For breakfast, the family decides to spend no more than $20.00 for the week.
Each day, the family drinks 2/7 of a liter of milk for breakfast.
For the entire week, the amount of milk consumed is
[tex]7\times\frac{2}{7}=2\; \text{liters}[/tex]Milk costs $4,49 per liter, so the cost of the total amount of milk consumed is
[tex]2\times\$4.49=\$8.98[/tex]So, the amount left for the granola is
[tex]\$20.00-\$8.98=\$11.02[/tex]Each day, the family eats 1/3 of a pound of granola for breakfast.
For the entire week, the amount of granola consumed is
[tex]7\times\frac{1}{3}=\frac{7}{3}\; \text{pounds}[/tex]Let x be the price per pound of the most expensive granola they can afford.
[tex]\begin{gathered} \frac{7}{3}\cdot x=\$11.02 \\ x=\$11.02\cdot\frac{3}{7} \\ x=\$4.72 \end{gathered}[/tex]Therefore, the most expensive granola they can afford is $4.72
Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?
Step 1
Given; Austin has a granola recipe that requires 5/6 pounds of oats to make one batch of granola. if Austin uses 2 1/2 pounds of oats while making granola, how many batches has he made?
Step 2
Using ratio
[tex]\frac{\frac{5}{6}pounds\text{ of oats}}{2\frac{1}{2}pounds\text{ of oats}}=\frac{1\text{ batch of granola}}{x}[/tex][tex]\begin{gathered} \frac{5}{6}x=\frac{5}{2} \\ 10x=30 \\ x=\frac{30}{10} \\ x=3 \end{gathered}[/tex]Answer;
[tex]3\text{ batches}[/tex]Answer:3
Step-by-step explanation:if austin has to make 1 granola with 5/6pounds but he is using only 5/2 pounds to make 1 granola so that he can make 3 granulas with 5/6
determine the inverse of the given function
f(x)= 2x-9/4
To find the inverse of a function:
Replace f(x) with ySwitch around x and yIsolate yReplace y with f⁻¹(x)Solving the Question[tex]f(x)= 2x-\dfrac{9}{4}[/tex]
⇒ Replace f(x) with y:
[tex]y= 2x-\dfrac{9}{4}[/tex]
⇒ Switch around y and x:
[tex]x= 2y-\dfrac{9}{4}[/tex]
⇒ Isolate y:
[tex]x+\dfrac{9}{4}= 2y\\\\\dfrac{1}{2}(x+\dfrac{9}{4})= 2y(\dfrac{1}{2})\\\\\dfrac{1}{2}x+(\dfrac{1}{2}*\dfrac{9}{4})= y\\\\\dfrac{1}{2}x+\dfrac{9}{8}= y\\\\y=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
⇒ Replace y with f⁻¹(x):
[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
Answer[tex]f^{-1}(x)=\dfrac{1}{2}x+\dfrac{9}{8}[/tex]
What is the ratio of male teachers to male students?
Data:
Students: 180
Half male.
Male students: 180/2=90
Male teachers: 2
Ratio of male teachers to male students:
You can write the ratio in three different forms:
[tex]\begin{gathered} 2\colon90 \\ \\ 2\text{ to 90} \\ \\ \frac{2}{90} \end{gathered}[/tex]Element X is a radioactive isotope such that every 20 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 770 grams, how long
would it be until the mass of the sample reached 400 grams, to the nearest tenth of a
year?
Answer:
[tex]t = 18.9[/tex]
Information given :
We know that:
- Element X is a radioactive isotope such that every 20 years, its mass decreases by half
- the initial mass of a sample of Element X is 770 grams
And we must find how long it would be until the mass of the sample reached 400 grams
Step-by-step explanation:
To find it, we need to use the following formula:-
[tex]A(t) = A(0)(0.5)^{\frac{t}{20} }[/tex]
- A(0) is the initial amount
From given information, A(0) = 770 grams
Now, replacing the value in t :
[tex]A(t) = (770)(0.5)^{\frac{t}{20} }[/tex]
Then, we must solve for t :-
[tex]400 = 770(0.5)^{\frac{t}{20} } \\\frac{400}{700}= (0.5)^{\frac{t}{20} } \\\\ 0.51948 = (0.5)^{\frac{t}{20} } \\\\log(0.51948) = log((0.5)^{\frac{t}{20} }) \\\\\\log(0.519,48) = \frac{t}{20} log (0.5)\\t=\frac{20*log(0.519,48)}{log(0.5)} \\t=\frac{20(-0.284431}{-0.301029} \\giving\\t=18.9[/tex]
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A population grows according to an exponential growth model. The initial population is 212 and the population after one year is 263.
Complete the formula where P is the population and n is the number of years.:
P=212*(___)n
Round your answer to three decimal places.
Answer: P=212*(1.240)n
Step-by-step explanation:
1) Find the % growth
263-212= 51
51/212 = 0.240566037735849
2) Add 1 to the decimal as the population isn't decreasing but increasing.
0.240566037735849 + 1 = 1.240
3) Fill in the equation
P=212*(1.240)n
Determine which of the following proportions are true.I 1mi2hr=12mi24hrII 7min9cents=36min24centsIII
1 and 3
1 * 12 = 12
2 * 12 = 24
so 1 is true
7 * 5.14 = 36
9 * 5.14 = 46.26
so 2 is not true
7 * 4 = 28
2 * 4 = 8
so 3 is true
Can you show me step by step how to get this answer please?
Answer: first six cannot go into three because three is too small so six is going to go into 31 Six can go into 31 five times because 6×5 = 30 then since you’re subtracting 31 and 30 you would be left with one you would have to bring the 1 from the 12 down and then it would be 11. 11 can go into six once so 6-11 =5 so then you have to bring the two from the 12 down so then that would equal 6-2=4 and your done! It was a little confusing so if it didn’t make sense I’m sorry
Find the equation of the line graphed below. Write the equation in the form y = mx + b and identify m and b m = b =
ANSWER:
m = -3/4
b = -3
[tex]y=-\frac{3}{4}x-3[/tex]STEP-BY-STEP EXPLANATION:
We have that the equation in its slope-intercept form is the following:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope and b is y-intercept} \end{gathered}[/tex]We calculate the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]To calculate the slope we use the intercepts that are (-4, 0) and (0, -3), we replace:
[tex]m=\frac{-3-0}{0-(-4)}=\frac{-3}{4}=-\frac{3}{4}[/tex]Now, the value of b would be -3, since the y-intercept is (0,-3), therefore, the equation would be:
[tex]y=-\frac{3}{4}x-3[/tex]O GRAPHS AND FUNCTIONSDomain and range from the graph of a continuous function
According to the graph we have:
Domain are the values of x. We can see that the graph extends horizontally from -5 to 3, but -5 and 3 are not included. Then, the domain is
[tex](-5,3)[/tex]Range are the values of y. Therefore, we see that the graph extends vertically from 4 to -3, so the range is:
[tex](-3,4)[/tex]Answer:
a. domain = (-5, 3)
b. range = (-3, 4)
Calc Limits. Attatched question.
The correct option regarding the continuity of f(x) at x = 2 is given by:
B. lim x -> 2 f(x) exists, but f(2) exist.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is, if these three conditions are respected:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
For this problem, the denominator of the function is:
8cos(0.5πx) + 2x²
At x = 2, the denominator of the function is:
8cos(0.5π(2)) + 2(2)² = 8cos(π) + 8 = -8 + 8 = 0 (as cos(π) = -1).
Then the function does not exist at x = 2, as the denominator is of 2.
From the graph of the function given at the end of the answer, we have that the lateral limits are as follows:
lim x -> -2^- f(x) = -infinity.lim x -> -2^+ f(x) = -infinity.Since the lateral limits are equal, the limit exists, hence option B is correct.
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Beginning with 23 grams of a radioactive element whose half-life is 45 years, the mass y (in grams) remaining after t years is given byy = 23(1/2)^t/45, t ≥ 0.How much of the initial mass remains after 170 years? (Round your answer to three decimal places.)
1) As we were told of the half-life formula along with the data, we can write out the following to get the remains after 170 years:
[tex]\begin{gathered} y=23(\frac{1}{2})^{\frac{t}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}} \\ y=23(\frac{1}{2})^{\frac{170}{45}}^ \\ y\approx1.677 \end{gathered}[/tex]2) So, according to this model we can tell there will be left approximately
[tex]1.677g[/tex]When x =1/2 and y = 1/8, -5x + 14y =
Answer:
-5x1/2= -2.5 14x1/8= 1.75
Step-by-step explanation:
-2.5+1.75=-0.75
Answer:
-3/4
Step-by-step explanation:
Plug in values of x and y into expression:
[tex]-5(\frac{1}{2})+14(\frac{1}{8})=[/tex]
[tex]-\frac{5}{2} +\frac{14}{8}=[/tex]
Find common denominator:
[tex]-\frac{5*4}{2*4} +\frac{14}{8}=[/tex]
[tex]-\frac{20}{8} +\frac{14}{8}=\frac{14}{8}-\frac{20}{8}=[/tex]
Solve numerator:
[tex]14-20=-6[/tex]
So,
[tex]=-\frac{6}{8}=-\frac{3}{4}[/tex]
A candy company has fixed costs (costs that it must pay regardless of how much candy they
make) of $500 per day, and it costs them an additional $3 to manufacture each box of candy.
They can sell their candy for $3 a box. If we jet x represent the boxes of candy sold, the number of
boxes they need to sell to break even can be found by solving the equation 3x + 500 = 3x. How
many boxes of candy to they need to sell to break even?
You can never achieve break even by selling any number of boxes of candy if it costs them an additional $3 to manufacture each box of candy.
What is Break even point?In economics, business, and particularly cost accounting, the break-even point is the point at which total cost and total income are equal, or "even."
Although these opportunity costs have been paid and then capital has received the risk-adjusted, projected return, there is no net loss or gain, and one has "broken even."
Fixed cost (in manufacturing) = $500
Manufacturing cost of each candy = $3
and selling price of candy = $3
let x be a box of candy sold,
hence for no of box to be sold for a break even,
3x + 500 = 3x
but if you see above equation, that has no solution
Hence by providing each candy at $3 with $500 fixed cost and selling cost again at $3 you cannot achieve a break-even point.
hence there is no solution, and you will never be able to achieve break even.
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The Faulk Corp. has a bond with a coupon rate of 4 percent outstanding. The Gonas Company has a bond with a coupon rate of 10 percent outstanding. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 7 percent. a. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds?
If the interest rates suddenly rise by 2 percent, the percentage change in the price of these bonds are : 19.73%, 16.56%.
Percentage changeUsing this formula to find the current price of a bond
P=C×1-1(1+YTM)^n/YTM +F /(1+YTM)^n
Where:
P =Current price of a bond
C = Coupon payment,
YTM = Yield to maturity
n = Time to maturity
F =Face value of a bond
The Faulk Corp. bond
C = Coupon rate / number of payments per year × face value = 4% / 2×$1,000 = $20
n = 13 years = 36 half-year periods
YTM = 7% annually = 7% / 2 = 3.5% semiannually
F = $1,000
hence,
P=20× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36
P=20× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36
P= $405.81 + $289.83
P=$695.61
Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%.
Price of the Faulk Corp. bond:
P=20× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36
P=20× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36
P= $353.32 +$205.03
P=$558.38
Percentage change:
Percentage change = $558.38 - $695.61/$695.61×100%
Percentage change =19.73%
Gonas Company bond:
C =Coupon rate / number of payments per year× face value = 10% / 2 × $1,000 = $50
n = 18 years = 36 half-year periods,
YTM = 7% annually = 7% / 2 = 3.5% semiannually
F = $1,000
P=50× 1- 1/(1+0.035)^26/0.035 +1,000/ (1+0.035)^36
P=50× 1- 1/(1.035)^36/0.035 +1,000/ (1.035)^36
P= $1,014.52 + $289.83
P=$1,304.35
Assuming the annual YTM rises by 2%, the semiannual YTM = 9% / 2 = 4.5%, bond :
P=50× 1- 1/(1+0.045)^36/0.045 +1,000/ (1+0.045)^36
P=50× 1- 1/(1.045)^36/0.045 +1,000/ (1.045)^36
P= $883.30 +$205.03
P=$1,088.33
Percentage change:
Percentage change = $1,088.33 - $1,304.35/$1,304.35×100%
Percentage change =16.56%
Therefore the percentage change in the price of these bonds are : 19.73%, 16.56%.
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A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 22 feet more than the length of the shortest side. Find the dimensions if the perimeter is 186 feet.
The three sides of the triangle will be 82, 63, and 41 feet.
What is a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The perimeter of the triangle is the sum of all three sides of the triangle.
That a flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side 22 feet more than the length of the shortest side.
Let the three sides of the triangle be A, B, and C. Here A is the longest side B is the shortest side and C is the third side.
Perimeter = A + B + C
A = 2B and C = 22 + B
Put the values in the equation as solve:-
Perimeter = A + B + C
186 = 2B + B + 22 + B
186 = 4B + 22
4B = 186 - 22
4B = 164
B = 164 / 4
B = 41 feet
Longest side = 2B = 2 x 41 = 82 feet
Shirtest side = B = 41 feet
Third side = 22 + B = 22 + 41 = 63 feet
Therefore, the three sides of the triangle will be 82, 63, and 41 feet.
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Find the nth term of this quadratic sequence
2,8, 18, 32, 50,
Answer:
72
Step-by-step explanation:
8 = 2×2^2
18 = 2×3^2
32 = 2×4^2
50 = 2×5^2
72 = 2×6^2
If f(x) = -3x-2, g(x) = - 4x² + 7x-2, and h(x) = 2x² + 4, find h(1).
Answer:
h(1) = 6
Step-by-step explanation:
h(1) will be
h(x) = 2x² + 4
h(1) = 2(1)² + 4 = 2 + 4
h(1) = 6
Find the slope of the line graphed below.
Answer:
[tex]\frac{-5}{2}[/tex]
Step-by-step explanation:
There are two blue dots on the graph. It does not matter which dot you startr at. Let's start at the bottom, right dot. How many space up and to the left you do you have to move to get to the second dot?
You need to move 5 dots straight up. Up is a positive direction. Then you have to move 2 spaces left. Left is a negative direction, so your slope will be negative.
- [tex]\frac{5}{2}[/tex] [tex]\frac{-5}{2}[/tex] [tex]\frac{5}{-2}[/tex] All of these mean the same thing.
Represent a quadratic function
Doris borrowed 7 dollars from Nikki. Doris then paid back 2 dollars. How much does Doris
still owe Nikki?
Answer:
He still owes Nikki $5.
Step-by-step explanation:
7 - 2 = 5
Answer:
5
Step-by-step explanation:
7-2=5
The bill for dinner was $61.66. You left $10.34 for the tip. What percentage of the original bill was the tip? Round your a
to the nearest whole percent.
Answer:
17%
Step-by-step explanation:
You want the percentage represented by a tip of $10.34 on a dinner bill of $61.66.
PercentageA percentage is a fraction that has been multiplied by 100%:
10.34/61.66 × 100%
≈ 0.168 × 100%
≈ 17%
The tip was about 17% of the original bill.
Which of the following is a true statement about a tangent and a radius?
A. A tangent and a radius of a hexagon are always equal lengths.
B. A tangent and a radius of a circle meet to form a 90 angle.
C. A tangent and a radius in a cylinder form two legs of a right triangle with the cylinders altitude serving as the hypotenuse.
D. A tangent and a radius intersect at the foci of an ellipse.
A tangent and a radius of a circle meet to form a 90 angle is a true statement about a tangent and a radius.
The straight line that "just touches" the curve at a particular location is known as the tangent line (or simply tangent) to a plane curve in geometry. A circle or sphere's radius is any line segment that connects the object's center to its perimeter in classical geometry; in more contemporary use, it also refers to the length of such line segments.
A tangent is a line that very slightly touches the circumference of a circle. The angle between a radius and a tangent is always exactly 90 degrees if the radius and circumference are drawn at the same location.
Hence the correct option is B
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If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a diamond or 7?
the probability that the card you select is a diamond or 7 is 4/13
WHAT IS PROBABILITY ?Mathematical representations of the likelihood of an event occurring or of a proposition being true are dealt with in the area of probability. A number between 0 and 1 represents the likelihood of an event, with 0 roughly denoting impossibility and 1 representing certainty.
CALCULATIONLets take diamond first total diamonds are 13 and total cards are 52 So prob is 13/52 which is 1/4
Lets take 7s
total 10s in the deck is 4 (one in each suite) (one in each suite)
Prob of 7s is 4/52 which is 1/13
Final answer =1/13+1/4=17/52 Total prob is addition of above two as it is "or."
Because the prob of the 7th diamond has been inserted twice, edit it as follows: 17/52-1/52=16/52=4/13
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Question four need to know what I did wrong I need to do it I need to understand
If there are 189 children, then there are 189 divided 7 = 27 groups of 7 children.
As mentioned in the problem, for every 7 children, there are 2 caretakers therefore, there are a total of 2 x 27 = 54 caretakers in the local daycare.
So, in total, there are 189 children + 54 caretakers = 243 people in the daycare facility.
In a paragraph of no less than 125 words, explain why you appreciate/love your chosen piece of music.
I adore BTS (the Korean boy band) because they encourage self-love. Their songs are artistically and romantically rich. They're well-known throughout the world and at the moment's top boy band in the US.
What is music about?In this sense, understanding the worth and excellence of various musical genres is referred to as appreciation. The word "appreciation" has philosophical roots; in that discipline, it is defined in relation to music as "a type of formal counterpart of emotional experience."
Someone's mood can be improved by listening to their music, which can also thrill or calm the listener. Importantly, music also enables us to experience almost all of the emotions we go through in life. There are countless options. Dopamine release in the mesolimbic reward system can be triggered by listening to extremely pleasurable music.
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Name the line of reflection used to map the preimage to its image.
Option A, Y- axis is the line of reflection used to map the preimage to its image.
The graph shows that if the graph is folded by a y-axis, Point G will cross Point G', which is two coordinates away from the y-axis.
Point F will cross point F', which is four coordinates away from the y-axis.
Points H will cross point H', which is in negative coordinates and 7 coordinates away from the y-axis.
Mirror images are symmetrical from any axis, which might be the x-axis or the y-axis. Flipping geometry refers to reflection. Mirror reflection is a type of reflection. When lines reflect an image, reflection lines form. A form is said to mirror another shape if each of its points is equidistant from each of the other shape's points.
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how do i do vertical analysis
To carry out the vertical analysis of an income statement, set the Revenue as the base figure to 100% for each line item.
What is a vertical analysis?Vertical analysis of a financial statement compares each line item on the financial statement as a percentage of a base figure.
The base figure is the revenue in the income statement or the total assets in the balance sheet.
The formula for vertical analysis is given as a financial statement line item divided by the total base figure X 100.
Examples of vertical analysis can be shown with AT$T and Verizon below:
AT&T Percent
Revenue $132,447 100%
Cost of Services (Expenses) 60,611 45.8% ($60,611/$132,447 x 100)
Selling & Marketing Expense 39,697 30.0%
Depreciation & other expenses 20,393 15.4%
Operating Income $11,746 8.9%
Verizon Percent
Revenue $127,079 100%
Cost of Services (Expenses) 49,931 39.3% ($49,931/$127,079 x 100)
Selling & Marketing Expense 41,016 32.3%
Depreciation & other expenses 16,523 13.0%
Operating Income $19,599 15.4%
Thus, we have performed the vertical analysis of AT$T and Verizon above.
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Question Completion:Income Statements of AT&T and Verizon (in millions) are:
AT&T Verizon
Revenue $132,447 $127,079
Cost of Services (Expenses) 60,611 49,931
Selling & Marketing Expense 39,697 41,016
Depreciation & other expenses 20,393 16,523
Operating Income $11,746 $19,599
Select all the equations where x = 3 is a solution.X-3 = 01 + x = 209 - x= 3O 6 = 2xOf = 3x2 = 9
Let's begin by listing out the given information:
[tex]undefined[/tex]Find the common difference and the next two terms of the arithmetic sequence.11,19,27,35The common difference isWrite the next two terms in the sequence:11,19,27,35,?,?
The common difference in the given arithmetic sequence is 8.
What is an arithmetic sequence?An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. The arithmetic mean can be calculated as one approach. Divide the total by the total number of values after adding up all the values. Add the numbers together, for instance: a + b + c + d and so on, if there is a set of "n" numbers.So, formula for common differences:
d = (aₙ₊₁ - aₙ)Now, insert terms in the formula as follows:
d = (aₙ₊₁ - aₙ)d = (19 - 11)d = 8Therefore, the common difference in the given arithmetic sequence is 8.
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What is the maturity value given the following:$10,800 at 8% for 8 months
The maturity value is the sum of the interest and the principal. The formula for calculating interest is expressed as
I = PRT
where
I is the interest after time t
P is the principal or initial amount
R is the interest rate
T is the time in years
From the information given,
P = 10800
R = 8/100 = 0.08
T = 8 months
We would convert 8 months to years. Recall,
12 months = 1 yr
8 months = 8/12 = 0.67
Thus,
t = 0.67 yr
By substituting these values into the formula, we have
I = 10800 x 0.08 x 0.67
I = 578.88
Thus,
Maturity value = 10800 + 578.88
Maturity value = $11378.88