Answer:
The 6-pack contains 0.130 liters more soda.
pls help me thank you
Find the total amount
$20,700 at 9% compounded
semiannually for 4 years
Answer:
41,246.046 which could be rounded to .05 cents at the end.
Step-by-step explanation:
[tex]20700(1.09)^8[/tex]
we use this equation since we are working with interest, and we are compounding interest twice per year, for 4 years or 8 times.
hope this helps, please rate and mark as brainelst.
Lodine-131 is a very useful radioactive isotope that is used to locate and treat cancerous tumors in the body and has a half life of 8 days. If a radiologist were to use 64 mg of this isotope, how much of it would still be left after 32 days?
Using an exponential function, it is found that 4 mg of the substance would still be left after 32 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, considering that the initial amount if of 64 mg, and we are working with half-lifes, the equation is given by:
[tex]A(t) = 64(0.5)^t[/tex]
32 days is 32/8 = 4 half-lifes, hence the amount remaining in mg is given by:
[tex]A(4) = 64(0.5)^4 = 4[/tex]
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NO LINKS PLEASE I NEED ANSWERS
NO LINKS PLEASE
Answer:
10. s = 1.50x
11. s = 28x + 5
Step-by-step explanation:
10. s (money); so multiply x (the amount of pencils) by the price which is 1.50. Which is equal to 112.50.
11. s (money); multiple x (the amount of shoes) by the price, 28, which equals 84. Then add 5 for the shipping. This equals 89.
what is this??
i need help
Answer:
uhmm sry i dont understand tooMrs.martin's class has 8 boys out of a total of 20 students.which is the ratio of girls to boys in her class?
Answer:
8:20 or if you want it simplified 2:5
Step-by-step explanation:
Meteorologists look for weather trends across US states in the same geographical region. Kentucky and Illinois share a border. The average annual temperatures (°F) from 1991 to 2000 for Kentucky were 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7. The average annual temperatures (°F) from 1991 to 2000 for Illinois were 53.7, 51.9, 50.9, 51.8, 51.4, 49.9, 50.8, 55.0, 53.3, and 52.0. Use the statistics calculator to determine the measures of center for Kentucky.
Kentucky mean =
Kentucky median =
Illinois mean = 52.07
Illinois median = 51.85
Both measures of center for Kentucky are
those of Illinois.
Answer:
the median is 55.6
Step-by-step explanation:
The average annual temperatures (°F) from 1991 to 2000 for Kentucky were 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.
We have to evaluate the measures of center.
Firstly, we will calculate the mean.
Mean = (Sum of all the observations)/ (Total number of observations)
Mean =
=
= 55.62
Now, we will calculate mode.
Mode is a statistical term that refers to the most frequently occurring number found in a set of numbers.
Consider the data 57.5, 55.1, 52.2, 55.6, 55.6, 54.4, 54.5, 58.3, 57.3, and 55.7.
Mode = 55.6
Now, we will calculate the median.
Firstly, we will arrange in the ascending order.
52.2, 54.4, 54.4,55.1 ,55.6, 55.6, 55.7, 57.3, 57.5, 58.3
Since there are 10 terms.
Median = th observation
Median = 5th observation.
Since, the 5th observation is 55.6.
Therefore, the median is 55.6
Question 1-5
Sarah is demonstraing the idea that polynomials are closed under addition. Her work and explanation are shown.
Select an equation and phrases to complete the statement.
Part A:
Add 3x4 + 6x - 7 to
Equation A 2x - (2x)2 + 4x-1
Equation B (2x)2 + 4.4x - 9
Equation C (-8x)-2 - (3x)3 +7
Part B:
This is closed because
of the sum are
and the sum is a polynomial.
This is closed under addition because the sum of the polynomial produces another polynomial.
What is a polynomial?A polynomial is an expression that involves the addition, subtraction and multiplication of variables.
Polynomials will be closed under an operation if the operation produces another polynomial.
(3x⁴ + 5x - 7) + (2x - (2x)² + 4x - 1) + [(-8x)⁻² - (3x)³ + 7]
= 3x⁴ - 27x³ - 4x² + 9x - 1 + (-8x)⁻²
This is closed under addition because the sum of the polynomial produces another polynomial.
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The amount of a radioactive substance remaining after t years is given by the function f(t) = m(0.5)", where m is the
initial mass and h is the half-life in years. Cobalt-60 has a half-life of about 5.3 years. Which equation gives the
mass of a 50 mg Cobalt-60 sample remaining after 10 years, and approximately how many milligrams remain?
Using an exponential function, it is found that the equation is:
[tex]f(1.8868) = 60(0.5)^{1.8868}[/tex]
Which means that approximately 16.22 mg remain.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the equation is:
[tex]f(h) = m(0.5)^h[/tex]
We work with a 50 mg Cobalt-60 sample, hence m = 60, and considering a half-life of 5.3 years, in 10 years we have h = 10/5.3 = 1.8868. Hence the equation is:
[tex]f(1.8868) = 60(0.5)^{1.8868} = 16.22[/tex]
Approximately 16.22 mg remain.
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Marvin's favorite hiking trail is 5. 91 miles long. If he has hiked it 8 times, how far has he hiked on this trail?
Answer: 47.28 miles
Step-by-step explanation: 5.91 times 8= 47.28
In 2005, 12.2 out of every 50 employees at a company were women. If there are 48,744 total company employees, estimate the number of women.
Answer:
12000
Step-by-step explanation:
Using this information, you can make a ratio: 12.2/50 = x/48744
By simplifying this ratio you get that 50x = 594676. Dividing both sides by 50 you get about 11900, which you can round up to 12000
Answer:
11,894 women
Step-by-step explanation:
ratio of women to employees = 12.2 : 50
Let x = number of women employees to 48744 employees
12.2 : 50 = x : 48744
⇒ 12.2 / 50 = x / 48744
⇒ 0.244 = x / 48744
⇒ x = 0.244 · 48744
⇒ x = 11893.536
⇒ x = 11894 (nearest whole number)
Therefore, there are approximately 11,894 women in a company with a total of 48,744 employees
Given a+b=7 and a-b=3, find the following
3^a÷3^b
Answer:
27
Step-by-step explanation:
a + b = 7
a - b = 3
2a = 10
a = 5
b = 7 - 5
b = 2
3⁵ / 3² = 3³ using law of indices
3³ = 27.
Answer:
27
Step-by-step explanation:
a + b = 7
a - b = 3
2a = 10
a = 5
b = 7 - 5
b = 2
3⁵ / 3² = 3³ using law of indices
3³ = 27
A student wants to learn how to spell 200 words on a list. The student learned how to spell the first 25 words on the list at a rate of 5 words per day. At this rate, how many days will it take for the student to learn how to spell the remaining words on the list
A. 14
B. 15
C. 35
D. 45
Equation in slope intercept form
y=mx+by=5x+25Now
5x+25=2005x=175x=175/5x=35Which problem solving strategy would be best to solve this problem?
Four people are in line at the movie theater. Jennifer is ahead of Jeanie. John is not first or last in line. Jarett is directly in front of Jennifer. Name the order in which the people are standing in line.
A. guess, check and revise
B. compute or simplify
C. work backwards
D. write an equation
Answer:
C. work backwards
Step-by-step explanation:
I did it
1 2/3x=1/2
what is x?
x/2.5=1.75
what is x?
Answer:
Step-by-step explanation:
1. 12/3x = 1/2
4/1x = 1/2
4/1x = 1/2 / 4/1
1/2 x 1/4 , x = 1/8.
2). x / 2.5 = 1. 75/ 1
cross multiply to get
x = 2.5 x 1.75
x = 4.375
You are going to the mall with your
friends, and you have $200 to spend.
you find a store that has all jeans for
$25 and all shirts for $10. you buy a
total of 14 items. how many of each
item did you buy?
Answer:3 jeans and 11 shirts with 15 dollars leftover
Step-by-step explanation:
3x25=75
11x10=110
110+75=185
200-185=15
25x4 will make the leftover money higher, so 3 and 11
Use the equation, 8^2x = 32^x+3 , to complete the following problems.
(a) Rewrite the equation using the same base.
(b) Solve for x. Write your answer in the simplest form.
Side note: For your answers, I ask that you show your work so that I can review it and hopefully understand how to do this myself in the future!
Answer:
Question (a)
Given equation:
[tex]8^{2x} = 32^{x+3}[/tex]
8 can be written as [tex]2^3[/tex]
32 can be written as [tex]2^5[/tex]
Therefore, we can rewrite the equation with base 2:
[tex]\implies (2^3)^{2x} = (2^5)^{x+3}[/tex]
------------------------------------------------------------------------------
Question (b)
To solve:
[tex](2^3)^{2x} = (2^5)^{x+3}[/tex]
Apply the exponent rule [tex](a^b)^c=a^{bc}[/tex] :
[tex]\implies 2^{3 \cdot 2x} = 2^{5(x+3)}[/tex]
[tex]\implies 2^{6x} = 2^{5x+15}[/tex]
[tex]\textsf{If }a^{f(x)}=a^{g(x)}, \textsf{ then } f(x)=g(x)[/tex] :
[tex]\implies 6x = 5x+15[/tex]
Subtract [tex]5x[/tex] from both sides:
[tex]\implies x = 15[/tex]
hello, me again polease help me with this, and show work
Answer:
Hope it helps u
Step-by-step explanation:
1.7
1.749
1.75
1.775
1.796
1.84
Answer:
the order would go 1.7, 1.749, 1.75, 1.775, 1.796, then 1.84.
Step-by-step explanation:
becuase if you ignore how long the numbers are, and focus on numerical order like 1, 2, 3, and apply that to this, this becomes the order.
Name the postulate that proves these two triangles congruent.
Answer:
the postulate that proves these two triangles congruent is AAA or angle angle angle.
4. Find the volume of the cone.
Answer:
A.
Step-by-step explanation:
πr^2 h/3
Hope this helps!
The table represents the exponential function g(x) . The graph represents the function f(x).
x g(x)
0 3
1 4
2 6
3 10
4 18
Which statement about the functions is true?
The y-intercept of g(x) is greater than the y-intercept of f(x).
The y-intercept of f(x) is greater than the y-intercept of g(x).
f(x) and g(x) share an x-intercept.
f(x) and g(x) have the same y-intercept.
The statement about both functions that is true is: B. The y-intercept of f(x) is greater than the y-intercept of g(x).
What is the Y-intercept of a Function?The y-intercept of a function is the output value (y) of the function when the input value (x) is zero. On a graph, it would be the value of y-coordinate of the point where the line cut across the y-axis.
From the table given for function g, the value of y when x is zero is 3. The y-intercept for g(x) is 3.
From the graph given for function f, the value of the point at which the line intercepts the y-axis is 6. Therefore, the y-intercept for f(x) is 6.
Therefore, the statement about both functions that is true is: B. The y-intercept of f(x) is greater than the y-intercept of g(x).
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80, 60, 45,...
Find the 9th term.
The ninth term of the series [tex]80,60,45.....[/tex] is [tex]50[/tex].
We need to determine the relationship between the consecutive terms of the series to evaluate the succeeding terms of the series.
How to find the terms in a series?
The difference between the first and second terms is [tex]60-80=-20[/tex].
The difference between the second and the third terms is [tex]45-60=-15[/tex]
So, the difference between the third and the fourth terms will be [tex]-10[/tex]. So, the fourth term will be [tex]45-10=35[/tex].
Similarly, the difference between the eighth and the ninth terms will be [tex]-15[/tex]. So, the ninth term will be [tex]35-(-15)=50[/tex].
Thus, the ninth term of the series is [tex]50[/tex].
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Use the following compound interest formula to complete the problem. a = p (1 startfraction r over n endfraction) superscript n superscript t sandra has two credit cards, p and q. card p has a balance of $726.19 and an interest rate of 10.19%, compounded semiannually. card q has a balance of $855.20 and an interest rate of 8.63%, compounded monthly. assuming that sandra makes no purchases and no payments with either card, after four years, which card’s balance will have increased by more, and how much greater will that increase be? a. card q’s balance increased by $7.22 more than card p’s balance. b. card q’s balance increased by $6.69 more than card p’s balance. c. card p’s balance increased by $3.43 more than card q’s balance. d. card p’s balance increased by $0.80 more than card q’s balance. please select the best answer from the choices provided a b c d
The difference between the amount in two cards of Sandra after 4 years will be $125.58 approx.
How to find the compound interest?If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]
For this case, Sandra has got 2 credit cards p and q. Calculating the final amount both card will have after 4 years:
Case 1: For card p:Initial amount = p = $726.19
The rate of interest is r = 10.19% = 10.19/100 = 0.1019 (converted percent to decimal)
Years for which amount is compounded = 4 years, Thus, t = 4
The interest is compounding semiannually, that means twice per year, thus, n = 2
Thus, the final amount in card p after 4 years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 726.19(1+0.1019/2)^{2 \times 4} \\\\a= 726.19 \times (1.05095)^8 \approx 1080.70\: \rm (in \: dollars)[/tex]
Case 2: For card q:Initial amount = p = $855.20
The rate of interest is r = 8.63% = 8.63/100 = 0.0863 (converted percent to decimal)
Years for which amount is compounded = 4 years, Thus, t = 4
The interest is compounding monthly, that means twelve times per year, thus, n = 12
Thus, the final amount in card q after 4 years would be:
[tex]a = p(1 + \dfrac{r}{n})^{nt}\\\\a = 855.20(1+0.0863/12)^{12 \times 4} \\\\a= 855.20\times (1.0071916)^{48} \approx 1206.28\: \rm (in \: dollars)[/tex]
Clearly card q has more amount than card p at the end of 4 years.
The difference is: 1206.28 - 1080.70 = 125.58 (in dollars)
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Find the coordinates of the midpoint of CD with endpoints C(-3,7) and D(3,-7).
Answer:
(0, 0) are the coordinates of the mid point
Step-by-step explanation:
[tex]coordinate \: of \: mid \: point \: = \\ ( \frac{x1 + x2}{2} \: \: \: \: \frac{y1 + y2}{2} ) \\ ( \frac{ - 3 + 3} {2} \: \: \: \: \: \: \: \frac{7 + - 7}{2} ) \\ ( \frac{0}{2} \: \: \: \: \: \: \: \: \frac{0}{2} ) \\ (0 \: \: \: \: \: \: \: \: \: \: \: 0)[/tex]
A student filled a right rectangular prism shaped box with one inch cubes to find the volume in cubic inches the students work is shown explain why the students reasoning is incorrect provide the correct volume in cubic inches and why the students reasoning is incorrect in your answer
The volume of the right rectangular prism is the amount of cubes in it
The formula to determine the volume of the right rectangular prism is V(n) = n
How to determine the volume?The question is incomplete; as the figure is not given.
So, I will provide a general solution
The volume of a one inch cube is:
[tex]V = 1^3[/tex]
[tex]V = 1[/tex]
Assume the number of one inch cubes used to fill the right rectangular prism is n.
Then the volume of the right rectangular prism would be:
[tex]V(n) = n * 1[/tex]
This gives
[tex]V(n) = n[/tex]
Hence, the general formula to determine the volume of the right rectangular prism is V(n) = n
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can someone help me with this question
Find the mean of the following data set rounded to the nearest hundredth.. 20, 19, 18, 20, 19, 22
Answer:
19.6
Step-by-step explanation
= Sum of terms / number of terms
= ( 20 + 19 +18+ 20 +19 +22 ) / 5
= 19.6
Graph the line that represents this equation: help please
Answer:
Here I graphed it for you.
Step-by-step explanation:
Q. A circular pie has an area of 706.5 cm? What is the radius of the pie?
answer choices
A. 225 cm
B. 30 cm
C. 15 cm
D. 112.5 cm
Answer:
C. 15 cm
Step-by-step explanation:
The formula to find the area of a circle is: π × r²
But since we need to solve for the radius, we use the formula:
[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]
r = radius
A = area
π = 3.14
Now we substitute the information given in the text into the equation
[tex]r = \sqrt{ \dfrac{ A }{ \pi } \phantom{\tiny{!}}}[/tex]
Substitute values into the equation
[tex]r = \sqrt{ \dfrac{ 706.5 }{ 3.14 } \phantom{\tiny{!}}}[/tex]
Divide 706.5 by 3.14
[tex]r = \sqrt{ 225 }[/tex]
Take the square root of 225
[tex]r = {15 }[/tex]
So, the radius of the pie is 15 cm
23
Hot dogs are sold in packages of 12. Buns are sold in packages of 8. What is
the least number of packages of buns you would have to buy if you want to
purchase an equal number of hot dogs and buns?
А 3
B 4
C5
D 6
Answer:
A) 3
Step-by-step explanation:
12 * 2 = 24
8 * 3 = 24
24 = 24