Suppose you invest $1000 in a savings account that pays 5% annual interest. If you make no additional deposits or withdrawals, how many years will it take for the account to grow to at least $1500? (Hint: graph the equation in Desmos and find the point where the account contains $1500)
Answers
The number of years it will it take for the account to grow to at least $1500 is 4
What is simple interest?The formula for simple interest is given as:
A = P ( 1 + rt)
Where:
A is the final amount = $1500P is the principal amount = $ 1000r is the annual interest rate = 5%t is the time taken = unknownSubstitute the values
1500 = 1000 ( 1 + 5t)
Divide both sides by 1000
1500/ 1000 = 1 + 5t
1. 5 = 1 + 5t
collect like terms
1. 5 - 1 = 5t
0. 5 = 5t
Make 't' the subject of formula
t = 5/ 0. 5
t = 10 years
Thus, the number of years it will it take for the account to grow to at least $1500 is 4
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Related Questions
5. A study of a population of 1,200 frogs revealed that 12 out of every 180 frogs in the population
have spots on their back. Based on the results of this study, how many frogs in the population do
NOT have spots on their back?
A. 80 C. 1,280
B. 168 D. 1,120
Answers
Answer:
1,280
Step-by-step explanation:
prob(spots) = 12/180 = 1/15
so of the 1200 frogs, (1/15)(1200) should have spots, so ..
how many should not have frogs ?
or
prob(not spots) = 14/15
number who don't have spots = (14/15)(1200) = 1,280
The heights of 18 year old men are approximately normally distributed with mean 68 inches in standard deviation 3 inches what is the probability that an 18-year-old man do that random is greater than 74 inches tall
Answers
The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.
We have,
We can use the standard normal distribution to solve this problem by standardizing the height value using the formula:
z = (x - μ) / σ
where:
x = the height value (in inches)
μ = the mean height (in inches)
σ = the standard deviation (in inches)
Substituting the given values, we get:
z = (74 - 68) / 3
z = 2.0
Using a standard normal table or calculator, we can find the probability that a random standard normal variable is greater than 2.0 to be approximately 0.0228.
Therefore,
The probability that an 18-year-old man picked at random is taller than 74 inches is approximately 0.0228 or 2.28%.
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If the ratio between boys and girls is 3 to 2 if there are 12 boys how many girls are there
Answers
Answer:
the ratio is 12:8 boys to girls
Step-by-step explanation:
if the amount of boys is 12 then multiply the 3 by 4 and using distribution multiply the 2 by 4 as well to get 8 girls
5. Find Y.
Trapezoid Worksheet
Identify Which kind of trapezoid
Answers
Answer:
y = 28
Step-by-step explanation:
(20 + 5y + 4)/2 = 3y - 2
5y + 24 = 6y - 4
y = 28
I need help this is for my grade
Answers
This is a square pyramid, use this formula: V = 1/3Bh
1/3*(24*8)*22 = 1408
Answer:
1,408 cm.
Step-by-step explanation:
The formula for a square pyramid, so you would use this formula: V = 1/3Bh
1/3*(24*8)*22 = 1408
Find the mean, median and mode of the data set. If there is no mode, enter the words "no mode". 140, 128, 124, 137, 143, 126, 130, 136
Answers
Answer:
mode = no mode. median = 133, mean = 133
Step-by-step explanation:
mode = most common value. all of the values appear once. so there is no mode.
median = arranging the data in numerical order, then finding middle value.
there are 8 values. we have 4 on one side (124, 126, 128, 130) and 4 on the other (136, 137, 140, 143).
median is halfway between 130 and 136. that is 133.
mean = add up the values/ how many there are
adding them up, you get 1064. there are 8 values.
mean = 1064/8 = 133
Suppose you are standing in a parking lot near a building, and the winter air temperature is 0 degrees Celsius. At that temperature, sound travels about 331 meters per second. If you sound a horn and it takes 0.7 seconds to hear the echo, how far away is the building?
Answers
The building is 231.7 m far away.Distance can refer to a physical length or an estimate based on other factors in physics or common use.
What is distance?Distance is a numerical representation of the space between two objects or locations. |AB| is a symbol for the distance between two points A and B.
Given data;
Speed of sound = 331 meters per second
Time = 0.7 sec
The distance from the building is;
d=v×t
d=331 m/sec × 0.7 sec
d=231.7 m
Hence the building is 231.7 m far away.
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7x – 2y = -5
Ordered pair of solution
Answers
Answer:
7x-2y= -5 if should be the answer
Step-by-step explanation:
because 7x is different and 2y is also different and -5 is alsi different so they can not be subtract and not be add
√3 + (4 + √x + 3)² / 6 = 3
Answers
Answer: x = 1
Step-by-step explanation:
Ben and Bob made a snowman been spent two hours more than double the time Bob spent
Answers
x = the time it took Bob to make a snowman
y = the time it took Ben to make a snowman
(but the variables can be any letters)
Because Ben spent 2 hours more than 2 times the time Bob spent, the equation would be:
y = 2x + 2
Hope this helps
In ΔHIJ, h = 33 cm, i = 61 cm and j=39 cm. Find the area of ΔHIJ to the nearest square centimeter.
Answers
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
Explain about the Heron's formula:Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in regards of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: √s(s - a)(s - b)(s - c)
where s = half the perimeter,
s = (a + b + c)/2.
given data:
In ΔHIJ,
h = 33 cm, i = 61 cm and j =39 cm.semi -perimeter s = (i + j + h) / 2
s = (33 + 61 + 39) / 2
s = 66.5
Now,
s - h = 66.5 - 33 = 33.5
s - i = 66.5 - 61 = 5.5
s - j = 66.5 - 39 = 27.5
area of ΔHIJ = √s(s - h)(s - i)(s - j)
area of ΔHIJ = √66.5*33.5*5.5*27.5
area of ΔHIJ = √336947.1875
area of ΔHIJ = 580.47
Thus, the area of ΔHIJ using the Heron's formula is found as 580.47 square centimeter.
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Calculate the length of a chord of a circle of radius 26cm if the chord is 10cm from the center of the circle
Answers
Answer: see explanation
Step-by-step explanation:
The 10 cm distance is measured perpendicularly to the chord, forming a right angle and bisecting the chord. Thus half of the chord, the segment from the center of the chord, and a radius to the end of the chord form a right triangle. The hypotenuse is 26 cm and one leg is 10 cm, so the other leg is given by the Pythagorean theorem: a^2 + 10^2 = 26^2, giving a = 24 cm. Since a is half the chord, the chord is 2a = 48 cm in length.
Hence, the length of a chord of a circle is \(48cm\).
What is the circle?
A circle is defined as a two-dimensional figure, which is round in shape where all the points on the surface of the circle are equidistant from the center point is called “\(P\)”.
Here given that,
A circle of radius \(26\)cm if the chord is \(10\)cm from the center of the circle.
So,
The \(10\)cm from the center of the circle is perpendicular of the chord and the hypotenuse is \(26\)cm .
As we know
\(H^2=B^2+P^2\) .......\((1)\)
Substituting the values in the equation \((1)\), we get
\((26)^2=(10)^2+B^2\\B^2=676-100\\B^2=576\\B=\sqrt{576}\\B=24cm\)
Hence, the length of a chord of a circle is \(48cm\).
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Consider functions f and g.
Answers
The correct option regarding the multiplication of the functions f(x) and g(x) is given by:
C. \((f \times g)(x) = \frac{x^2 + 6x + 8}{x^2 + 2x - 15}, x \neq -5, x \neq 3\)
Multiplication of functionsTo multiply two rational functions, we multiply the numerators of each function and the denominator of each function to generate the rational functions.
In the context of this problem, before multiplying the functions, we can simplify them.
Function f(x) is given by:
\(f(x) = \frac{x^2 - 16}{x^2 + 3x - 10}\)
The numerator and the denominator can be simplified as follows:
Numerator: (x + 4)(x - 4): applying subtraction of perfect squares.Denominator: (x + 5)(x - 2): due to it's roots.Function g(x) is given by:
\(g(x) = \frac{x^2 - 4}{x^2 - 7x + 12}\)
The numerator and the denominator can be simplified as follows:
Numerator: (x + 2)(x - 2): applying subtraction of perfect squares.Denominator: (x - 3)(x - 4): due to it's roots.Then the multiplication function is:
\((f \times g)(x) = \frac{(x + 4)(x - 4)}{(x + 5)(x - 2)} \times \frac{(x + 2)(x - 2)}{(x - 3)(x - 4)}\)
The common terms (x - 4) and (x - 2) are simplified, hence the function is given by:
\((f \times g)(x) = \frac{x + 4}{x + 5} \times \frac{x + 2}{x - 3} = \frac{x^2 + 6x + 8}{x^2 + 2x - 15}\)
Hence option C is correct, with x = -5 and x = 3 being removed from the function due to the fact that they are the zeros of the denominator.
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A certain virus infects one in every 300 people. A Test used to detect the virus in a person is positive 85% of the time if that prerson has the virus and 5% of the time if the person does not have the virus. This 5% result is called a false positive. Let "A" be the event the person is infected and "B" the event the person tests positive. Find the probability that a person has the virus given that they have tested positive find the P(A/B)= Round to nearest tenth of a % Don't include % sign.
Answers
The probability that a person has the virus given that they have tested positive find the P(A/B)=0.0045
We can use Bayes' theorem to find the probability that a person has the virus given that they have tested positive:
P(A | B) = P(B | A) * P(A) / P(B)
where P(B | A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus (1/300), and P(B) is the total probability of testing positive.
To find P(B), we can use the law of total probability, which states that:
P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)
where P(B | not A) is the probability of testing positive given that the person does not have the virus. This is the false positive rate, which is 5% or 0.05 in this case. P(not A) is the complement of P(A), which is 299/300.
Substituting the values, we get:
P(B) = 0.85 * 1/300 + 0.05 * 299/300
= 0.059
Now we can plug in the values into Bayes' theorem:
P(A | B) = 0.85 * 1/300 / 0.059
= 0.0045 or 0.45%
Therefore, the probability that a person has the virus given that they have tested positive is 0.45% or 0.0045 (rounded to the nearest tenth of a percent).
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My cookbook's pancake recipe states that it makes 12 standard sized pancakes. The nutritional information says 2 pancakes is a serving containing 150 calories. For breakfast, I prepared half a recipe, but made smaller sized pancakes, so ended up preparing 8 pancakes. I ate 4 of them. How many calories did I consume?
Answers
Answer:
225 calories
Step-by-step explanation:
1 recipe makes
12 standard sized pancakes
2 pancakes are 1/6 of the recipe
1/6 of the recipe has 150 calories
6 × 150 calories = 900 calories
The full recipe of 12 pancakes has 900 calories
1/2 recipe was made
1/2 recipe has 1/2 × 900 calories = 450 calories
1/2 recipe made 8 pancakes
4 pancakes are half of the half recipe or 1/4 recipe
1/4 × 900 calories = 225 calories
Here is Takeshi's work determining a third point on the graph of an exponential function, `h(x)`.
Explain why the work is incorrect.
Answers
Answer:
Step-by-step explanation:
Let h(x) = y
The exponentail function is of the form :
\(y = ab^x\)
We have :
\(y_{_1} = ab^{x_{_1}}\\y_{_2} = ab^{x_{_2}}\\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{ab^{x_{1}}}{ab^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = \frac{b^{x_{1}}}{b^{x_{2}}} \\\\\implies \frac{y_{_1}}{y_{_2}} = b^{(x_1-x_2)}\)
Given points : (4, 9) and (5, 34.2)
We have:
\(\frac{34.2}{9} = b^{(5-4)}\\\\\implies 3.8 = b\)
Writing the equation with x, y and b:
\(y = ab^x\\\\\implies 9 = a(3.8^4)\\\\a = \frac{9}{3.8^4} \\\\a = 0.043\)
a = 0.043
b = 3.8
When x = 6, y will be:
\(y = (0.043)(3.8^6)\\\\y = 128.47\)
This is not the y value in the question y = 59.4
Therefore (6, 59.4) does not lie on the graph h(x)
A sample was done , collecting the data below. Calculate the standard deviation,to one decimal place
Answers
By definition, the standard deviation is
\(\sigma = \sqrt{\frac{\sum_{i=1}^{n}\left(x_i-\bar{x}\right)^2}{n}}\)It seems hard so let's do it step by step, first, let's find the mean of the data
\(\begin{gathered} \bar{x}=\frac{24+29+2+21+9}{5} \\ \\ \bar{x}=17 \end{gathered}\)Now we have the mean value, let's do each value of the set minus the mean value
\(\begin{gathered} x_1-\bar{x}=24-17=7 \\ \\ x_2-\bar{x}=29-17=12 \\ \\ x_3-\bar{x}=2-17=-15 \\ \\ x_4-\bar{x}=29-17=4 \\ \\ x_4-\bar{x}=9-17=-8 \end{gathered}\)Now we have the difference between each element and the mean value, let's do the square of all values
\(\begin{gathered} (x_1-\bar{x})^2=7^2=49 \\ \\ (x_2-\bar{x})^2=12^2=144 \\ \\ (x_3-\bar{x})^2=(-15)^2=225 \\ \\ (x_4-\bar{x})^2=4^2=16 \\ \\ (x_5-\bar{x})^2=(-8)^2=64 \end{gathered}\)Now we have the square of the difference we sum them
\(\begin{gathered} \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=\left(x_1-\bar{x}\right)^2+\left(x_2-\bar{x}\right)^2+\left(x_3-\bar{x}\right)^2+\left(x_4-\bar{x}\right)^2+\left(x_5-\bar{x}\right)^2 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=49+144+225+16+64 \\ \\ \sum_{i=1}^5\left(x_i-\bar{x}\right)^2=498 \end{gathered}\)Now we have the sum we must divide by the number of elements, in that case, 5 elements
\(\frac{\sum_{i=1}^5\left(x_i-\bar{x}\right)^2}{5}=99.6\)Now we take the square root of that value to have the standard deviation!
\(\sigma=\sqrt{99.6}=9.979\)We write it using only one decimal the result would be
\(\sigma=9.9\)With no rounding.
Final answer:
\(\sigma=9.9\)WHAT IS THE ANSWER!!!!!
EXPLAIN
Answers
Answer:
314 < S <=512
Step-by-step explanation:
Your salary will be more than 314 so S > 314 but not more(which mean it can be equal to 512) than 512 so S <= 512
Grady is excavating the foundation of a house. If the hole will be
40 feet long, 24 feet wide, and 4 feet deep, how many cubic feet
of dirt must be removed from the site?
Answers
Answer:
3,840 cubic feet
Step-by-step explanation:
V=LWH
V= 40X24X4
V=3,840 cubic feet
In a fruit basket, there are 9 bananas, 7 apples, and 3 plums,
Enter a numerical value to answer the question completely.
Answers
Answer:
Bananas to apples are 9:7
Plums to apples are 3:7
apples to plums are 7:3
Bananas to plum are 3:1
Step-by-step explanation:
For every Plum there are 3 bananas.
The ratio of apples to plums are 7:3.
For every apple there are 7/9 banana.
If 2 pounds of rib steak and 6 pounds of hamburger meat costs $12.30 and 3 pounds of rib steak and 2 pounds of hamburger meat costs $9.70, what is the cost per pound of each type of meat?
Answers
The cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.
To find the cost per pound of each type of meat, we can set up a system of equations based on the given information.
Let's denote the cost per pound of rib steak as 'x' and the cost per pound of hamburger meat as 'y'.
From the first statement, we know that:
2x + 6y = 12.30 ---(Equation 1)
From the second statement, we know that:
3x + 2y = 9.70 ---(Equation 2)
Now we can solve this system of equations to find the values of 'x' and 'y'.
Multiplying Equation 1 by 3 and Equation 2 by 2 to eliminate the 'x' term, we get:
6x + 18y = 36.90 ---(Equation 3)
6x + 4y = 19.40 ---(Equation 4)
Subtracting Equation 4 from Equation 3, we get:
14y = 17.50
Dividing both sides by 14, we find:
y = 1.25
Substituting the value of 'y' back into Equation 1, we can solve for 'x':
2x + 6(1.25) = 12.30
2x + 7.50 = 12.30
2x = 4.80
x = 2.40
Therefore, the cost per pound of rib steak is $2.40 and the cost per pound of hamburger meat is $1.25.
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What is (3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)?
Answers
Answer:
Hope this helps ;) don't forget to rate this answer !
Step-by-step explanation:
To solve this problem, we need to perform the indicated operations in order. The first step is to simplify the expressions inside the parentheses.
(3x7 + 7x5 - 3x² + 7) + (x7 - 3x5 + 2x³ + 3)
= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)
The next step is to combine like terms within each parentheses:
= (21x + 35x - 3x² + 7) + (7x - 15x + 2x³ + 3)
= (56x - 3x² + 7) + (-8x + 2x³ + 3)
Finally, we can add the two expressions:
= (56x - 3x² + 7) + (-8x + 2x³ + 3)
= 56x - 3x² - 8x + 2x³ + 3 + 7
= 56x - 3x² - 8x + 2x³ + 10
The final answer is 56x - 3x² - 8x + 2x³ + 10.
A teacher has a bag of marbles. There are 6 red, 6 blue, 8 green, 7 purple, and 8 yellow marbles in the bag. As the students enter the classroom, they draw a marble and keep it. If the first student in the room draws a yellow, and the second draws a purple, what is the probability that the third student will draw a yellow also?
Question 12 options:
25%
20%
33%
21%
Answers
How do we determine the function, minimum or maximum, and the value of the minimum or maximum?
Answers
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed.
Answers
The 99% confidence interval for the population proportion p is (0.776, 0.824).
To find the 99% confidence interval for a proportion, we can use the formula:
CI = p^ ± z*(SE)
where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.
For a 99% confidence interval, the critical value z is 2.576.
Substituting the given values into the formula, we have:
CI = 0.80 ± 2.576*(0.03/√200)
Simplifying this expression, we have:
CI = 0.80 ± 0.024
This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.
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I took a picture of the question
Answers
The transformation in the picture is option c Reflection.
Given,
Reflection transformation:
A reflection is a transformation that works similarly to a mirror by switching all pairs of points that are directly across from one another along the line of reflection. A mathematical formula or the two sites it passes through can be used to define the line of reflection.
According to the law of reflection, r = I the angle of incidence and reflection are equal. θ r = θ I . At the point where the ray strikes the surface, the angles are measured in relation to the perpendicular to the surface.
Here,
In the picture the transformation is reflection.
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Whats 5 × 10⁵ = ? ...
Answers
Answer:
\(500,000\)
__________________
Additional Comment:
If you found this answer helpful, please mark Brainliest! :)
Answer:
500,000
Step-by-step explanation:
If you first multiply 10 ×10 five times as the 10 power is 5 then if you multiply 5 with that number comes from the multiplication of 10×10 five times then you will get your answer
If this help you then plz mark me as a brainliestA school paid a total of $98.00 for 5 aluminum baseball bats and a total of $75 for 6 wooden baseball bats. How much more did EACH aluminum bat cost than each wooden bat?
Answers
Answer:
Each aluminium bat costs $7.1 more than wooden bat. PLS GIVE BRAINLIEST PLSSS
Step-by-step explanation:
Aluminium bats:
5 = $98
1 = 98/5
1= $19.6
Wooden bats:
6 = 75
1 = 75/6
1 = $12.5
$19.6 - $12.5
= $7.1
which is greater 0.45 or 9/10???
Answers
Answer:
9/10 bc it would be .90 in decimals
Step-by-step explanation:
Answer:
9/10 is
Step-by-step explanation:
9/10 as a decimal is 0.9 and if you line them up, 0.9 is greater than 0.45
Plsss help ASAP pls this is due at 12:00
Answers
Answer:
$74.49
(basically $74.50)
Step-by-step explanation:
hope that helps :))