Answer:
3.0 grams of the element are left after 18 minutes
Step-by-step explanation:
Recall that an exponential decay that can be studied with the following formula for the amount of material (A) as a function of time (t):
[tex]A(t)=A_0(1-r)^t[/tex]
where:
[tex]A_0[/tex] is the starting amount of the substance (in our case 820 grams)
r is the rate of decay (which in our case given as 26.8% can be written in decimal form as 0.268
and t is the time in minutes (in our case t = 18 minutes)
Then we have:
[tex]A(t)=A_0(1-r)^t\\A(18)=820*(1-0.268)^18\\A(18)=820*(0.732)^18\\\\A(18)=2.985\,grams[/tex]
which can be rounded to 3.0 grams
Answer: 3.0
Step-by-step explanation:
a=820
r= rate= 26.8%=0.268
b=1-r=1-0.268=0.732
y=820(0.732)^18
y=2.985474
y=3
The sum of 3 times a and b
Answer:
3+(axb)
Step-by-step explanation:
The algebraic representation of the expression The sum of 3 times a and b is 3a + b
How to determine the algebraic representation of the expressionFrom the question, we have the following parameters that can be used in our computation:
The sum of 3 times a and b
By definiton:
sum means plus
Using the above as a guide, we have the following:
3 * a + b
When solved, we have
3a + b
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Question
Translate the sentence into an algebraic expression
The sum of 3 times a and b
0.0398 rounded to the nearest cent
Answer:
0.04
Step-by-step explanation:
0.0398
when rounding if its over 5 you round up if its under you round down
The number 0.0398 rounded to the nearest cent; is 0.04.
According to the question;
We are required to round off 0.0398 to the nearest cent.To round off to the nearest cent;
We must know that cents is synonym for Hundredths;
The number to be rounded off is 0.0398In essence, since 9 which is after the digit, 3 which occupies the hundredth position is greater than 5; it is rounded off to 1 and added to 3.Consequently; 0.0398 rounded to the nearest cent is 0.4
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Which expression is equivalent to 1/5(15+10x-5)
Answer:
simplify the expression: 2x+2
Step-by-step explanation:
The equivalent expression of the given expression is is 2 + 2x
To solve this expression, we should simply proceed to multiply the value outside the bracket and simplify.
steps required;
collect like termsmultiply through the bracket by the value outsideCollect like termsThis is done to add up or subtract similar or like values with each other.
[tex]\frac{1}{5}(15+10x-5)=\frac{1}{5}(15-5+10x)=\frac{1}{5}(10+10x)\\[/tex]
Multiply ThroughMultiply the entire value inside the bracket by 1/5.
[tex]\frac{1}{5}(10+10x)=2+2x[/tex]
This is the simplified expression of what we are given.
The equivalent expression is 2 + 2x.
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A store owner sells two pairs of running
shoes for each pair of high tops.
He plans to order 144 pairs of shoes
How many pairs should be high tops?
Answer:
He will order 72 pairs of high tops
Explanation:
Given the store owner sells two pairs of running shoes for each pair of high tops
For every pair of high tops, he sells 2 pairs of running shoes
1 high top = 2 running shoes
He has planned to order 144 pairs of shoes
Therefore, 144 pair of running shoes = 144/2 = 72 pairs of high tops
Therefore, he will order 72 pairs of high tops
A pole that is 3.5 m tall casts a shadow that is 1.66 m long. At the same time, a nearby building casts a shadow that is 4.5 m long. How tall is the building?
Answer:
About 9.5 meters tall. Make sure to include the meters and the wiggly equal sign indicating about
Step-by-step explanation:
This is just a ratio
1.66:3.5 = 4.5:x
Cross multiply
1.66x = 15.75
Divide by 1.66 on both sides
x = about 9.5
write an expression where you multiply 0.035 times the power of ten so that the product is greater than 1 and less than 100 please help
Answer:
[tex]0.035\times 10^{3}[/tex]
Step-by-step explanation:
Given: The value of 0.035
Now, as we know 0.035 has three decimal place which mean if we multiply by 1000 then we have the product 35 which is greater than 1 and less than 100, however if we multiply 0.035 by 10000 then the output will be greater than 100, which is invalid.
Lets us use hit and trail method.
[tex]0.035\times 1000 = 35 < 100\\\\0.035\times 10000= 350 >100[/tex]
Now lets put the value in expression
[tex]0.035\times 10^{3}[/tex]
Mary and Lamar establish a tutoring service at a local mall. They tutor college students in math and English. They charge $40 per hour for tutoring. In the month of January they charged for 200 tutoring hours. The expenses of their business are given in the table below. Expense Amount/Month Rent of Space $4000 Electricity $325 Advertising $375 Using the formula Profit = $40(number of hours) – (expenses) , calculate their profit for the month of January.
Answer:
8000
Step-by-step explanation:
Answer: The profit is $3300
Step-by-step explanation:
The data we have is:
They charge $40 per hour.
In january, the charged for 200 hours.
The expenses are:
rent $4000
electricity $325
advertising $375
if we want to know the balance we must calculate:
The total expenses are: $4000 + $325 + $375 = $4700
The amount that they won is: $40*200 = $8000
Then the profit will be:
P = $40*200 - ($4000 + $325 + $375) = $8000 - $4700 = $3300
The equation used to predict the total body weight (in pounds) of a female athlete at a certain school is ModifyingAbove y with caret equals negative 121 plus 3.38 x 1 plus 1.48 x 2, where x1 is the female athlete's height (in inches) and x2 is the female athlete's percent body fat, measured as x2%. Use the multiple regression equation to predict the total body weight for a female athlete who is 68 inches tall and has 21% body fat.
To predict the total body weight for a female athlete who is 68 inches tall and has 21% body fat, substitute the given value for each independent variable into the multiple regression equation.
Substitute the values for x1 and x2 into the multiple regression equation.
Answer:
do u still need help??
Step-by-step explanation:
11. In 2010, the population in the United States will be about 3.09x10'. Spending for health care will be
about $8754 per person. About bow much will the US spend on health care in 2010? Write in scientific
notation and round to the ncarest hundredths.
Answer:
[tex]\$ 2.70\times 10^{12}[/tex]
Step-by-step explanation:
Complete question is here: In 2010, the population in the United States will be about 3.09x10^8. Spending for health care will be about $8754 per person. About how much will the US spend on health care in 2010? Write in scientific notation and round to the nearest hundred.
Given: Per person expenditure on healthcare is $8754.
Total population in 2010 is 3.09x10^8.
Now, lets find out total money U.S will spend on health care.
[tex]\textrm{Total population} \times amount\ spent\ per\ person\ on\ healthcare}[/tex]
= [tex]8754\times 3.09\times 10^{8} = 27049.96\times 10^{8}[/tex]
= [tex]\$ 2.705\times 10^{12}[/tex] ≅ [tex]\$ 2.70\times 10^{12}[/tex]
∴ In 2010, U.S will spend [tex]\$ 2.70\times 10^{12}[/tex] on health care.
Answer:
about $2.70 × 1012
Step-by-step explanation:
$8754(3.09 × 108)
= $27,049.86 × 108
≈ $2.70 × 1012
E
What are the dimensions of the product?
2
4 -3 |x| -2
гу со
| 6 1 о| |
o1 x 2
O2 x 2
О 3x 2
o3х3
Answer:
The dimension of the product is 2×2.
Step-by-step explanation:
The given problem is based on Matrices and it is a matrix multiplication or Matrix product.
For any Two Matrix multiplication it is necessary, number of columns of matrix A must be equal to number of rows of matrix B.
Then only multiplication of matrix exist.
Then the product of multiplication i.e Matrix C will have the order number of rows of Matrix A by number of columns of Matrix B
Let A be the first Matrix multiplied by matrix B
Matrix A is of order 2×3
Rows=2, column =3
Matrix B is of order 3×2
Rows=3, column =2
So here number of columns of matrix A is equal to number of rows of matrix B i.e 3
And the product order will be number of rows of Matrix A by number of columns of Matrix B .i.e 2×2
Answer:
b on edge or 2x2
Step-by-step explanation:
Assume the adults have IQ scores that are normally distributed with a mean of 105 in a standard deviation of 20 find the probability that a randomly selected adult has an IQ less than 145
Answer:
The correct answer is that the probability of a randomly selected adult has an IQ less than 145 is 97.8%
Step-by-step explanation:
According to the graphic of a standard distribution attached, we have:
68.3% of the population will have an IQ +/- one time the standard deviation plus the mean. It means that 68.3% (Rounding to one decimal place) of the adults will have an IQ between 85 and 125.
95.5% of the population will have an IQ +/- two times the standard deviation plus the mean. It means that 95.5% (Rounding to one decimal place) of the adults will have an IQ between 65 and 145.
The remaining 4.5% of the adults will have either an IQ below 65 or above 145. In this case, we only want to know the percentage below 65 because the question is about the probability of an IQ less than 145. For calculating the percentage of adults that have an IQ less than 65, we use this fraction:
4.5%/2 = 2.3% (Rounding to one decimal)
and we add this percentage to 95.5:
Probability that a randomly selected adult has an IQ less than 145 = 95.5 + 2.3 = 97.8%
Hope the moderator will not delete the answer because I'm uploading a graphic; this graphic is exclusively for academic purposes.
PLZ HELP ME WILL GIVE BRAINLIEST
1. Explain how 2 x 10^-4 is the same as 2 ÷ 10^4 using expanded notation.
3. Explain the difference between (-10)^2 and -10^2. What are the values of each expression?
4. Explain the power of products property and give an example.
Answer:
1. [tex]2 \times 10^{- 4} = 2 \div 10^{4}[/tex]
2. [tex](- 10)^{2} = 100[/tex] and [tex]- 10^{2} = - 100[/tex]
3. [tex](a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........[/tex]
Example: [tex](30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times 3^{4} \times 5^{4}[/tex]
Step-by-step explanation:
1. We have [tex]2 \times 10^{- 4}[/tex], and we have to prove that this term is equivalent to [tex]2 \div 10^{4}[/tex].
Now, [tex]2 \times 10^{- 4}[/tex]
= [tex]2 \times \frac{1}{10^{4} }[/tex]
{Since we know the property of exponent as [tex]a^{- b} = \frac{1}{a^{b} }[/tex] }
= [tex]\frac{2}{10^{4} }[/tex]
= [tex]2 \div 10^{4}[/tex]
2. [tex](- 10)^{2} = (- 10) \times (- 10) = 100[/tex] and
[tex]- 10^{2} = - [(10) \times (10)] = - 100[/tex]
3. The power of products property gives
[tex](a.b.c. ........)^{n} = a^{n}.b^{n}.c^{n}. ..........[/tex] ........ (1)
For example, we can write, [tex](30)^{4} = (2 \times 3 \times 5)^{4} = 2^{4} \times 3^{4} \times 5^{4} = 810000[/tex]
I have the first part but I don't know how to do the second part
h e l p
[tex]\bf \begin{array}{cll} \stackrel{ordinal}{position}&\stackrel{term}{value}\\ \cline{1-2} 1&12\\ 2&12+d\\ 3&12+d+d\\ 4&12+d+d+d\\ &12+3d \end{array}\qquad \implies ~\hfill \begin{array}{llll} \stackrel{\textit{4th term}}{12+3d}~~=~~\stackrel{\textit{4th value}}{3}\\\\ 3d=-9\implies d = \cfrac{-9}{3}\\\\ \stackrel{\textit{common difference}}{d = -3} \end{array}[/tex]
well, we know the common difference is -3, to go from the 4th term to the 8th term, we need to add "d" 4 times or namely 3+4(-3), likewise to go from the 13th term to the 19th term we have to add "d" 6 times, or namely -24 + 6(-3).
[tex]\bf \stackrel{\textit{8th term}}{3+4(-3)}\implies 3-12\implies -9 \\\\\\ \stackrel{\textit{19th term}}{-24 + 6(-3)}\implies -24-18\implies -42[/tex]
a chain saw rental for $12 a day. A sharpening fee of $5 is charged for each rental. write an equation for the number of dollars (y) that must be paid to rent a chain for x days. How many days can one rent a chain saw for a cost of $125?
Answer:
y= 12x+5 and It would be 10 days.
Step-by-step explanation:
Y= total
+5 = each rental
X= # of days
125= 12x+5; x=10
The equation to determine the cost of renting a chainsaw for x days is y = 12x + 5. For a cost of $125, one can rent the chainsaw for 10 days.
To write an equation for the number of dollars (y) that must be paid to rent a chainsaw for x days, take into account the daily rental fee and the one-time sharpening fee. The daily rental fee is $12, and there is an additional one-time sharpening fee of $5 for each rental. The total cost y is therefore the sum of the daily rental fees for x days and the sharpening fee.
The equation is:
y = 12x + 5
To find out how many days one can rent a chainsaw for a cost of $125, we can set y equal to $125 and solve for x:
125 = 12x + 5
Subtract 5 from both sides to get:
120 = 12x
Divide both sides by 12 to solve for x:
x = 10
Therefore, one can rent a chainsaw for 10 days at a cost of $125.
From the equation, find the axis of symmetry of the parabola.
y = x^2+ 3x + 1
A. X= 3/2
B. Y= 1
C. X=3
D. X= -3/2
Answer:
D
Step-by-step explanation:
Quadratic has a general form of:
[tex]ax^2 + bx + c = 0[/tex]
The quadratic given here is:
[tex]y = x^2 + 3x + 1[/tex]
Matching it with the general form, we can see that:
a = 1 [coefficient of x^2]
b = 3
c = 1
Now, if we look at the formula for axis of symmetry, we can easily solve this out. The axis of symmetry is given by:
Axis of Symmetry is [tex]x=-\frac{b}{2a}[/tex]
We know a = 1 and b = 3, so we have:
[tex]x=-\frac{b}{2a}\\x=-\frac{3}{2(1)}\\x=-\frac{3}{2}[/tex]
Hence,
D is the correct answer.
Answer:
is D
Step-by-step explanation:
gcf of 35 and 15 and 3
Answer:
1
Step-by-step explanation:
Greatest Common Factor is the highest number that divides exactly into two or more numbers. It is the "greatest" thing for simplifying fractions.
No number (except 1) is divisible by both 35, 15, and 3. Therefore, the GCF is 1.
Answer:
35: 5×7 GCF: 5×3=15
15: 5×3
3: 1×3
Step-by-step explanation:
35 15 3
/ \ / \ / \
5 × 7 3 × 5 1 × 3
Write a number that completes analogy:
x² is 441 as x³ is to.............
Answer:
9261
Step-by-step explanation:
the problem is payed out like this formula
x² = 441
you take the square root of 441 to find x which is 21 and then you just take cubic of 21 which is 9261
Answer:
9261
Step-by-step explanation:
x² = 441
you take the square root of 441 to find x which is 21 and then you just take cubic of 21 which is 9261
bernard ate part of a small pizza he started with 11/12 of a pizza but only ate 2/3 of it. Which is the best estimate of the amount bernard ate
Answer:1/4
Step-by-step explanation:
11/12 - 2/3
22/24 - 16/24 =6/24= 1/4
Tommy's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 51 regular sodas and 34 diet sodas. What percentage of the sodas served were regular?
Answer:
72
Step-by-step explanation:
What is the solution to the linear equation?
d – 10 – 2d + 7 = 8 + d – 10 – 3d
d = –5
d = –1
d = 1
d = 5
The solution to the linear equation d – 10 – 2d + 7 = 8 + d – 10 – 3d is d = 1.
EquationAn equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
d – 10 – 2d + 7 = 8 + d – 10 – 3d
Simplifying:
-d - 3 = -2d - 2
Collecting like terms:
-d + 2d = -2 + 3
d = 1
The solution to the linear equation d – 10 – 2d + 7 = 8 + d – 10 – 3d is d = 1.
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Carol wants to make a quilt using a scale of 1.5 inches=2 feet. Her scale drawing is 7.5 inches by 10.5 inches. What is the area of the actual quilt?
_[blank]_ square feet
I will mark the first one to answer my question brainleist
Answer:
140 ft
Step-by-step explanation:
a bakery used 25% more butter this month than last month if the bakery use 240 kg of butter last month how much butter did he use this month
Answer: [tex]300\ Kg[/tex]
Step-by-step explanation:
Let be "x" the amount of butter (in kilograms) that the bakery used this month.
You need to divide the percentage by 100 in order to write it in decimal form. This is:
[tex]\frac{25}{100}=0.25[/tex]
According to the data given in the exercise, the total amount of butter they used last month is 240 kilograms.
Since 25% more butter was used this month than last month, you can write the folllowing equation:
[tex]x=240+(240 )(0.25)[/tex]
Evaluating, you get that the value of "x" is:
[tex]x=240+60\\\\x=300[/tex]
Therefore, the bakery used 300 kilograms of butter this month.
Final answer:
The bakery used 300 kg butter this month.
Explanation:
If a bakery used 25% more butter this month than last month and it used 240 kg of butter last month, then to calculate the amount of butter used this month, we need to add an additional 25% to the amount from last month. To find 25% of 240 kg, you multiply 240 kg by 0.25 (since 25% is the same as 0.25 when expressed as a decimal).
25% of 240 kg = 240 kg × 0.25 = 60 kg
Now, we add that 60 kg to the original 240 kg to find the total amount of butter used this month.
Total amount of butter used this month = 240 kg + 60 kg = 300 kg.
Therefore, the bakery used 300 kg of butter this month.
what is the value of n if n divided by 256 = 8 1/3 times 8 1/3?
The value of 'n' in the given mathematical equation n/256 = 8 1/3 * 8 1/3 is approximately 17766.4.
Explanation:The question asks what is the value of n if n divided by 256 = 8 1/3 times 8 1/3. To find the answer, first we need to calculate the value of 8 1/3 times 8 1/3. Converting 8 1/3 to a decimal result in approximately 8.33. Then, we multiply 8.33 by itself to get approximately 69.4.
Since n divided by 256 gives this value, to find n, we simply multiply 69.4 by 256. This results in approximately 17766.4. Therefore, given the condition in the problem, the value of n would be approximately 17766.4.
To find the value of n, we need to solve the equation: n/256 = 8 1/3 * 8 1/3. First, let's convert 8 1/3 to a fraction: 8 1/3 = 25/3. Next, multiply 25/3 by itself to get (25/3) * (25/3) = 625/9. Now we can solve for n by multiplying both sides of the equation by 256: n = (256 * 625/9).
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A bicycle store costs $3250 per month to operate. The store pays an
average of $35 per bike. The average selling price of each bicycle is $85
How many bicycles must the store sell each month to break even?
Answer:
65 bikes
Step-by-step explanation:
The store buys the bikes that they sell for $35, and they sell them for $85, so in order to find the actual amount of money earned from one sale, you have to subtract how much they sell the bikes for by how much they bought them for, so:
85 - 35 = 50
Then, you divide the $3250 by the 50:
3250 / 50 = 65
So now we know that the store must sell 65 bikes a month to break even.
-13(v-6)=-5v+2(5v+12)
Answer:
v = 3Step-by-step explanation:
[tex]-13(v-6)=-5v+2(5v+12)\qquad\text{use the distributive property}\\\\(-13)(v)+(-13)(-6)=-5v+(2)(5v)+(2)(12)\\\\-13v+78=-5v+10v+24\qquad\text{cobine like terms}\\\\-13v+78=(-5v+10v)+24\\\\-13v+78=5v+24\qquad\text{subtract 78 from both sides}\\\\-13v+78-78=5v+24-78\\\\-13v=5v-54\qquad\text{subtract}\ 5v\ \text{From both sides}\\\\-13v-5v=5v-5v-54\\\\-18v=-54\qquad\text{divide both sides by (-18)}\\\\\dfrac{-18v}{-18}=\dfrac{-54}{-18}\\\\v=3[/tex]
ALWAYS use significant figure rules. Remember that these rules apply to all numbers that are measurements. An object moves in uniform circular motion at 25 m/s and takes 1.0 second to go a quarter circle. What is the radius of the circle? R = _____ m 0.063 m 0.99 m 16 m 50. m
Answer: 16 m
Step-by-step explanation:
We have the following data:
[tex]V=25 m/s[/tex] is the velocity of the object moving in uniform circular motion
[tex]t=1 s[/tex] is the time it takes to the object to go [tex]\frac{1}{4}[/tex] of a complete circle
We need to find the radius [tex]r[/tex] of the circle, and this can be found by the following equation:
[tex]V=\frac{2 \pi r}{T}[/tex] (1)
Where [tex]2 \pi r[/tex] is the circumference of the circle and [tex]T=4 t=4(1 s)[/tex] is the period for a complete circle.
Hence, isolating [tex]r[/tex] we have:
[tex]r=\frac{V T}{2 \pi}[/tex] (2)
[tex]r=\frac{(25 m/s)(4 s)}{2 \pi}[/tex] (3)
Finally:
[tex]r=15.9 m \approx 16 m[/tex] (4)
7 bees 5 cockroaches 8 spiders 4 deer 4 boars how many legs are there in total
There are total 168 legs.
Given, 7 bees 5 cockroaches 8 spiders 4 deer 4 boars.
We have to calculate the total number of legs.
Since, 1 bees has 6 legs, so 7 bees has in total [tex](7\times 6=42)[/tex] legs.
1 cockroach has also 6 legs, so 5 cockroach has in total of [tex](6\times 5=30)[/tex] legs.
1 spider has 8 legs so 8 spider has in total of [tex](8\times 8=64)[/tex] legs.
1 deer has 4 legs so 4 deer has in total of 16 legs.
1 boar has 4 legs so 4 boars has in total of 16 legs.
Hence the total number of legs the above animal has will be,
[tex]42+30+64+16+16=168[/tex] legs.
Therefore, There are total 168 legs.
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What is the value of 3/y if y = 1 2/3?
Answer:
9/5
Step-by-step explanation:
1 2/3=5/3
3/(5/3)=(3/1)(3/5)=9/5
How many grams of hydrogen must react if the reaction needs to produce 31.75 g of NH3
Answer:
5.603 g H2
Step-by-step explanation:
M(NH3) = 14 + 1*3 = 17 g/mol
M(H2) = 2*1 = 2 g/mol
3H2 + N2 -----> 2NH3
from reaction 3 mol 2 mol
from reaction 3*2 g 2*17 g
given x g 31.75 g
We can write a proportion.
(3*2)/x = 2*17/31.75
(2*17)x = (3*2)*31.75
x = (3*2)*31.75/(2*17) = 3*31.75/17 =5.603 g H2
Cam has a piece of plywood that is 6 7/8 feet wide. He is going to cut shelves from the plywood that are each 1 1/6 feet wide. Which is the best estimate for the number of shelves Cam can make?
A. 1
B. 2
C. 4
D. 7
Answer:
C.
Step-by-step explanation:
So how I would estimate is by see that each piece is going to be 1 and 1/6 but you have 6 and 7/8 feet of plywood so 1 can go into 6 six times but since you got that 1/6 for each piece is lower it down do about 4, so he can make about four. lol
Answer: Cam can make 4 shelves.
Step-by-step explanation: