It will take 7.30 years until Dale can by his mask
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
[tex]A=Pe^{rt}[/tex] , where
A is the future value of the investment, including interestP is the principal investment amount (the initial amount)r is the interest rate in decimalt is the time the money is invested forDale invests $6000 in an account at 9.5% interest compounded continuously. The mask costs $12000. We need to find how long will it take Dale until can buy this mask
∵ Dale invests $6000
∴ P = 6000
∵ The interest rate is 9.5% ⇒ compounded continuously
∴ r = 9.5% = 9.5 ÷ 100 = 0.095
∵ The mask costs $12000
∴ A = 12000
Substitute these values in the formula above
∵ [tex]12000=6000e^{0.095t}[/tex]
- Divide both sides by 6000
∴ [tex]2=e^{0.095t}[/tex]
- Insert ㏑ for both sides
∴ [tex]ln(2)=ln(e^{0.095t}[/tex])
- Remember that [tex]ln(e^{n})=n[/tex]
∴ [tex]ln(2)=0.095t[/tex]
- Divide both sides by 0.095
∴ t = 7.29628611
∴ t = 7.30 ⇒ to the nearest hundredth year
It will take 7.30 years until Dale can by his mask
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It will take Dale 7.64 years to save enough money to buy the mask we can use the method of compound interest.
To find how long it will take Dale to save enough money to buy the mask, we can use the following formula for compound interest:
A = P * e^(rt)
where:
A is the final amount
P is the principal amount
r is the interest rate
t is the time in years
We know that A = $12000, P = $6000, and r = 9.5%. We need to solve for t.
12000 = 6000 * e^(0.095t)
e^(0.095t) = 2
ln(2) = 0.095t
t = ln(2) / 0.095
t = 7.64
Therefore, it will take Dale 7.64 years to save enough money to buy the mask.
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Find the original price if the sale price of the cell phone is $205.50
Answer:
$293.6
Step-by-step explanation:
Here is the complete question: A cell phone is on sale for 30% off. Find the original price if the sale price of the cell phone is $205.50.
Given: Sale price of cell phone is $205.50
Discount= 30%
As 30% discount is given on original price or we can say 70% of original price is $205.50.
∴ Let the original price be x.
⇒ [tex]\frac{70}{100} \times x= 205.50[/tex]
Now, cross multiplying both side.
⇒ [tex]x= \frac{100}{70} \times 205.5[/tex]
∴ x= $293.6
The original price of cell phone is $293.6.
A)400
B)500
C)550
D)560
500
Step-by-step explanation:
The median is always the middle line in the box of the data set even if the data set is uneven.
1+9i and 5-3i midpoint
Answer:6i-6
Step-by-step explanation:
9i-3i=6i
1+5=6
A cross country runner ran 2 miles in 1/4
hour. What is the average speed of the
cross country runner in miles per hour?
Need help ASP plssss
Charlie guesses that his dog weighs 34.5 pounds. The dog actually weighs 32.7 pounds.
What is the percent error in Charlie’s guess, to the nearest tenth of a percent?
0.05%
0.5%
5.2%
5.5%
Answer:
error pecentage is 5.5% i think because 1.8 divde by 32.7 is 0.5504... * 100 is 5.504
Step-by-step explanation:
The percent error in Charlie's guess regarding his dog's weight is 5.5%, calculated using the difference between the actual and estimated values divided by the actual value, times 100%.
Explanation:To calculate the percent error in Charlie's guess, we use the formula for percent error which is:
Percent Error = (|Actual Value - Estimated Value| / Actual Value) × 100%
Substitute the values into the formula:
Percent Error = (|32.7 - 34.5| / 32.7) × 100%
Percent Error = (1.8 / 32.7) × 100%
Percent Error = 0.054983922826 × 100%
Percent Error = 5.5% (rounded to the nearest tenth)
Therefore, the percent error in Charlie's guess is 5.5%.
- 8x - 16y = -166
8x + 7y - 76
Answer:
x=-1189/36, y=242/9. (-1189/36, 242/9).
Step-by-step explanation:
-8x-16y=-166
8x+7y=-76
----------------
-9y=-242
9y=242
y=242/9
8x+7(242/9)=-76
8x=-76-1694/9
8x=-2378/9
x=(-2378/9)/8
x=-1189/36
F) As a truck driver, Roland averages 400 miles every 6 hours of driving. How long will it take him to drive
2100 miles if he has to take a 2-hour break after every 6 hours of driving? It may help to make a chart.
Answer:
31.5 hours
Step-by-step explanation:
time * speed = distance
speed=400/6=66.67 miles per hour
2100/(400/6)=31.5 hours
What is 1/3 x 20/9 simplified to the lowest term
Answer: 20/27
Step-by-step explanation:
multiply numerators and denominators
1/3 x 20/9 = 20/27
you can not simplify further
What is the inequality?
Find the diagonal of a square whose sides are of the given measure.
Given = 3v3
Answer:
The measure of the diagonal is [tex]3\sqrt{6}\ units[/tex]
Step-by-step explanation:
Let
c -----> the diagonal of a square in units
a ----> the length side of a square
Remember that a square can be divided into two congruent right triangles
see the attached figure to better understand the problem
Applying the Pythagoras Theorem
[tex]c^{2}=a^{2}+a^{2}[/tex]
we have
[tex]a=3\sqrt{3}\ units[/tex]
substitute
[tex]c^{2}=(3\sqrt{3})^{2}+(3\sqrt{3})^{2}[/tex]
[tex]c^{2}=54[/tex]
[tex]c=\sqrt{54}\ units[/tex]
simplify
[tex]c=3\sqrt{6}\ units[/tex]
Four times a number added to 8 times the number equals 48. Find the number
Answer:
4*6+8*6=48
Step-by-step explanation:
Answer:
The number is 4.
Step-by-step explanation:
4x+8x=48
12x=48
x=48/12
x=4
i need help plsss n ty
Answer
○ A. [tex]\displaystyle y - 5 = 2(x - 10)[/tex]
Step-by-step explanation:
First, find the rate of change [slope]:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-5 - 7}{-10 + 4} = \frac{-12}{-6} = 2[/tex]
Then, according to the Point-Slope Formula, [tex]\displaystyle y - y_1 = m(x - x_1),[/tex]all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY CAREFUL inserting the coordinates into the formula with their CORRECT signs:
[tex]\displaystyle y - 5 = 2(x - 10)[/tex]
I am joyous to assist you anytime.
the ratio of blueberries to strawberries is 1:7if there are 210 strawberries how many berries are there
Answer: 30
Step-by-step explanation:
1:7
x:210
find x
210 is 30 times bigger than 7 so 30 is 30 times bigger than 1
30 is the answer
Answer:
30 blueberries
Step-by-step explanation:
divide the total by the 7, it's a lot simpler since it's a 1:7 but yeah so it's 30:210 blueberries to strawberries
If [tex]sin\theta = \frac{1}{3}[/tex] , [tex]\frac{\pi }{2} \ \textless \ \theta \ \textless \ \pi[/tex]. Find the exact value of
[tex]sin (\theta + \frac{\pi }{6})[/tex]
Answer:
- 0.183
Step-by-step explanation:
Given that [tex]\sin \theta = \frac{1}{3}[/tex]
and [tex]\frac{\pi }{2} < \theta < \pi[/tex]
We have to find the exact value of [tex]\sin (\theta + \frac{\pi }{6} )[/tex].
Now, [tex]\sin \theta = \frac{1}{3}[/tex]
⇒ [tex]\theta = \sin ^{-1} (\frac{1}{3} ) = 19.47[/tex]
Now, since [tex]\frac{\pi }{2} < \theta < \pi[/tex],
So, [tex]\theta = 180 - 19.47 = 160.53[/tex]
{Since [tex]\sin \theta = \sin (180 - \theta)[/tex]
Now, [tex]\theta + \frac{\pi }{6} = 160.53 + 30 = 190.52[/tex]
Hence, [tex]\sin (\theta + \frac{\pi }{6} )[/tex].
= [tex]\sin 190.52[/tex]
= - 0.183 (Approximate) (Answer)
find the solution of w(-15-w)=0
Answer:
w(-15-w)= 0
w= 0 or (-15-w) = 0
Now,
-15-w =0
w= -15
So,The solution of w(-15-w) = 0
w= 0, -15
Answer:
w=-15,0
Step-by-step explanation:
w(-15-w)=0
-15w-w^2=0
-(w^2+15w)=0
w(w+15)=0
w=-15,0
Solve for x 4x+8=7.8+5x
4x+8=7.8+5x
Subtract 4x from both sides:
8 = 7.8 +x
Subtract 7.8 from both sides:
x = 0.2
If y=2 2/3 when x=1/4, find y when x=1 1/8
Answer:
x = 1/4 when y = 8/3
Step-by-step explanation:
Divide both by 1/4
x = 1 when y = 32/3
When x = 1 1/8 = 9/8
y = 32/3 x 9/8
y = 12
9. A stock's price has been continuously declining at a rate of 5% per week. If the stock started at a price of
$62.50 per share, algebraically determine the number of weeks it will take for the price to reach $20.00 per
share. Round your answer to the nearest tenth of a week
Final answer:
It will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.
Explanation:
To determine the number of weeks it will take for the stock's price to reach $20.00 per share, we need to find the number of weeks it will take for the price to decrease from $62.50 to $20.00. Since the price is declining at a rate of 5% per week, we can set up an equation:
$62.50 - ($62.50 imes 0.05 imes ext{number of weeks}) = $20.00
Simplifying the equation, we have:
$62.50 - (0.05 imes 62.50 imes ext{number of weeks}) = $20.00
$42.50 = (0.05 imes 62.50 imes ext{number of weeks})
Dividing both sides by 0.05 and 62.50, we get:
ext{number of weeks} = rac{42.50}{0.05 imes 62.50}
Calculating this, we find that it will take approximately 13.6 weeks for the stock's price to reach $20.00 per share.
15 - 4x = 6 - 3x
whats the answer.
Answer:9
Step-by-step explanation: First you add the 3x to both sides(the -4x and the -3x) and then you get 15-1x=6. Next you subtract 15 from 15 and 6, so you get -1x=-9. So then you divide both sides by -1 (do -1x over -1 equals -9 over -1). Last you do the dividing and you get x=9.
Isolate the variable x by moving terms involving x to one side and constants to the other side. Simplify the equation step-by-step to find that x = 9.
To solve the equation 15 - 4x = 6 - 3x, we need to isolate the variable x. Follow these steps:
Start by getting all the terms involving x on one side of the equation. We can do this by adding 3x to both sides:Therefore, the solution to the equation 15 - 4x = 6 - 3x is x = 9.
44. What percent of 75 is 30?
Answer:
40%
Step-by-step explanation:
30/75 = 0.4
Move decimal point back 2 places to convert to percent.
0.4 = 40%
Answer: 40%
Step-by-step explanation:
let x equal the percent
75x=30
x=2/5=40%
Cameron is making pumpkin bread. The recipe calls for 4 3/4 cups of flour. She has 2 2/3 cups. How much more flour does she need?
Answer:
25/12 or 2 1/12
Step-by-step explanation:
4 3/4=19/4
2 2/3=8/3
19/4-8/3=57/12-32/12=25/12
How can I factor 130x - 13
Answer:
Divide by 13, you will get 10x - 1
To factor the expression 130x - 13, find the greatest common factor, which is 13, and factor it out. The factored form is 13(10x - 1).
To factor the expression 130x - 13, you need to look for a common factor in both terms. In this case, both terms can be divided by 13, which is the greatest common factor of the two numbers. By factoring out 13, you get:
13(10x - 1)
This process is known as factoring by common factor or GCF factoring. It simplifies the expression to a product of a constant (13) and a binomial (10x - 1). This method is very useful in solving equations, simplifying expressions, and can be a first step in more complex factoring processes.
if m<1=125*, determine the measure of <3
A 85
B 125
C 55
D 105
angle = 125 degree because it is Vertically Opposite to the angle 1.
Please answer with evidence!!!!!
Without multiplying, determine the sign of the product (356,864)(−194,758). (5 points)
Group of answer choices
The sign of the product is positive because a positive multiplied by a negative is a positive.
The sign of the product is negative because a positive multiplied by a negative is a negative.
The sign of the product is negative because the second number is negative.
The sign of the product is positive because the first number is positive.
Answer:
The sign of the product is negative because a positive multiplied by a negative is a negative.
Step-by-step explanation:
Since you asked for evidence I will multiply even though the question asks you to solve without multiplying.
1×-1=-1
-1×-1=1
1×1=1
A negative multiplied by a positive is always negative. Doesn't matter which order you put it in. Meaning a positive multiplied by a negative is also always negative.
A positive multiplied by a positive is always positive.
A negative multiplied by a negative is always positive.
356,864 × −194,758 = negative sign answer
A number added to itself equals 5 less than the number
Answer:
The number is -5.
Step-by-step explanation:
x+x=x-5
2x=x-5
x-2x=5
-x=5
x=-5
a first number plus twice a second number is 7 twice the first number plus the second totals 29 find the numbers
Final answer:
The student's question involving a system of equations can be solved to find that the two numbers are 17 and -5. By setting up a system of equations based on the given conditions and solving it using the elimination method, we obtain the values for the two unknown numbers.
Explanation:
System of Equations to Find Two Numbers
Let's define the first number as x and the second number as y. The problem states that x plus twice y equals 7 and twice x plus y equals 29. These statements can be turned into a system of linear equations:
x + 2y = 7
2x + y = 29
Using the substitution or elimination method, we can solve these equations for x and y. First, multiply the first equation by 2 to align the coefficients of x:
(2)(x) + (2)(2y) = (2)(7)
The equations now become:
2x + 4y = 14
2x + y = 29
Subtracting the second equation from the first gives us:
3y = -15
Divide both sides of this new equation by 3 to get the value of y:
y = -5
Now that we have a value for y, substitute it back into one of the original equations to find x:
x + 2(-5) = 7
x - 10 = 7
x = 17
The two numbers that solve the system are x = 17 and y = -5.
Two buses depart two cities moving in the same direction. The speed of the first bus is 54 mph which is 60% of the speed of the second bus. The faster bus caught up to the other bus one hour and thirty minutes after the departure. will give brainliest
Answer:
The second city is 54 miles behind the first city
Step-by-step explanation:
The first bus is assumed to go ahead of the second bus and is moving at 54 mph. The second bus is moving at a speed such as 54 mph is 60% (0.6) of its speed.
The speed of the second bus is then 54/0.6 = 90 mph
When 1 and a half hour has passed, the first bus has moved a distance of
[tex]X_1=54\times 1.5[/tex] = 81 miles
The second bus (behind the first bus) has moved
[tex]X_2=90\times 1.5[/tex] = 135 miles
The problem states they both meet in that time, it can only be possible if the second bus departed a distance 135 - 81 = 54 miles behind the first city
So, the second city is 54 miles behind the first city
One positive integer is 3 less than twice another. The sum of their squares is 698. Find the integers.
Answer:
The value of positive integers are 21.22 and 12.11
Step-by-step explanation:
Given as :
The sum of squares of two integer = 698
Let The one positive integer be x
And The other positive integer be y
According to question
one positive integer = 3 less than twice the other positive integer
So, x = 2 × y - 3
I.e x = 2 y - 3
And x² + y² = 698
So, Put the value of x
I.e ( 2 y - 3 )² + y² = 698
or, 4 y² + 9 - 12 y + y² = 698
Or, 5 y² - 3 y - 698 = 0
Now solving this quadratic equation
y = [tex]\frac{-b\pm \sqrt{b^{2}-4\times a\times c}}{2\times a}[/tex]
Or, y = [tex]\frac{3\pm \sqrt{-3^{2}-4\times 5\times -698}}{2\times 5}[/tex]
Or, y = [tex]\frac{3\pm \sqrt{13969}}{10}[/tex]
Or, y = [tex]\frac{3\pm 118.19}{10}[/tex]
∴ y = 12.11 , - 11.51
So , The value of y = 12.11
And the value of x = 2 × 12.11 - 3
I.e x = 21.22
Hence The value of positive integers are 21.22 and 12.11 Answer
To find the two integers, we can set up two equations based on the given information. By substituting the value of x from the first equation into the second equation, we can solve for y. Then, substituting the value of y back into the first equation, we can find the value of x.
Explanation:To solve this problem, we can set up two equations based on the given information. Let's say the first integer is x and the second integer is y. We are given that x is 3 less than twice y, so we can write the equation: x = 2y - 3. We also know that the sum of their squares is 698, so the equation becomes x^2 + y^2 = 698. Now we can substitute the value of x from the first equation into the second equation and solve for y.
Substituting x = 2y - 3 into the equation x^2 + y^2 = 698, we get (2y - 3)^2 + y^2 = 698. Expanding this equation, we get 4y^2 - 12y + 9 + y^2 = 698. Combining like terms, we have 5y^2 - 12y + 9 = 698. Rearranging this equation and simplifying, we get 5y^2 - 12y - 689 = 0. Now we can solve this quadratic equation to find the value of y.
Using the quadratic formula, y = (-(-12) ± sqrt((-12)^2 - 4(5)(-689))) / (2(5)). Simplifying the equation further, we have y = (12 ± sqrt(144 + 13780)) / 10. Taking the positive value, y = (12 + sqrt(13924)) / 10. Evaluating this expression, we find y ≈ 9.7394. Now we can substitute this value back into the first equation to find x.
Using x = 2y - 3, we have x = 2(9.7394) - 3. Simplifying this equation, we get x ≈ 16.4788. Therefore, the two integers are approximately 16.4788 and 9.7394.
given that -4 is a zero of the function f(x)=x3+3x2-16x-48f(x)=x3+3x2-16x48, find the other zeros and write f(x)f(x) in factored form
Answer:
f(x) = (x + 4)(x - 4)(x + 3)
The other zeros of the function are at 4 and -3.
Step-by-step explanation:
Given function is f(x) = x³ + 3x² - 16x - 48.
Now, given that - 4 is a zero of the given function.
So, the function has a factor equals to (x + 4).
Now, f(x) = x³ + 3x² - 16x - 48
⇒ f(x) = x³ + 4x² - x² - 4x - 12x - 48
⇒ f(x) = x²(x + 4) - x(x + 4) - 12(x + 4)
⇒ f(x) = (x + 4)(x² - x - 12)
⇒ f(x) = (x + 4)(x - 4)(x + 3)
Therefore, the other zeros of the function are at 4 and -3. (Answer)
Answer:
f(x) = (x + 4)(x - 4)(x + 3)
Step-by-step explanation:
PLEASE HELP!!! I WILL AWARD BRAINLIEST!!!
Given: BD = BF
DE ⊥ BC ,
FK ⊥ AB
Prove: ED ≅ FK
△BDE≅△________, By rule_________
Answer:
ΔB D E = ΔB F K, By rule A A S similarity
Step-by-step explanation:
a right angle is congruent to a right angle, so < B D E is congruent to
< B F K
< D B F is equal to < D B F
Side B D = B F is given
Thus, creating A A S similarity