Answer:
[tex]3\%[/tex] p.a.
Step-by-step explanation:
The formula for simple interest is [tex]I=PRT[/tex] ([tex]I =[/tex] interest, [tex]P =[/tex] principal, [tex]R =[/tex] rate)
First, let's express the interest earned in one and three years:
[tex]I_{1} = PRT_{1}[/tex] (finding the interest earnt in one year)
[tex]I_{1} = \$ 500\times R \times 1[/tex]
[tex]=\$ 500R[/tex]
[tex]I_{2} = PRT_{2}[/tex] (finding the interest earnt in three years)
[tex]I_2 = \$ 500 \times R \times 3[/tex]
[tex]=\$ 1500R[/tex]
From the information "The difference between the total interest earned after 3 years and the total interest earned after 1 year is $30", we can write:
[tex]I_{2}-I_{1} = \$ 30[/tex]
[tex]\$ 1500R - \$500 R = \$ 30[/tex]
[tex]\$ 1000R = \$ 30[/tex]
[tex]R = 0.03[/tex]
[tex]=3\%[/tex] p.a.
∴ The annual interest rate is [tex]3\%[/tex]
Hope this helps :)
The annual interest rate if You deposit $500 in an account that earns simple interest. The difference between the total interest earned after 3 years and the total interest earned after 1 year is $30 is 3%.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
The principal amount, P = $500,
Time, t = 1 year and T = 3 year,
Calculate the interest by the formula given below,
[tex]SI = P\times R\times T / 100[/tex]
Here, SI is the simple interest.
So for 1 year time,
Substitute the values,
SI = 500 × R × 1 / 100
SI = 5R
Now for 3 year
SI = 15R
But 15R - 5R = 30 (Given in question)
R = 3%
Therefore, the annual interest rate if You deposit $500 in an account that earns simple interest. The difference between the total interest earned after 3 years and the total interest earned after 1 year is $30 is 3%.
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I need Help Pleaseeee
Answer:
m∠C = 54°, m∠CDB = 100°
Step-by-step explanation:
in ΔABC, m∠A= 37° and m∠B = 89°
The sum of all 3 angles in any triangle is 180° so
m∠C = 180-37-89 = 54°
m∠CDB = 180-80 = 100° because any line has a 180°angle
CALCULATE PR :)
Merry Xmas btw
Answer:
PR = 7.9
Step-by-step explanation:
By sine rule:
[tex] \frac{12.5}{ \sin \: 66 \degree} = \frac{PR}{ \sin \: 37 \degree} \\ \\ \frac{12.5}{ 0.9135454576} = \frac{PR}{ 0.6018150232} \\ \\ PR = \frac{12 \times 0.6018150232}{0.9135454576} \\ \\ PR = \frac{12 \times 0.6018150232}{0.9135454576} \\ \\PR = \frac{7.22178028}{0.9135454576} \\ \\ PR = 7.90522269 \\ \\ PR \approx \: 7.9[/tex]
Una casa de dos plantas esta construida en un terreno rectangular de 66m² , tal como lo muestra los siguientes pasos si x es el frente de la casa y x+5 el largo. De la ecuacion cuadratica que define el area del terreno es x² + 5x-66=0 ¿Cuanto mide el frente de la casa?
Answer:
El frente de la casa es 6 metros.
Step-by-step explanation:
El area de la casa está dada por el área de un rectángulo:
[tex]A = f*l = x (x+5) = 66[/tex]
En donde f es el frente = x , l es el largo = x+5 y A es el área = 66m²
Si la ecuación cuadrática que define el área del terreno viene dado por:
[tex] x^{2} + 5x - 66 = 0 [/tex]
Resolviendo la ecuación cuadrática para x tenemos:
x₁ = -11 y x₂ = 6
Tomando el valor positivo, podemos decir que el frente de la casa es 6 metros.
Espero que te sea de utilidad!
PLEASE HELP ME I DONT UNDERSTAND
Answer:
[tex]d=4\sqrt{5}[/tex]
Step-by-step explanation:
Write down both endpoint coordinate points:
[tex](-5,-3)(-1,5)[/tex]
Use the distance formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2} \\\\(x_{1},y_{1})(x_{2},y_{2})[/tex]
Insert values:
[tex]d=\sqrt{(-1-(-5))^2+(5-(-3))^2} \\\\d=\sqrt{(-1+5)^2+(5+3)^2}[/tex]
Simplify parentheses:
[tex]d=\sqrt{(4)^2+(8)^2}[/tex]
Simplify exponents:
[tex]d=\sqrt{16+64}[/tex]
Add:
[tex]d=\sqrt{80}[/tex]
Find the square root. Find multiples of 80 that are perfect squares:
[tex]16*5=80\\\\\sqrt{16*5}\\\\\sqrt{16}*\sqrt{5} \\\\[/tex]
[tex]d=4\sqrt{5}\\\\d=8.94427190...[/tex]
:Done
Rewrite using radicals
Answer:
√7; ∛13²; ⁵√x³; and the last is b root of m to the power of a
Step-by-step explanation:
When you take a number to the power of a fraction, you write it as the root of the denominator to the power of the numerator. The denominator is the bottom number and the numerator is the top number.
A local animal shelter has 600 cats and dogs. There are 2 times more cats than dogs. Let x represent the number of cats and let y represent the number of dogs. Which system of equations represents this situation?
Answer:
2x + y = 600
Step-by-step explanation
Answer:
1,200x + 600y or 2x + y= 600
Step-by-step explanation:
knowing that there are 600 cats and 2 times the amount of cats we will have 1,200 cats which is 1,200x + 600y
How many baby's does it take to paint a wall
Answer:
12 I think?
Step-by-step explanation:
The answer to the famous joke is "It depends on how hard you throw them." It's important to note that this joke is dark humor and can be considered offensive or inappropriate.
It plays on a shocking and insensitive idea, which is why it's not suitable for all audiences. Jokes like this should be used with extreme caution, as they can cause discomfort or distress to others.
Humor should be inclusive and respectful of everyone's feelings and sensitivities. While jokes can be a form of entertainment, it's essential to choose them wisely and be mindful of their potential impact on others. In most social settings, it's best to avoid jokes that involve sensitive subjects or potentially harmful content.
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------------The given question is incomplete, the complete question is:
"What is the answer to the famous joke, "How many babies does it take to paint a wall?"---------------
For an end-of-year party, Ms. Wilson purchased 98 stickers and 56 lollipops. Each student will receive an equal number of stickers and an equal number of lollipops. There will be no stickers or lollipops leftover.
Based on this information, what is the greatest number of students that Ms. Wilson can have in her class?
Answer:
14 i think
Step-by-step explanation:
tbh, just guess and check
98/7=14 each student gets 7 stickers
56/14=4 each student gets 4 lollipops
there are 14 students.
The product of t and 6 is greater than 12
Answer:
A possible answer for t could be 3
Step-by-step explanation:
I honestly don't know if this is right, but yeah here ya go!
All values of t which are greater than 2 , are the solutions of given inequality.
Inequality :It is given that,
The product of t and 6 is greater than 12.
So that, inequality is,
[tex]6*t > 12[/tex]
Divide both side by 6.
[tex]6*t > 12\\\\t > \frac{12}{6} \\\\t > 2[/tex]
Therefore, all values of t which are greater than 2 , are the solutions of given inequality.
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Help hep help hep plz plz plz
Answer:
w=4
Step-by-step explanation:
.Draw a quadrilateral in the Cartesian plane, whose vertices are (– 4, 5), (0, 7), (5, – 5) and (– 4, –2). Also, find its area.
Answer:
Part 1
The drawing of the quadrilateral is included here
Part 2
The area of the quadrilateral is 60.5 unit²
Step-by-step explanation:
Part 1
Please find attached the given drawing of the quadrilateral created with Microsoft Excel
Part 2
The given quadrilateral ABCD comprises of a trapezium AECD and triangle ABE
The height of the trapezium, h₁ = 4 units
For segment BC, we have;
The slope = (-5 - (-2))/(5 - (-4)) = -1/3
The equation of the line BC in point and slope form is y - (-5) = -1/3×(x - 5)
Which gives;
y = -1/3×(x - 5) - 5 = -x/3 + 5/3 - 5 = -x/3 - 10/3
The y-intercept is (0, -10/3)
The lengths of the opposite parallel sides of the trapezium AECD are;
a = 5 - (-2) = 7 and b = 7 - (-10/3) = 31/3
The area of the trapezium AECD = ((a + b)/2) × h₁ = ((7 + 31/3)/2) × 4 = 104/3 unit²
The height of triangle
The area of ABE, h₂ = 5
The base of triangle ABE = b = 31/3
The area of triangle ABE = 1/2 × b × h₂ = 1/2 × 31/3 × 5 = 155/6 unit²
The area of quadrilateral ABCD = The area of the trapezium AECD + The area of triangle ABE
∴ The area of quadrilateral ABCD = 104/3 unit² + 155/6 unit² = 60.5 unit².
1. If an item is discounted 20%, the sale price is what percent of the original price?
2. If the original price of the item is $400, what is the dollar amount of the discount?
3. How much is the sales price?
Answer:
1. it would be 80% of the original price
2.400×.20=$80
80 dollars would be the amount you would discount from the original price.
3.the sales price is $320
400-80=320
Step-by-step explanation:
Hope this helped :)
also hi!
NEED HELP ASAPPP!!
A sales promotion for Christmas is advertising all PS5 games for $45.25 per game, up to 6 games, with a $10 subscription fee. The total cost, y, for x number of PS5 games can be modeled by a linear function.
What is the range of the function for this situation?
A. {0,1, 2, 3, 4, 5, 6}
B. {0,55.25, 100.50, 145.75, 191.00, 236.25, 281.50}
C. 0 ≤ y ≤ 281.50
D. 0 ≤ x ≤ 6
Answer:
0 ≤ y ≤ 281.50
Step-by-step explanation:
i did the math
How much interest would $4000 earn in one year at a rate of 3.2%?
In a party Tom paid $540 including the cake and drink for his friend the cost of a person attending the party is $15 the cost of cake and drinks are $75 and $90 respectively find the number of friends that attended the party
Sylvia and Patrick plotted the information they gathered on the weight of cars and the mileage they get. Then they each drew a line on the graph that they felt best fit the data. Sylvia’s line is a line of best fit because her line is close to most of the data points . Patrick’s line is not a line of best fit as his line does not fit the data points exactly .
Answer:
Sylvia’s line is a line of best fit because her line is close to most of the data points. Patrick’s line is not a line of best fit as his line is not close enough to all the data points.
Delvin is 14 years old. His age is 2 times his brothers age plus 6. Write an
equation then solve to find the value of b, Delvin's brothers age. *
2b - 6 = 14b = 10
2b + 6 = 14 b = 4
2b - 14 = 6 b = 10
Answer:
2b+6=14, b=4
Step-by-step explanation:
maths
y varies directly with x. If x= 1 and y = 0.25 what is y if x = 9
Type your answer...
Answer:
y=2.25
Step-by-step explanation:
0.25x9=2.25
I also really need help on this to
which ratio is same as 2/3
The ratio 4/6 is the same as 2/3 because they have the same proportion.
To find a ratio that is the same as 2/3, multiply or divide both the numerator and the denominator by the same non-zero number.
1. Multiplying by the same number:
If you multiply both the numerator and the denominator of 2/3 by 2, you get:
= (2 × 2) / (3 × 2)
= 4/6
So, the ratio 4/6 is the same as 2/3.
2. Dividing by the same number:
Divide both the numerator and the denominator of 2/3 by 3, you get:
= (2 ÷ 3) / (3 ÷ 3)
= 2/3
So, the ratio 2/3 remains the same.
In conclusion, the ratio 4/6 is the same as 2/3.
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Yo can somebody please help me with this math problem !
Answer:
45
Step-by-step explanation:
this question was asked three times by the same account and I detailed the answer on the first
A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each T-shirt printed with your design costs an additional $8.
A. write a linear model that represents the Total cost of purchasing your team's T-shirt with your design as a function of the number of T-shirts.
B. your team has 35 members. If a T-shirt is purshased for every member. what would be the cost?
Answer:
Part A)
[tex]C(t)=25+8t[/tex]
Part B)
[tex]C(35)=\$305[/tex]
Step-by-step explanation:
We will let t represent the total number of t-shirts printed.
We are charged an initial fee of $25. So, for our linear model, our constant is 25. And each t-shirt printed costs an additional $8. So, for t t-shirts, it will cost an additional 8t dollars.
Part A)
So, from the above information, we can write the following function:
[tex]C(t)=25+8t[/tex]
Where C(t) is the total cost for t shirts.
The 25 represents our initial fee and the 8t represents the cost for t t-shirts.
Part B)
So, if we have a team of 35 members, we will need 35 t-shirts.
Then the total cost will be given by:
[tex]\begin{aligned}C(35)&=25+8(35)\\&=25+280\\&=\$305\end{aligned}[/tex]
So, it will cost a total of $305.
What is -4 1/2 as a decimal?
Answer: -4.5
Step-by-step explanation:
60x^10y divided by 5x^4y
Help me plssss!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
the 0.1 is rate of change decreasing and 10.1 is original amount
the survey report suggest that 2 out of three boy likes to play baseball what is the decimal expansion of two thirds
4 A nurse is administering pain medication to
a patient. The patient's chart says that
the patient received 650 milligrams of
medication yesterday, and today he is to
receive 75% less medication than he did
yesterday. How many milligrams of pain
Someone please answer and justify thanks :)
medication should the nurse administer to
the patient today?
F 162.5 milligrams
G 262.5 milligrams
H 487.5 milligrams
J 575.0 milligrams
in (1,8) is y greater than x + 5
Answer:
True.
Step-by-step explanation:
Note the point values: (x , y) = (1 , 8) ∴ x = 1, y = 8
Plug in the corresponding numbers to the corresponding variables in the equation:
y > x + 5
(8) > (1) + 5
8 > 1 + 5
8 > 6
8 is greater than 6, ∴ y is greater than x + 5.
~
Answer:
yes it would
Step-by-step explanation:
x=1 + 5 is six
y=8
8 > 6
8 > 1
i think that's right lol
the two lines graphed on the coordinate grid each responds an equation witch orderd pairs represents a solution to both equations
Answer:
Step-by-step explanation:
Graphing ordered pairs is only the beginning of the story. Once you know how to place points on a grid, you can use them to make sense of all kinds of mathematical relationships.
You can use a coordinate plane to plot points and to map various relationships, such as the relationship between an object’s distance and the elapsed time. Many mathematical relationships are linear relationships. Let’s look at what a linear relationship is.
how do you solve -3 + 5 +6g =11 - 3g?
Final Answer: [tex]g = 1[/tex]
Steps/Reasons/Explanation:
Question: How do you solve [tex]-3 + 5 +6g = 11 - 3g?[/tex]
Step 1: Simplify [tex]-3 + 5 + 6g[/tex] to [tex]6g + 2[/tex].
[tex]6g + 2 = 11 - 3g[/tex]
Step 2: Subtract [tex]2[/tex] from both sides.
[tex]6g = 11 - 3g - 2[/tex]
Step 3: Simplify [tex]11 - 3g - 2[/tex] to [tex]-3g + 9[/tex].
[tex]6g = -3g + 9[/tex]
Step 4: Add [tex]3g[/tex] to both sides.
[tex]6g + 3g = 9[/tex]
Step 5: Simplify [tex]6g + 3g[/tex] to [tex]9g[/tex].
[tex]9g = 9[/tex]
Step 6: Divide both sides by [tex]9[/tex].
[tex]g = 1[/tex]
~I hope I helped you :)~