This is a mathematical problem that can be solved using algebra. Let P be the original amount borrowed, and R be the interest rate as a decimal (for example, 5% would be represented as 0.05).
We know that at the end of 25 years, the amount borrowed has trebled, so the total amount is 3P. We also know that the interest is calculated using simple interest, which is calculated as P x R x T, where T is the number of years.
So we can set up the equation:
3P = P + P x R x 25
To find R, we can solve for R by dividing both sides of the equation by P:
3 = 1 + 25R
Then by subtracting one from both sides we have :
2 = 25R
Then by dividing both sides by 25 we can find the rate as :
R = 2/25
Finally, to find the interest rate as a percentage, we multiply R by 100:
rate = 2/25 x 100 = 8%
So the interest rate is 8% per annum
One serving of trail mix has 69 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates in grams? (Round your answer to one decimal place.)
Answer:
We can use the equation:
amount of a given nutrient / % of recommended daily amount = recommended daily amount
Here, we know that 69 grams of carbohydrates is 22% of the recommended daily amount, so we can plug in the given values and solve for the recommended daily amount:
69 / 0.22 = Recommended Daily Amount
Recommended Daily Amount = 69 / 0.22 = 313.64 grams (rounded to one decimal place)
So, the total recommended daily amount of carbohydrates in grams is 313.6 grams.
Solve for the interior of angle, x.
90°
130°
130⁰
130
120%
Xo
Please help will give brainlest!!!If the area of the triangle is 10 cm 2, what is the missing height?
W =
Step-by-step explanation:
what is the usual formula for the area of a triangle ?
it is
base × height / 2
so, we know the area (10 cm²).
when we use the formula, we get
10 = 5 × w / 2
20 = 5 × w
w = 20/5 = 4 cm
Answer:
the height is equal = 4 cm
are the two triangles below similar? If so, write a similarity statement in state which similarity criteria can be used to prove it?
A. Similarity Statement
1. ABC DEF
2. ABC FDE
3. ABC EFD
4. The triangles are not similar
B. Criteria
1. AA
2. SAS
3. SSS
4. Not applicable, the triangles are not similar
The triangles are similar as follows:
ABC ~ DEF
The criteria is AA(angle angle)
How to find similar triangles?Similar triangles are the triangles that have corresponding sides as a ratio of each other and corresponding angles congruent to each other.
Therefore, the corresponding angles of the triangles are suppose to be congruent and the corresponding sides in proportion for it to be similar.
Hence, If two triangles have two of their angles equal, the triangles are similar by AA(angle angle).
Therefore, the triangles are similar by AA.
Triangle ABC is similar to triangle DEF.
The criteria for the similarity is AA.
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Use technology to find points and then graph the function y = x + 2| -4,
following the instructions below.
Plot at least five points that fit on the axes below. Click a point to delete it.
-10
done plotting points
63
-3
A graph of the absolute function y = |x + 2| - 4 with five points that fit on the axes is shown in the image attached below.
What is an absolute value function?In Mathematics, an absolute value function is a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and it typically measures the distance of a point on the x-axis to the x-origin (0) of a cartesian coordinate (graph).
Next, we would use an online graphing calculator to plot the given absolute value function y = |x + 2| - 4 as shown in the graph attached below.
By observing critically the graph (see attachment), the five ordered pairs (points) that fit on its axes include the following:
Ordered pair = (-6, 0).Ordered pair = (-4, -2).Ordered pair = (-2, -4).Ordered pair = (0, -2).Ordered pair = (2, 0).Read more on absolute value function here: brainly.com/question/28308900
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work out for brainliest
The expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
In a right triangle, the hypotenuse (the longest side) is opposite the right angle, and the other two sides are called the legs. In this case, the hypotenuse is 2p + 8 and one of the legs (the base) is p - 5.
To find the third side (the other leg), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. In other words:
(hypotenuse)^2 = (leg 1)^2 + (leg 2)^2
Substituting the given values, we get:
(2p + 8)^2 = (p - 5)^2 + (leg 2)^2
Simplifying and solving for leg 2, we get:
leg 2 = sqrt((2p + 8)^2 - (p - 5)^2)
Now we can use the perimeter formula, which is the sum of the lengths of all the sides of the triangle. In this case, the perimeter of the triangle is:
perimeter = (leg 1) + (leg 2) + (hypotenuse)
Substituting the given values and the expression we found for leg 2, we get:
perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)
Therefore, the expression for the perimeter of the right triangle with hypotenuse 2p + 8 and base p - 5 is: perimeter = (p - 5) + sqrt((2p + 8)^2 - (p - 5)^2) + (2p + 8)
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which segment is the diameter
Answer:
2× radius of the circle
Step-by-step explanation:
The line segment joining two points on the circle and passing through the centre is the diameter.
What percent is 40 out of 160?
Answer:
Step-by-step explanation:
57
Answer: 25%
Step-by-step explanation:
(Look at picture) Ty for the help
3s + a = 38 and 3s + 2a =52
Step-by-step explanation:
answer is (a,s) = (14,8)
Write an equation in slope-intercept form for the line through the points (2, -1) and (10, 3).
Answer:
Since slope of line passing through two points (x
1
,y
1
) and (x
2
,y
2
) is m=
x
2
−x
1
y
2
−y
1
We now find the slope of the line passing through the points (2,3) and (4,6) as shown below:
m=
4−2
6−3
=
2
3
Therefore, the slope of the line is
2
3
.
Now use the slope and point (2,3) to find the y-intercept.
y=mx+b
⇒3=(
2
3
×2)+b
⇒3=3+b
⇒b=3−3=0
Write the equation in slope intercept form as:
y=mx+b
⇒y=
2
3
x+0
⇒y=
2
3
x
Step-by-step explanation:
do you know the ansawer ?
Answer:
1/70
Step-by-step explanation:
(63-40) (21-10) 23 11 23-22 1
(---------)-(--------)=------ - ------ = -------- = --
( 70 ) ( 35 ) 70 35 70 70
Calculate the squares of these measures 20 ft = ft²
helpppppppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
x = 10 (yes)
x = 14 (yes)
x = 6 (no)
x = 4 (no)
Step-by-step explanation:
Plug in each x value into the function and determine if it is true or not.
44 [tex]\leq[/tex] 35 + x
44 [tex]\leq[/tex] 35 + (10)
44 [tex]\leq[/tex] 45
45 is greater than or equal to 44, so it is a solution
44 [tex]\leq[/tex] 35 + (14)
44 [tex]\leq[/tex] 49
49 is greater than or equal to 44, so it is a solution
44 [tex]\leq[/tex] 35 + (6)
44 [tex]\leq[/tex] 41
41 is not greater than or equal to 44, so it is not a solution
44 [tex]\leq[/tex] 35 + (4)
44 [tex]\leq[/tex] 39
39 is not greater than or equal to 44, so it is not a solution
I hope this helps! :)
what is the constant of 5x-2y+3x-9
Answer:
-9
Step-by-step explanation:
The constant doesn't have a letter attached to it
how to round 456.173 to the nearest hundredth?
Answer:
456.17
Step-by-step explanation:
Rounding to the nearest hundredths' is asking is the number given 456.173 closer to 146.170 or 146.171. You can see that the number is closer to 146.170 which is the same number as 146.17
Rule
Look at the digit in the thousandths' place. In this case 3. If this number is 5 or greater round up, if this number is 4 or smaller round down. We will round down.
456.17
Answer:456.17
Step-by-step explanation:
If the thousandth place is 5-9, for example 456.178, the answer rounded to hundredth place will be 456.18.
But if the thousandth place is 1-4, the answer rounded to hundredth will be 456.17.
So the answer is 456.17.
A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale
The equation that represents the linear function is y =32x
What is a linear equation explain?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
A linear function is represented as
y = mx + c
The slope is calculated as
m = y₂ - y₁/x₂ - x₁
m = 576 - 64/18 - 2
m = 512/16
m = 32
The linear equation is then calculated as
y = 32( x - 2 ) + 64
y = 32x - 64 + 64
y = 32x
Hence, the equation that represents the linear function is y =32x
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The complete question is -
A linear function has the table of values shown. The information in the table shows the number of tickets sold on opening night of a movie as a function of the number of hours since the tickets have been on sale. Number of Hours (x) 2 6 18
Number of Tickets Sold (y) 64 192 576
1.Write the equation that gives the number of tickets sold, y, as a linear function of the number of hours, x, since the tickets have been on sale.
Which ratio is the odd one out 8:39, 6:30, 2:10, 4:20, 1:5
Answer:
8:39 is the answer.
The rest, when simplified, change to 1:5.
If a1=8 and an= an-1
Answer:
Step-by-step explanation:
242424
-2X + y = 9
y = -3.
help PLEASE
Answer:
To find the value of x, we can substitute the value of y in the equation:
-2X + (-3) = 9
We can then solve for X by isolating it on one side of the equation:
-2X = 12
X = -6
So, the value of X is -6.
Step-by-step explanation:
A cake manufacturer determines that the profit from making
x cakes per day is given by the function
P(x) = -x²+36x - 40 dollars.
a Calculate the profit if: i 0 cakes ii 20 cakes
are made per day.
b How many cakes need to be made per day for the profit to
be $270?
Answer:
a)
i) To calculate the profit if 0 cakes are made per day, we can substitute x = 0 into the function:
P(x) = -x²+36x - 40
P(0) = -0² + 36(0) - 40 = -40 dollars
So, the profit from making 0 cakes per day is -40 dollars.
ii) To calculate the profit if 20 cakes are made per day, we can substitute x = 20 into the function:
P(x) = -x²+36x - 40
P(20) = -20² + 36(20) - 40 = 760 dollars
So, the profit from making 20 cakes per day is 760 dollars.
b) To find out how many cakes need to be made per day for the profit to be $270, we need to solve the equation P(x) = 270.
We can substitute the function P(x) into this equation:
-x²+36x - 40 = 270
Next we can solve this equation for x by using any method you prefer ( factoring, Quadratic formula, etc)
x = (36 +/- √(36² -4*(-40)(-1)))/ 2(-1)
x = (36 +/- √(1296 + 320))/ -2
x = (36 +/- √1616)/ -2
x = (36 +/- 40)/ -2
x = -2 +/- 20
x = 18 or -22
The number of cakes need to be made per day for the profit to be $270 is 18 or -22, but -22 is not a valid solution because the number of cakes must be a non-negative value, so the number of cakes need to be 18
Which angle is vertical to 1?
Answer:
Have a good day!:)
Step-by-step explanation:
When two lines intersect at a point, they form two pairs of angles that do not share a side. These pairs are called vertical angles, and they always have the same measure. ∠1 and ∠3 are vertical angles. ∠2 and ∠4 are vertical angles.
A study was developed to evaluate effectiveness of a weight loss diet plan. An ad was placed in two towns to locate study participants who were to follow the diet. In Town A, the clinicians asked each dieter to report how much weight they had lost over the previous 6 weeks while following the diet. In Town B, the clinicians weighed each dieter at the beginning of the study and again after 6 weeks on the diet program. The weight lost was calculated as the difference between the beginning weight and the weight after 6 weeks. At the end of the study, it was determined that Town B had lost significantly less weight than Town A. a) What is the population of interest in this situation? b) Identify source(s) of bias in this study.
Answer:
a) The population of interest in this situation is individuals who are following a weight loss diet plan.
b) There are several sources of bias in this study:
Self-report bias: Town A relies on self-reported weight loss, which may not be accurate as participants may not accurately report their weight loss or may exaggerate their progress.
Measurement bias: Town B uses a different method of measuring weight loss than Town A, which could introduce a bias in the results.
Selection bias: Participants in this study are self-selected, which means that individuals who are more motivated or more likely to succeed in the diet may be more likely to sign up for the study. This can lead to a bias in the results as the sample may not be representative of the population of interest.
Hawthorne effect: Participants in Town B may have changed their behaviors simply because they knew they were being weighed, which could lead to a bias in the results.
Placebo effect: Participants in Town A may have lost weight due to the mere act of participating in a study and receiving attention, which could lead to a bias in the results.
what is
4 divided by 4/5
Answer:
5
Step-by-step explanation:
What is 1/5 x ( 7 x -4) =
Answer:
7x2−4x/5
Step-by-step explanation:
7x2−4x over 5
Shop a charges $275.00 for an oil change and has a gross oil profit of 39.1%. What is the profit per lube
The profit from Lube for Store A would be = $8.31.
What is the profit per unit?Unit profit can be obtained by subtracting the cost of the product from the selling price.
Data and calculations:
Selling price for oil change = $275
Percentage of total oil revenue = 39.1%
Cost of oil per gallon = $21.25
Selling price per gallon = $29.56 ($21.25 x $1,391)
Total income = $8.31 ($29.56 - $21.25)
Therefore, the profit from Lube for Shop A would be= $8.31.
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Complete question:
Shop A charges $275.00 for an oil change and has a gross oil profit percent of 39.1% for its total oil gross profit %. Shop B charges $275.00 for an oil change and has a gross oil profit percent of 28.4% for its total oil gross profit %. Both shops pay $21.25 per gallon of oil. What is the Profit per Lube for Shop A?
A farmer notes that in a field of horses and chickens there are 34 heads and 104 feet. How many of each animal are there
Answer: 18 horses and 16 chickens
Step-by-step explanation:
horses = h , chickens = c
h + c = 34
4h + 2c = 104, or simplified, 2h + c = 52
Now we just use systems of equations to solve. I will subtract the second equation from the first.
(2h + c = 52) -
(h + c = 34)
so simplified, our system becomes h = 18. Therefore, there are 18 horses. Now we can plug this value into h for any of the equations to get c, the amount of chickens.
18 + c = 34
c = 16.
Therefore, there are 18 horses and 16 chickens.
Assuming a Perfectly Competitive firm has the following cost function: TC = 1000 + 600Q – 10Q2 + 0.05Q3 . Minimum AVC is
Therefore , to calculate the average AVC, use the formula: TC at 0 output is 5, which equals fixed cost (FC) of 5.
How are AVC, AFC, and TC calculated?The fixed cost per unit of output is known as the AFC, and the variable cost per unit of output is known as the AVC. We previously stated that Bob's Bakery can produce 100 loaves with FC = 40, VC = 500, and TC = 540. ATC = TC/Q = 540/100 = 5.4 as a result. Additionally, AVC = 500/100 = 5 and AFC = 40/100 = 0.4.
Here,
Total cost is equal to total fixed cost plus total variable cost, or TC.
In order to obtain the VC at each output, we must first subtract 5 from the TCs for all subsequent output levels.
AVC is now equal to VC divided by Q.
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Casandras fish bowl holds 9/10 gallon of water. It is now 2/3 full. How much water is in the bowl?
The amount of water in Casandra's bowl, given the gallons of water it can hold and the fraction full it is, is 0.6 gallons
How to find the quantity of water ?Casandra' s fish bowl is able to hold a total of 9 / 10 gallons of water which is also 0.9 gallons of water. This means that you can find out how much water is in the bowl if told the fraction of the bowl that is currently full up to.
This time, the bowl is said to be 2 / 3 full which means that out of the capacity of 9 / 10 gallons or 0 . 9 gallons, the bowl is two - thirds full.
The amount of water in the bowl is therefore:
= Capacity of fish bowl x Proportion of water in the bowl
= 9 / 10 x 2 / 3
= 0. 9 x 2 / 3
= 0 . 6 gallons
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help with this please
Answer: A, B, and E can be used to satisfy the equation
Step-by-step explanation:
A applies because 45 is the same exact number as 45, so the equal sign accurately compares them.
B applies because that symbol means less than or equal to, and 45 is not less than but is equal to 45.
C does not apply because that symbol means is not equal to, but 45 is equal to 45.
D does not apply because that is the less than symbol, and 45 is not less than 45.
E applies because it is greater than or equal to symbol, and 45 is not greater than but is equal to 45.
F does not apply because that is the greater than symbol and 45 is not greater than 45.
Hope this helps!
