Answer:
sum was 300000
Step-by-step explanation:
let sum of money is placed is x rs
Term T = 3 years, rate R = 10%
Then simple interest for for 3 years is
[tex]SI= \frac{PTR}{100}\\ SI=\frac{x\times 3\times 10}{100} \\SI = 0.3x[/tex]
Sum of x will become x+0.3x = 1.3x after 3 years. now this 1.3x is kept for compound interest for two years. ie
[tex]A =P[1+R]^t\\471900=1.3x[1+\frac{10}{100} ]^2\\x=\frac{471900}{1.573} \\x=300000[/tex]
Sum was 300000
At the simple interest rate, the rate is applied only to the initial sum, while
at the compound interest, the rate is applied to the amount in the account.
The sum of money is approximately Rs 355,847.466Reasons:
Let P represent the sum of money invested, we have;
[tex](P + P \cdot r \cdot t_1) \times (1 + r)^{t_2} = \mathbf{ 471900}[/tex]Where;
P = The initial sum invested
r = The simple and compound interest rate applied = 10% = 0.1
t₁ = The number of years the money is placed at simple interest = 3 years
t₂ = The number of years the money is placed at compound interest = 2 years
Therefore;
[tex]\mathbf{(P + P \times 0.1 \times 3) \times (1 + 0.01)^{2}} = 471900[/tex]
Which gives;
[tex]P \cdot (1 + 0.3 ) \times (1 .01)^{2} = 471900[/tex]
[tex]\displaystyle P =\mathbf{\frac{471900}{(1 + 0.3 ) \times (1 .01)^{2} }} \approx 355,847.466[/tex]
The sum of money invested, P ≈ Rs 355,847.466
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H E L P ME OUT
According to the figure above the atmospheric pressure at an altitude of 22 kilometers is about:
Answer:
300mb
Step-by-step explanation:
We can read the atmospheric pressure at an altitude of 22 kilometers can be read by tracing directly from the graph.
22 kilometers is half way between 20 kilometers and 24 kilometers on the vertical axis.
The reading is shown in the attachment.
From the reading the atmospheric pressure is about 300mb
The correct answer is A
Rewrite 5a-(a-3b) in standard form.
Answer:
NOTE: Standard form is Ax+By=C
Distribute -1
5a -a +3b
Rewrite
5a +3b = -a
Multiply every term by -1 so -a will be positive
-5a -3b = a
from the top of a barn 25 feet tall, you see a cat on the ground. The angle of depression to the cat is 40°. How many feet must the cat walk to reach the barn.
Answer:
21 feet (20.977)
Step-by-step explanation:
1. Draw a picture, it makes it much easier. Draw a right triangle with the vertical labeled 25 and the horizontal labeled X, then label the angle adjacent to the horizontal and hypotenuse 40°
2. Use tangent because X is opposite of 40 and 25 is adjacent to angle 40. the equation would be Tan40/1 = X/25
3. You then cross multiply to get 25Tan(40) = X
4 You then plug it into a calculator and get the full answer of 20.97749078, but I always round up to either 20.98 or 21 feet, whatever your teacher allows
BONUS: Name the restrictions, solve, & SHOW your check.
x + 1 = √(5x+11)
x = 5
Solution:
Given equation is [tex]x+1=\sqrt{5x+11}[/tex].
[tex]\Rightarrow x+1=\sqrt{5x+11}[/tex]
Squaring on both sides of the equation to remove the square root.
[tex]\Rightarrow (x+1)^2=(\sqrt{5x+11})^2[/tex]
[tex]\Rightarrow (x+1)^2=5x+11[/tex]
Using algebraic identity: [tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex]\Rightarrow x^2+2x(1)+1^2=5x+11[/tex]
[tex]\Rightarrow x^2+2x+1=5x+11[/tex]
Combine all terms in one side of the equation.
[tex]\Rightarrow x^2+2x+1-5x-11=0[/tex]
Arrange like terms together.
[tex]\Rightarrow x^2+2x-5x+1-11=0[/tex]
[tex]\Rightarrow x^2-3x-10=0[/tex]
Now solve by factorization.
[tex]\Rightarrow x^2-5x+2x-10=0[/tex]
[tex]\Rightarrow (x^2-5x)+(2x-10)=0[/tex]
Take common terms on left side of the term.
[tex]\Rightarrow x(x-5)+2(x-5)=0[/tex]
Now, take (x – 5) common on both terms.
[tex]\Rightarrow (x+2)(x-5)=0[/tex]
⇒ x + 2 = 0 (or) x – 5 = 0
⇒ x = –2 (or) x = 5
If we put x = –2 in the given equation,
[tex]-2+1=\sqrt{5(-2)+11}[/tex]
[tex]\Rightarrow-1=1[/tex]
It is false. So, x = –2 is not true.
If we put x = 5 in the given equation,
[tex]5+1=\sqrt{5\times5+11}[/tex]
[tex]5+1=\sqrt{36}[/tex]
[tex]\Rightarrow6=6[/tex]
It is true. So, x = 5 is true.
Hence x = 5 is the solution.
Choose the expression that represents a linear expression.
9x − 2
3x2 + 4x − 5
5x3 + 6x2 − 7x + 8
4x4 − 5x3 + 6x2 − 7x + 8
Answer:
Step-by-step explanation:
A linear expression has the highest power of the variable to 1, i.e ax+b
Then only the first option is in a linear expression format
9x-2
The linear expression from the given options is 9x - 2.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given are four expressions consisting of variable x.
Linear expressions are those expressions for which the highest degree of the variable in the expression is 1.
Look at the expressions with the power of the variable equals one and no other term in the expression has power of the variable more than 1.
The expression is 9x - 2.
In 3x² + 4x - 5, the highest degree of the variable is 2.
In 5x³ + 6x² - 7x + 8, highest degree of the variable is 3.
In 4x⁴ - 5x³ + 6x² - 7x + 8, highest degree of the variable is 4.
Hence the linear expression is 9x - 2.
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Which of the following numbers is rational?
Select all that apply.
7.6
22/7
1.01
n
Answer: 7.6, 22/7, 1.01
Step-by-step explanation:
Which describes the location of vertex M after translation
Answer:
A
Step-by-step explanation:
A horizontal translation of - 3 means to subtract 3 from the original x- coordinate.
A vertical translation of - 3 means to subtract 3 from the original y- coordinate, thus
M(2, 2 ) → M'(2 - 3, 2 - 3 ) → M'(- 1, - 1 ) → A
The areas of a figure and its transformed image are the same which transformation could NOT have been applied to the original figure to create the image ?
Answer: Dilation by a scale factor of 0.75
Step-by-step explanation:
Jordan paid $6.00 for 8 apples. How much did he pay per apple?
Answer:
Cost per Apple is $0.75
Step-by-step explanation:
Step 1: Divide cost by the apples
$6.00 / 8 = x
$0.75 = x
Cost per Apple is $0.75
Answer:
0.75
Step-by-step explanation:
Just divide $8.00 by $6.00
are y=2x+6 and 6t=2x+9 perpendicular
Answer:
Therefore,
[tex]y=2x+6[/tex] and
[tex]6y=2x+9[/tex] are not Perpendicular.
Step-by-step explanation:
Given:
[tex]y=2x+6[/tex] ............................Equation of line( 1 )
[tex]6y=2x+9\\y=\dfrac{1}{3}+\dfrac{3}{2}[/tex] ............................Equation of line( 2 )
Solution:
So the Equations are written in
[tex]y=mx+b[/tex]
Where m is the slope of the line
On Comparing we get
[tex]Slope = m1 = 2[/tex]
[tex]Slope = m2 = \dfrac{1}{3}[/tex]
So for the lines to be Perpendicular.
Product of slopes = - 1
m1 × m2 = -1
So Product of slopes of the given lines are
[tex]m1\times m2=2\times \dfrac{1}{3}=\dfrac{2}{3}[/tex]
Which is not equal to -1
Therefore,
[tex]y=2x+6[/tex] and
[tex]6y=2x+9[/tex] are not Perpendicular.
Todd has 17 inches of rope. That’s 1/3 the length he needs. What is the total amount of rope needed
Answer:
51 inches of rope?
Step-by-step explanation:
If 17 inches is 1/3 if what he needs, then have 3 of 17 inches of rope which is
= 17 × 3= 51.. so it will be 3/3
Answer:
51 inches
Step-by-step explanation:
Total length of the rope possessed by Todd = 17 inches.
But what he has corresponds to [tex]\[\frac{1}{3}\][/tex] of his actual requirement.
Let his total requirement be represented by x.
Then [tex]\[\frac{1}{3} * x = 17\][/tex]
Simplifying,
[tex]\[x = 17 * 3\][/tex]
[tex]\[x = 51\][/tex]
Hence the total length of the rope required by Todd is 51 inches which is 3 times what he has currently.
Together, teammates Pedro and Ricky got 2686 base hits last season. Pedro had 278 more hits than Ricky. How many hits did each player have?
Final answer:
Pedro had 1,482 hits, while Ricky had 1,204 hits. We determined these numbers by setting up a system of linear equations and solving for both players' hits using substitution.
Explanation:
To solve the problem of determining how many base hits teammates Pedro and Ricky had last season, we can set up a system of linear equations. Let's let P represent the number of hits Pedro had, and R represent the number of hits Ricky had. According to the problem, together they had 2,686 hits, so we can write the first equation as:
P + R = 2,686
The second piece of information tells us that Pedro had 278 more hits than Ricky, which gives us the second equation:
P = R + 278
We can substitute the second equation into the first equation to find the value of R:
P = (R + 278)
(R + 278) + R = 2,686
2R + 278 = 2,686
2R = 2,686 - 278
2R = 2,408
R = 1,204
Now, we know Ricky had 1,204 hits. To find out how many hits Pedro had, we substitute R's value back into the second equation:
P = 1,204 + 278
P = 1,482
So, Pedro had 1,482 hits and Ricky had 1,204 hits.
The given expression represents the area. Find the side length of the square.
The length of one side is _______.
Answer:
2x + 5
Step-by-step explanation:
Make sure you remember the area of a square with side which is [tex]s^{2}[/tex]. Once you figure that out, you need to find the length of a side, make sure you factor the expression of the area as a perfect-square trinomial.
An example of that is...
[tex]a^{2} +2ab+b^{2}[/tex] [tex]= (a +b)^{2}[/tex]
^^key point^^
Break it down and take the length out of the Square of Sum and you should get your answer.
Example: Use Square of Sum and get [tex](2x+5)^{2}[/tex] then, get rid of parentheses >> 2x + 5 and you should get your answer :)
How do you write 984 in scientific notation
Answer: 9.84 x 10²
Step-by-step explanation: To write 984 in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.
So here we have 9.84.
Next, count the number of places that we would need to move the decimal point in 9.84 in order to get back to the original number, 984.
Since we would need to move the decimal point two places to the right to get back to the original number, we have an exponent of 2.
Notice that our exponent is positive because we would need to move the decimal point to the right.
Now, scientific notation is always expressed as a power of 10. In this case, we have 10 to the 2nd or 10 to the 2nd power.
So 984 can be written in scientific notation as 9.84 x 10².
Someone pls help me find area pls
Jim owns a restaurant on the edge of a canyon. He wants to install a cable car over the canyon. He needs to know the width of the canyon.
The width of the canyon is 315 ft.
What is an isosceles triangle?An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.
Given that, Jim owns a restaurant on the edge of a canyon. He wants to install a cable car over the canyon. He needs to know the width of the canyon. (please refer to the figure attached)
m ∠ ABC = 180°-80° (Linear pair)
m ∠ ABC = 100°
In Δ ABC,
∠ A + ∠ B + ∠ C = 180° (sum of interior angles of a triangle)
∠ A = 180°-(100°+40°)
∠ A = 40°
Since, ∠ A = 40° and ∠ C = 40°
Therefore, ∠ A = ∠ C
Therefore, AB = BC (Side opposite to equal angles are equal)
That means, Δ ABC is an isosceles triangle
∵ BC = 315 ft
∴ AB = 315 ft
AB is the width of the canyon.
Hence, The width of the canyon is 315 ft.
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Find the smallest zero of f(x + 5). x =
Answer:
The answer is -5.
Question 2 of 10
2 Points
Assume that the lines De and my intersect as in the diagram below. Which
of the following statements are true?
Check all that apply.
O
A.
XAE and _DAY are vertical angles.
B. DĖ and are perpendicular.
c. XAE and DAY are complementary.
D. ZXAE and ZEAY form a linear pair.
SUBMIT
Answer:
XAE and EAY form a linear pair.
done
DE and XY are perpendicular.
XAE and DAY are vertical angles.
Step-by-step explanation:
This answer explains the mathematical concepts related to angles and lines i.e., vertical angles, perpendicular lines, complementary angles, and linear pair. Vertical angles are equivalent, perpendicular lines intersect at right angles, complementary angles sum to 90 degrees, and a linear pair of angles sum to 180 degrees.
Explanation:Without the actual diagram presented in your question, I can only provide some general insights into your question which is related to angles and lines. Firstly, vertical angles are the angles opposite each other when two lines intersect. They are always equal.
Secondly, two lines are perpendicular if they intersect at a right angle(90 degrees). In terms of angles, two angles are complementary when they add up to 90 degrees. Finally, a linear pair refers to two angles that are adjacent (share a common vertex and side but have no common interior points) and whose non-common sides are opposite rays, i.e., they add up to 180 degrees.
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3. Solve the inequality –2(z + 5) + 20 > 6.
[tex]\boxed{-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}}[/tex]
Solution:
Given inequality is:
[tex]-2(z+5)+20>6[/tex]
We have to solve the given inequality
[tex]-2\left(z+5\right)+20>6\\\\\mathrm{Subtract\:}20\mathrm{\:from\:both\:sides}\\\\-2\left(z+5\right)+20-20>6-20\\\\\mathrm{Simplify}\\\\-2\left(z+5\right)>-14[/tex]
[tex]Multiply\ both\ sides\ by\ -1\ \left(reverse\:the\:inequality\right)[/tex]
Whenever we multiply or divide an inequality by a negative number, we must flip the inequality sign
[tex]\left(-2\left(z+5\right)\right)\left(-1\right)<\left(-14\right)\left(-1\right)\\\\\mathrm{Simplify}\\\\2\left(z+5\right)<14\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\\frac{2\left(z+5\right)}{2}<\frac{14}{2}\\\\\mathrm{Simplify}\\\\z+5<7\\\\\mathrm{Subtract\:}5\mathrm{\:from\:both\:sides}\\\\z+5-5<7-5\\\\simplify\ the\ above\\\\\boxed{z < 2 }[/tex]
Thus the solution to inequality is:
[tex]-2\left(z+5\right)+20>6\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:z<2\:\\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:2\right)\end{bmatrix}[/tex]
160 students attended Music Night on Thursday night. The attendance on Friday was 120% of the attendance on Thursday night. The attendance on Saturday night was 75% of the attendance on Friday night. How many people attended Music Night on Friday night? How many people attended on Saturday night? What was the total attendance for the 3 nights?
Answer:
160+192+144=496
Step-by-step explanation:
120% of 160=Friday
75% of (1.2*160)=Sat
160=Thursday
Answer:
160+192+144=496
Step-by-step explanation:
120% of 160=Friday
75% of (1.2*160)=Sat
160=Thursday
Step-by-step explanation:
Kate can make 15 paper fortune tellers in 18 minutes. At this rate, how many paper fortune tellers can she make in 30 minutes?
Answer:
27 paper fortune tellers
Step-by-step explanation:
fortune tellers = time
3 = 6
6 = 9
9 = 12
12 = 15
15 = 18
18 = 21
21 = 24
24 = 27
27= 30
so 30 fortune tellers will be made in 30 minutes
hope this helps!!!
Answer:
Actually, it's 25 paper fortune tellers.
Step-by-step explanation:
15 = 18
15 divided by 3 = 18 divided by 3
5 = 6
5 x 5 = 6 x 5
25 = 30
Please help meeeeeeeee
1 second = 2 megabytes
[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]
2 seconds = 4 megabytes
Step-by-step explanation:
Given,
Time taken to download 5 megabytes = [tex]2\frac{1}{2}=\frac{5}{2}[/tex] seconds
[tex]\frac{5}{2}\ seconds = 5\ megabytes[/tex]
Multiplying both sides by [tex]\frac{2}{5}[/tex] to find unit rate
[tex]\frac{2}{5}*\frac{5}{2}\ second = \frac{2}{5}*5\\1\ second = 2\ megabytes[/tex]
1 second = 2 megabytes
[tex]1\frac{1}{2}\seconds = \frac{3}{2}\ seconds[/tex]
[tex]\frac{3}{2}\ seconds = \frac{3}{2}*2[/tex]
[tex]\frac{3}{2}\ seconds = 3\ megabytes[/tex]
[tex]1\frac{1}{2}\ seconds=3\ megabytes[/tex]
2 seconds = 2*2 megabytes
2 seconds = 4 megabytes
Keywords: fraction, multiplication
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There are 5 red marbles, 8 blue marbles, and 12 green marbles in a bag.
What is the theoretical probability of randomly drawing a red marble?
20%
41.7%
62.5%
25%
Answer:
20%
Step-by-step explanation:
If there are 25 marbles in the bag and 5 of them are red then you just divide 25 by 5 which is 5 which is 1/5 the 25 witch 20%
Answer:
20%
Step-by-step explanation:
Nice seeing you a year later <3
What is the distance from the point (a, -b, -4) to the origin?
O V22-62-16 units
O V22-b2+16 units
O Va+b2+ 16 units
O
Va2 +62 - 16 units
Answer:
[tex]\sqrt{a^2+b^2+16}\text{ units}[/tex]
Step-by-step explanation:
The distance is found using the distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]
Then the distance from the given point to the origin is ...
[tex]d=\sqrt{(a-0)^2+(-b-0)^2+(-4-0)^2}\\\\=\boxed{\sqrt{a^2+b^2+16}\ \dots\text{ units}}[/tex]
Ming spent half of her weekly allowance aying mini golf. To earn more money her parents let her wash the car for $5. What is her weekly allowance if she ended with $9
Answer:
Her weekly allowance is $8.
Step-by-step explanation:
Let the weekly allowance of Ming is $x.
If she spends half of her weekly allowance playing mini-golf and to earn more money her parents let her wash the car for $5, then the remaining amount of money that she has = [tex](\frac{x}{2} + 5)[/tex] dollars.
Now, given that [tex](\frac{x}{2} + 5) = 9[/tex]
⇒ [tex]\frac{x}{2} = 4[/tex]
⇒ x = $8
Therefore, her weekly allowance is $8. (Answer)
1/4 10/9 simplify the complex fraction shown
Answer:
Step-by-step explanation:
[tex]\frac{1}{4}*\frac{10}{9}=\frac{1*5}{2*9}=\frac{5}{18}[/tex]
The simplified fraction is 9/40.
To simplify the complex fraction 1/4 over 10/9, you can multiply both the numerator and the denominator by the reciprocal of the denominator of the complex fraction, which is 9/10. This is sometimes referred to as the skillfully chosen factor. By doing so, you are simplifying the expression by getting rid of the complex fraction structure.
Here's the step-by-step simplification:
Multiply both the numerator (1/4) and the denominator (10/9) by 9/10.
Simplifying the numerator: (1/4) * (9/10) = 9/40.
Simplifying the denominator: (10/9) * (9/10) = 1 because the nines and tens cancel out.
Now you have a simple fraction: 9/40 over 1, which is just 9/40.
The simplified fraction is 9/40. When multiplying fractions, you multiply the top numbers and divide by the bottom numbers in the fractions.
Mrs. Webster wants to divide 6 pints of
water into 5-pint servings. How many
servings are possible? Explain how you
found your answer.
Answer:
18 servings each pint being 1/3 serving size that 3 servings per pint 3×6 =18
Someone help me plzzzzz
Answer:
200
Step-by-step explanation:
200 × 33% = 66 so
200 is answer
Answer:
A) 200
Step-by-step explanation:
33% of x is 66
33/100 = 66/x
33x = 6600
x = 6600/33
x = 200
i don't btgcygljhbihlihnjknkl;n
What is the mean of -15, -12,8, and 9?
Answer:
mean = -0.25
Step-by-step explanation:
Explanation:-
mean:- The sum of all the observations and then divided the number of observations and it is denoted by 'μ'
given data is -15 , -12 , 8 and 9
Given observations is '4' so n = 4
[tex]mean= \frac{-15-12+8+9 }{4}[/tex]
[tex]mean= \frac{-27+17}{4}[/tex]
[tex]mean = -0.25[/tex]
The mean of given data is - 0.25
The mean of -15, -12, 8, and 9 is calculated by summing the numbers to get -10 and then dividing by 4, leading to a mean of -2.5.
The mean of a set of numbers is calculated by summing up all the numbers and then dividing the total by the count of the numbers. In this case, to find the mean of -15, -12, 8, and 9, you would add these four numbers together and then divide by 4, because there are four numbers in this set.
The calculation would look like this:
(-15) + (-12) + 8 + 9 = -10
To find the mean, you would then divide -10 by the number of values in the set, which is 4:
Mean = -10 / 4 = -2.5
Therefore, the mean of the numbers -15, -12, 8, and 9 is -2.5.