite}}\\\\\csc(\theta) = \frac{7}{\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33*33}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{\sqrt{33^2}}\\\\\csc(\theta) = \frac{7\sqrt{33}}{33}\\\\[/tex]
Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.
------------------------------------
Recall that sine is the reciprocal of cosecant, and vice versa.
So we'll use the same idea as before, but flip the original fraction.
[tex]\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(\theta) = \frac{\sqrt{33}}{7}\\\\[/tex]
The denominator is already a rational number, so there's not much else to do here.
--------------------------------------
Cotangent is the ratio of adjacent over opposite
[tex]\cot(\theta) = \frac{\text{adjacent}}{\text{opposite}}\\\\\cot(\theta) = \frac{4}{\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33}*\sqrt{33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33*33}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{\sqrt{33^2}}\\\\\cot(\theta) = \frac{4\sqrt{33}}{33}\\\\[/tex]
The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).
Identify the diameter of the circle. Then find the circumference. Round to two decimal places. (C = 2*pi*r)
Answer:
diameter=22
circumference=22pi
Step-by-step explanation:
diameter=2*radius
so 2*11=22
circumference=2pi*r
=2*11*pi
=22pi
Green Red Blue Yellow
Event A: lands on yellow.
Event B: lands on green.
Events A and B are_______ events.
Answer:
independent
Step-by-step explanation:
Answer:
Disjointed
disjointed events: events that have no outcomes in common
so that's why it is disjointed
Calculate the volume of this planter box in cubic centimeters.
If there are four of these planter boxes, would they fit in a 1 square meter area near the back
door? Show calculations to explain your answer.
(Pictures Attached)
Answer:
V=786,240cm³
Step-by-step explanation:
Volume=Length × base × height
v= 52cm×42cm×360cm
Hi can someone please help me with this thanks
What is the value of f(1)?
A. 0
B. 1
C. 2
D. 4
Answer:
The value of f(1) is A. 0
Step-by-step explanation:
In this question, when they ask what is the value of f(1), they want you to tell them what is the "y" coordinate of the point with the "x" coordinate equal to 1. In our case, the point with the "x" coordinate equal to 1 has the "y" coordinate equal to 0. Therefore, the value of f(1) is A. 0
Express in roster form. Set of B is the set of all elements x such that x is an element of natural numbers and x is a multiple of 8
Answer:
[tex]B = \{8, 16, 24, 32, 40, ...... \}[/tex]
Step-by-step explanation:
Given
[tex]x \to[/tex] element of natural number
[tex]x \to[/tex] multiple of 8
Required
Express in roster form
[tex]Natural[/tex] [tex]numbers[/tex] are 1, 2, 3, 4, 5, 6, ......
[tex]Natural[/tex] [tex]numbers[/tex] that are multiples of 8 are 8, 16, 24, 32, 40, ......
So, the set in roster form is:
[tex]B = \{8, 16, 24, 32, 40, ...... \}[/tex]
Algorithm to accept the height of a building in metres and convert it into centimetres.Also draw the flowchart
Answer:
1200cm
Step-by-step explanation:
Given data
We know that 1meter is equivalent to 100cm
i,.e 1*100
so, if height is 1.2meters
Height in centimeters is 1.2*100
Hence height in centimeters is 1200cm
please help i have no clue what i’m doing
Answer:
x = 24
x = 20
Step-by-step explanation:
x/3 - 2 = 6
Add 2 to both sides
x/3 = 8
multiply both sides by 3
x = 24
-----------------------------
x/5 +1 = 5
Subtract 1 from both sides
x/5 = 4
multiply both sides by 5
x = 20
Answer:
1. add two both sides and then multiply by 3 each side to get to the answer of 24.
Check: 24/3 = 8 - 2 = 6
2. x/5 + 1 = 5
subtract 1 from each side and then multiply by 4 on each side to get to the result of 20.
check: 20/5 is 4 + 1 = 5
Brainlist please :)
Each year the Mannel Department Store has a big end-of-summer
sale. At the sale, they give customers an additional 25% off on all
marked-down merchandise.
a. A beach towel had an original price of $22.00. It was marked
down 10%. What is the final price after the additional
25% discount?
b. A patio table and four chairs originally cost $350.00. They were
marked down 50%. What is the final cost of the table and chairs
with the additional discount?
Answer:
Es ydjwj rjsbt djeiweke
Arianna earns a weekly salary of $400 plus a 6.5% commission on sales at a gift shop. How much would she make in a workweek if she sold $4800 worth of merchandise?
Answer:
712
Step-by-step explanation:
400+6.5%of 4800
312+400=712
Tanya has 130 ml of juice
Answer:
The answer is below
Step-by-step explanation:
A drink is made by adding water to juice.
Instructions
Add an amount of water that is between 3 times and 5 times the amount of juice
Tanya has 130 ml of juice.
If she follows the instructions, work out the minimum and maximum amounts
of the drink she can make.
Solution:
The minimum amount of water that can be added to the juice is 3 times the amount of the juice, hence:
Minimum amount of water = 3 * 130 ml of juice = 390 ml of water
Therefore minimum amount of drink = 390 ml of water + 130 ml of juice
minimum amount of drink = 520 ml
The maximum amount of water that can be added to the juice is 5 times the amount of the juice, hence:
Maximum amount of water = 5 * 130 ml of juice = 650 ml of water
Therefore maximum amount of drink = 650 ml of water + 130 ml of juice
Maximum amount of drink = 780 ml
draw the graph of the equation 3x-4y=12 from the graph find the value of y when x= 8
Answer:
y = 3
Step-by-step explanation:
3x - 4y = 12
3(8) - 4y = 12
24 - 4y = 12
- 4y + 24 = 12
- 4y + 24 - 24 = 12 - 24
- 4y = - 12
- 4y ÷ - 4 = - 12 ÷ - 4
y = 3
Slope: [tex]\frac{3}{4}[/tex]
y - intercept: (0, - 3)
what is the correct measure of m? 15, 5, n, m
Answer:
subtract 5 , m=(-15)
Step-by-step explanation:
15-5
=10
n:
5-10
=(-5)
m:
(-5)-10
=(-15)
hope it help
A population of bacteria contains 150 bacteria in generation 1 and triples in
population every generation. This sequence represents the number of
bacteria for the first few generations:
Wait, is this a question?
150
450
1,350
Sorry if that's not the question lol
Please give real answers with an explaination. 50 points + 5-star rated. No Docs/No Files/No Links only answer with explaination.
Answer:
x = 135°
Step-by-step explanation:
4 sides and the diagonal are the same.
Therefore, it is square with each interior angle = 90°
The diagonal bisects the interior angle to 45° , 45°
x + 45° = 180° [ straight line angle ]
x = 180 - 45 = 135°
Answer plzzzzz and No links
Answer:
384 in^2
Step-by-step explanation:
Surface Area (or SA for short) formula:
SA=2lw+2lh+2hw
(l=length, w= width, h= height)
9*12=108*2=216
9*4=36*2=72
12*4=48*2=96
216+72+96=384
Answer:384 in^2
Hope this helps!
Which expression is equivalent to 44+100 as the product of GCF and sum?
A.5(8+20)
B.4(40+96)
C.2(22+50)
D.4(11+25)
*explain how you got the answer!*
Answer:
C.
Step-by-step explanation:
First you solve the bracket...
(22+50)= 72
72×2=144
Answer:
the answer is D because it has to greatest factor
A (5(8+20)=40+100
B (4(40+96)=160+384
C (2(22+50)=44+100
D (4(11+25)=44+100
please help me I will mark as a brainliest
Answer:
think that this might help you
5
8
y
Find the exact value of y.
y =
Answer:
[tex]y=2\sqrt{10}[/tex]
Step-by-step explanation:
By applying geometric mean theorem in the given right angle,
[tex]\frac{AD}{DB}=\frac{DB}{CD}[/tex]
By substituting values in the given ratio,
[tex]\frac{5}{y}= \frac{y}{8}[/tex]
[tex]y^2=8\times 5[/tex]
[tex]y^2=40[/tex]
[tex]y=2\sqrt{10}[/tex]
Exact value of y is [tex]2\sqrt{10}[/tex].
A pool was filled with 8.2 times 10 Superscript 3 gallons from one hose and 9.4 times 10 Superscript 3 gallons from another hose.
What is the total amount of water in the pool? Express the answer in scientific notation.
1.76 times 10 Superscript 2 gallons
17.6 times 10 Superscript 2 gallons
17.6 times 10 Superscript 3 gallons
1.76 times 10 Superscript 4 gallons
Answer:
1.76 x 10⁴ gallons
Step-by-step explanation:
8.2 x 10³ + 9.4 x 10³ = 17.6 x 10³
Although correct 17.6 x 10³ is not in scientific notation
which is
1.76 x 10⁴ gallons
Answer:
D.
Step-by-step explanation: