a) Using a base 2, the exponential function can be written as follows:
A(t) = 100(2)^(-t/235)
b) The amount of substance remaining after 1000 years is given as follows: 5.2 grams.
What is the exponential function?The exponential function for this problem is defined as follows:
A(t) = 100(0.5)^(t/235).
Which gives the amount of a substance after t years, considering a half life of 235 years.
The base can be changed to 2 as follows:
A(t) = 100(2)^(-t/235).
As exchanging the sign of the exponent, the numerator and the denominator of the base are exchanged, and 0.5 = 1/2.
The amount of the substance after 1000 years is calculated as follows:
A(1000) = 100 x (0.5)^(1000/235) = 5.2 grams.
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What is the result of this operation?
Answer: B
Step-by-step explanation:
If you chose D it would be wrong because you have to remember that the two negatives cancel out!
Which expressions are equivalent to
[tex] {5}^{18} [/tex]
select all that apply
Answer:
B and C
Step-by-step explanation:
(5⁷)¹¹ = 5⁷⁷
5⁹ × 5² = 5¹¹
Answer:
[tex] {5}^{12} \times {5}^{6} and \: \frac{ {5}^{24} }{ {5}^{6} } \\ option \: b \: and \: c[/tex]
Step-by-step explanation:
[tex] {a}^{b} \times {a}^{c} = {a}^{(b + c)} \\ \frac{ {a}^{b} }{ {a}^{c} } = {a}^{(b - c)} [/tex]
[tex] {5}^{12} \times {5}^{6} = {5}^{(12 + 6} = {5}^{18} \\ \frac{ {5}^{24} }{ {5}^{6} } = {5}^{(24 - 6)} = {5}^{18} [/tex]
Solve
e + 0.05 = 9.21
Answer: e = 9.16
Step-by-step explanation: Although it's not necessary, I would first get rid of the decimals by multiplying both sides of the equation by 100.
That gives is 100e + 5 = 921 which has no decimals.
Now just subtract 5 from each side to get 100e = 916 and
dividing both sides by 100 from here, e = 9.16.
find the number of different ways that an instructor can choose 3 students from a class of 24 students for a field trip.
There are 2024 ways in which the instructor can choose 3 students from a class of 24 students for the field trip.
A combination is a mathematical technique for calculating the number of possible arrangements in a set of items where the order of the selection is unimportant.You can choose the items in any order in combinations.
Permutations and combinations are often confused. In permutations, however, the order of the selected items is critical. For example, the arrangements ab and ba are equal in combinations (considered as one arrangement), but different in permutations.
There is a way you can calculate combinations using a formula. This formula is:
[tex]nC_r = \frac{n! }{ r!(n-r)! }[/tex]
where
n = total no. of items;
r = items selected for the combination;
"!" is the factorial
Given,
Total number of students in class , n = 24
Number of students selected, r = 3
So, the number of ways that 3 students can be selected from 24 students is
[tex]24C_3=\frac{24 !}{3!(24-3) !}\\\\=\frac{24 !}{3!*21 !}\\\\=\frac{3!*24*23*22*21 !}{3!*21 !}\\\\=\frac{24*23*22}{3*2*1}\\\\=2024[/tex]
Hence, the students can be selected in 2024 ways for the field trip.
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The r in the simple interest formula stands for rate which best describes how to use rate in formula
The best option is to Convert it to a decimal and multiply is the best way to describe rate in simple interest formula. The correct option is A.
What is simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principal, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest (S.I.) is a method for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount. The correct option is A.
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find f(20) if f(x)=[tex]\frac{1}{4}x+5[/tex]
Answer:
f(20) = 10
Step-by-step explanation:
at a certain gas station, 35% of the customers use regular unleaded gas, 35% use extra unleaded gas, and the remainder use premium unleaded gas. of those using regular gas, only 50% fill their tanks. of those customers using extra unleaded, 30% fill their tanks, whereas of those using premium unleaded, 30% fill their tanks. if the next customer fills the tank, what is the probability that extra unleaded gas was requested? (give your answer in percentage terms with one decimal point of precision.)
The probability that extra unleaded gas was requested is 35%.
To find the probability that the next customer requested extra unleaded gas, we need to first find the total probability that any customer requests extra unleaded gas.
Since 35% of customers request extra unleaded gas, the probability that a customer requests it is 35%. Of those customers, 30% fill their tanks, so the probability that a customer requesting extra unleaded gas fills their tank is 30%.
Therefore, the probability that a customer requesting extra unleaded gas fills their tank is (35%) * (30%) = 0.105, or about 10.5%.
This is the probability that the next customer requested extra unleaded gas and fills their tank. To find the probability that the next customer simply requested extra unleaded gas, regardless of whether they fill their tank or not, we need to add the probabilities of them requesting extra unleaded gas and either filling or not filling their tank.
The probability that the next customer requested extra unleaded gas and filled their tank is 0.105, as we calculated above. The probability that the next customer requested extra unleaded gas and did not fill their tank is (35%) * (70%) = 0.245, or about 24.5%.
To find the total probability that the next customer requested extra unleaded gas, we need to add these two probabilities: 0.105 + 0.245 = 0.35, or 35%. This is the probability that the next customer requested extra unleaded gas.
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in 12 years a man will be twice as old as he was 12 years ago . find his present age
His present age is 36 years.
Let his present age = x
Given,
2(x − 12) = x +12
2x - 24 = x + 12
2x - x = 12 + 24
x = 36
Therefore, his present age is 36 years.
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Which expression is equivalent to −6(b − 7)? −6b − 42 −6b + 42 −6b − 7 6b + 7
The expression that is equivalent to −6(b − 7) is: B. -6b + 42.
How to Find Equivalent Expressions?Expressions that are equivalent to each other will give the same value when simplified and solved in their simplest forms.
Simply put, two expressions will be equivalent if they have the same number of terms or they will give the same quantity when you plug in the values of all the variables that are given in the expressions.
Given the expression, -6(b - 7), the steps below shows how we can simplify to determine the expression that is equivalent to it
-6(b - 7) [given]
Open the parentheses by using the distributive property of equality, which involves multiplying each of the terms within the parentheses by the term outside of the parentheses:
-6(b) -6(-7) [distributive property]
-6b + 42
-6b + 42 is the equivalent expression of -6(b - 7).
Thus, the answer is: B. -6b + 42.
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There are 30 students in Mrs. Woodward's class and 1/5 of the class has their own cell phone. Of the students that have cell phones, 1/2 of them are allowed to use social media. How many of the students have a cell phone and can use social media?
Answer: 3 people
Step-by-step explanation:
1/5 of 30 will give us the number of students.
6
1/2 of 6, will give us the number of people who can use social media.
3 people.
10. Open-Ended Complete the addends so you need to regroup to add. Then find the sum. 4, _ 37 + 1,28_
The addends 4, _ 37 + 1,28_ is completed so there will be need to regroup to add.
the addends. 4, 837 + 1,287
the sum is 6124
What is regrouping?Regrouping refers to rearranging numbers into groups according to place value to assist kids in handling greater numbers.
When performing operations like addition and subtraction on two-digit integers or bigger, regrouping is the process of forming groups of tens. Regrouping refers to the process of performing an operation by rearranging groups in place value.
Using regrouping for the addition problem
addend 4 8 3 7
addend 1 2 8 7
sum 4
1 regrouped to tens column
addend 4 8 3 7
addend 1 2 8 7
sum 2 4
1 regrouped to hundreds column
addend 4 8 3 7
addend 1 2 8 7
sum 1 2 4
1 regrouped to thousands column
addend 4 8 3 7
addend 1 2 8 7
sum 6 1 2 4
the sum is 6124
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A map of an amusement park is shown on the coordinate plane with the approximate location of several rides.
Determine the distance between the Trolley Train and the Silly Slide.
25 units
7 units
5 units
3 units
The distance between the Trolley Train and the Silly Slide is 5 units. The 3rd option is the answer
How to determine the distance between the Trolley Train and the Silly Slide?From the map, the coordinate of the Trolley Train is (-2, -6) and the coordinate of the Silly Slide is (2, -3)
The formula for finding the distance between the two points is given as:
d=√(x₂ – x₁)² + (y₂ – y₁))²).
where
x₁ = -2,
y₁ = -6 (Trolley Train)
x₂ = 2
y₂ = -3 (Silly Slide)
d = √((2 – (-2))² + (-3 – (-6))²)
d = √((4)² + (3)²)
d = √25
d = 5 units
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Jeremy spent a total of $79.16 on a shirt and one pair of jeans. He knows the jeans cost $49.95 but he does not know the cost of the shirt, s. He created the model shown to find the cost of the shirt.
The model to show the cost of the shirt is x+49.95=79.16. Therefore, the cost of shirt is $29.21.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Jeremy spent a total of $79.16 on a shirt and one pair of jeans.
Let the cost of shirt be x.
The jeans cost is $49.95
Now, the cost of shirt + the cost of jeans = Total cost
⇒ x+49.95=79.16
⇒ x=79.16-49.95
⇒ x=$29.21
Therefore, the cost of shirt is $29.21.
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In a school Auditorium, there are three types of rows arrangement
possible for watching programs: rows of 20 students per row, or rows
of 25 students ver row, or rows of 40 students per row. Find the least
number of students required for any one of these arrangements so
that all the students can be accommodated in each of these
arrangements.
I think
it should be 200 as it's the first common multiple of 20 40 and 25
Stanley had a poster made from a picture of
his dog Tasha. The poster image is eight
times the size of the picture. If the poster
image is 120 cm. in height, what was the
height of Stanley's original picture of Tasha
(in centimeters)?
Answer:
15 c m.
Step-by-step explanation:
120 divided by 8 =15
make g the subject of 3e+4g=7+9eg
Answer:
the answer is g = (7 - 3e) / (4 - 9e)
Step-by-step explanation:
The subject of an equation is the value or values being solved for. An equation typically consists of two parts: an expression on the left side of an equal sign and an expression on the right side of the equal sign.
The given equation subject of equation is 3e + 4g = 7 + 9eg
Subtraction of 9eg from both sides of the equation
3e + 4g - 9eg = 7 + 9eg - 9eg
3e + 4g - 9eg = 7
Subtract 3e on both sides of the equation
3e + 4g - 9eg - 3e = 7 - 3e
4g - 9eg = 7 - 3e
Factorize g on left side of the equation,
g (4 - 9e) = 7 - 3e
Then divide (4 - 9e) on both sides of the equation,
g = (7 - 3e) / (4 - 9e)
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Kaylee conducted a scientific experiment. For a certain time, the temperature of a
compound rose 1 degrees every of an hour. What was the rate, in degrees per
hour, that the temperature of the compound rose? Enter your answer as a whole
number, proper fraction, or mixed number in simplest form.
The rate was the temperature increased by 1 degree for every 1 hour that passed.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
Kaylee carried out a scientific experiment. For a period of time, the temperature of a compound grew by one degree per hour.
The rate at which the temperature of the compound rose is 1 degree per hour. This means that for every hour that passed, the temperature of the compound increased by 1 degree.
The units for the rate are degrees per hour, which means that the temperature increased by 1 degree for every 1 hour that passed.
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The factors of the function are (x + 1), (x - 1) and (x-4). Which equation could describe the function?
The function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
What are factors?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
Given, the factors of a function are (x+1), (x-1) and (x-4)
We know that if the factors of a function are (x-a) and (y-b), it would mean that the function is (x-a)(y-b) = 0
Similarly, taking the above factors given in a function, the function would be:
(x+1)(x-1)(x-4)=0
⇒ (x²-1)(x-4)=0
⇒ x³-4x²-x+4 = 0
Hence, the function having the factors (x+1), (x-1) and (x-4) is x³-4x²-x+4 = 0
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each student at william elementary can only participate in one fall activity. there are 65 students on the football team and twice that number in band. there are 61 students on each of the two soccer teams. how many students participate in fall activities
Answer:191
Step-by-step explanation:
65x2=130
130+61=191
Rugged cabin co. provides pre-made materials to build cabins. to ensure materials are in supply and ready for quick delivery, the company offers cabins in only three sizes. each cabin has rectangular floor plan where the length is equal to 5 feet more than twice the width. which expression represents the area, in square feet, for each cabin size?A. 2w^2 + 5w, where w is the widthB. 2w^2 + 5, where w is the widthC. 2w^2, where w is the widthD. 10w^2 + 5 w, where w is the width
The expression that represent the area of the cabin for rectangular floor plan is 2w² + 5w.
What is the area of rectangular shape?
In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter.
Given that the length of a cabin is equal to 5 feet more than twice the width.
Assume that the width of the cabin be w.
Then the mathematical expression of twice the width is 2w.
Then the mathematical expression of 5 feet more than twice the width is 2w + 5.The length of the cabin is 2w + 5 feet.
The area of rectangular shape is product of length and width.
The area of the cabin is (2w + 5)w
Apply distributive property:
= 2w × w + 5 × w
= 2w² + 5w
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Consider the function
What is
f(x) = -2/3x + 5.
ƒ ( − 1/2 )
?
Answer:
Step-by-step explanation:
0
Answer:
f(1/2) = 5 1/3
Step-by-step explanation
All you need to do is replace each x in the function with -1/2, and you have your answer!
Hope this helps :)
Sometimes business partners do not share the ownership of a
business equally. Instead, they own a percentage of the
business, and each receives that percent of the profits.
Alvarez, Brown, and Chow are partners in a business that
earned $500,000. Alvarez owns 40% of the business. Chow
received $175,000. How much money did Alvarez make?
Alvarez received $200,000 which is 40% of the profit.
Define percentage.A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it. Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.
Given
Profit $500000
Alvarez owns 40% of the business.
Percentage
500000 × 40%
200000
Alvarez received $200,000 which is 40% of the profit.
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Solve the inequality.
$-12
in a poll, respondents were asked whether they were planning to vote in the local election. 315 respondents indicated that they were planning to vote and 217 said that they were not. what is the probability that the next respondent questioned will indicate that they are planning to vote?
The probability that the next respondent questioned would say they plan to vote is 0.59.
What is probability?
The ratio of the number of favorable outcomes to the total number of outcomes of an event is defined as probability.
We know that the probability of an occurrence =the number of favorable outcomes divided by the total number of events.
Given that, 315 respondents stated they planned to vote, while 217 said they did not.
Now, the probability of voting is:
P(voting)=315(315+217)
= 315/532
= 0.59
As a result, the likelihood that the next respondent questioned would say they plan to vote is 0.59.
The probability that the next respondent questioned would say they plan to vote is 0.59.
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Match each theorem with its description.
(3) Isosceles triangle Theorem
(8) Same side Interior angle Theorem
(2) Triangle sum Theorem
(1) Vertical angle Theorem
(7) Alternate exterior angle Theorem
(5)Corresponding angle Postulate
(6)Alternate exterior angle Theorem
(4) Triangle midsegment Theorem
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Isosceles triangle Theorem: A triangle's opposite angles are also congruent if its two sides are.
Same side Interior angle Theorem:
The same side interior angles are additional when two parallel lines are cut by a transversal.
Triangle sum Theorem:
According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
Vertical angle Theorem:
When two straight lines collide, two sets of linear pairs with identical angles are created.
Alternate exterior angle Theorem:
The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.
Corresponding angle Postulate:
The related angles are equivalent if a transversal cuts two parallel lines.
Alternate exterior angle Theorem:
The alternate interior angles or alternate exterior angles that emerge from cutting two parallel lines by a transversal are congruent.
Triangle midsegment Theorem:
The section connecting a triangle's two sides at their midpoints is parallel to and only half as long as the third side.
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[140,166,132,165,152,168,181,158,173,180,182,163,177,180,142,147,149,178]
Answer: Mode: 180
Quartiles:
Q1 --> 149
Q2 --> 165.5
Q3 --> 178
Mean: 162.944....
Median: 165.5
Step-by-step explanation:
AIM: SWBAT solve two-step equations using a balance model
THINK ABOUT IT!
Mark is working at a grocery store and is stacking apples. Before he stacks them, he puts them on a
balance to weigh them. On the right side of the balance, he put 15 apples. On the other side of the
balance, he puts two boxes of apples and three additional apples (pictured below). The weight on
either side of the balance is equal, which keeps the balance balanced.
Step A: Write an equation to represent the balance.
Step B: If there is the same number of apples in each box, how many apples are in each box
A. The equation that represents the balance is, 2x + 3 = 15.
B. Each box contains, x = 6 apples.
How to Write and Solve an Equation?Given the problem above, to write an equation that would represent the balance, we would assume both sides of the balance are separated by the equal sign, "=".
Therefore, let the unknown number of apples in each box be be represented as x.
A. Apples in the two boxes would be 2x, the total apples on the left of the balance would be expressed as:
2x + 3
On the right, we have 15 apples, therefore, the equation that represents the balance is: 2x + 3 = 15
B. Solve to find x, the number of apples in each box:
2x + 3 = 15
2x + 3 - 3 = 15 - 3
2x = 12
x = 12/2
x = 6
This means that there were 6 apples in each box.
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james is painting an L- shaped piece of wood that is made up of two rectangular prisms
6 in
5 in
1 in
7 in
11 in
How many square inches does he need to paint?
Applying the surface area of a rectangular prism, the number of square inches hat will be painted is, 346 in.².
How to Find the Surface Area of a Rectangular Prism?The surface area of a rectangular prism = 2(wl + hl + hw), where:
length - lwidth = wheight = hThe L-shaped piece of wood is composed of two rectangular prisms, therefore:
The square inches of paint needed = surface area of prism 1 + surface are of prism 2 - 2(area where both prism meet).
Prism 1 surface area:
l = 7 in.
w = 6 in.
h = 5 + 1 = 6 in.
Surface area = 2·(6·7+7·7+7·6) = 266 in.²
Prism 2 surface area:
l = 7 in.
w = 11 - 6 = 5 in.
h = 1 in.
Surface area = 2·(5·7+1·7+1·5) = 94 in.²
Area where both prism meet = (l)(w) = (7)(1) = 7 in.²
Number of square inches that needs to be painted = 266 + 94 - 2(7)
= 346 in.²
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Can you please give me the answer you don’t have to solve all but please!!!!!!
Answer: Reduction: 1/3
Step-by-step explanation:
Remember that if you are dilating it to be larger, it will be a whole number. If it is less than one, then it is dilating to be smaller.
Answer: Reduction 1/3.
Step-by-step explanation: When a shape is transformed into a smaller version of the original, it's a reduction. Reductions are less than 1 so the answer I provided above is what you're looking for.
Have a great day! :)
9. Solve for x.
12x + 3
11x +9
a. x = 9
b. x = 12
C. X = 6
d. x = 23
