The function f(x) = 86(1.29)x represents a weekly weed growth rate of 29%. To convert this to a daily growth rate, we use the formula (1+0.29)^(1/7) - 1, which equates to an approximate daily growth rate of 4%. Therefore, the function can be rewritten as: f(x) = 86(1.04)x.
Explanation:Your question involves the function that represents the weed growth in a garden: f(x) = 86(1.29)x. Here, 1.29 refers to the growth rate of 29% per week. However, you want to rewrite the function to show how quickly the weeds grow each day.
To get a daily growth rate from a weekly one, we use the formula: daily growth rate = (1 + weekly growth rate)^(1/7) - 1. For the given function, this translates to a daily growth rate of (1 + 0.29)^(1/7) - 1, which is approximately 0.04, or 4%. Therefore, the function rewrite will be:
f(x) = 86(1.04)xThis function shows that the weeds grow at approximately 4% each day. So, the correct answer is Option B: f(x) = 86(1.04)x; grows approximately at a rate of 4% daily.
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To find the daily growth rate of the weeds, we divide the weekly growth rate by 7. The correct function is f(x) = 86(1.04)x, which represents a daily growth rate of approximately 0.4%.
Explanation:To find how quickly the weeds grow each day, we need to convert the rate of growth from weekly to daily.
Since there are 7 days in a week, we can divide the weekly growth rate by 7 to get the daily growth rate.
In this case, the function f(x) = 86(1.29)x represents the weekly weed growth, so to find the daily growth rate, we use the function f(x) = 86(1.29/7)x.
Simplifying this expression, we get f(x) = 86(1.04)x.
Therefore, the correct answer is A. f(x) = 86(1.04)x; it grows approximately at a rate of 0.4% daily.
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You invest $1,300 in an account that has an annual interest rate of 5%, compounded annually. How much money will be in the account after 10 years? Round your answer to the nearest whole number.
Answer:
A=Pe^rt
P= princible (1300)
e= (2.71828)- function on a graphing calculator
r = interest rate (.05 or 5%)
t = time (10 years)
A = 1300e^.05(10)
A = 1300e^.5
A = 2143.337652
A = 2143
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1300\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]
[tex]\bf A=1300\left(1+\frac{0.05}{1}\right)^{1\cdot 10}\implies A=1300(1.05)^{10}\implies \stackrel{\textit{rounded up}}{A=2118}[/tex]
Black Diamond Ski Resort charges $50 for ski rental and $15 an hour to ski, Bunny Hill Ski Resort charges $75 for ski rental and $10 an hour to ski Create an
equation to determine at what point the cost of both ski slopes is the same
15x - 75 = 10x - 50
15x - 50 = 10x - 75
15x + 50 = 10x + 75
15x + 75 = 10x + 50
Answer:
15x + 50 = 10x + 75
Step-by-step explanation:
The cost at Black Diamond for ski rental and x hours of skiing is ...
50 +15x
The cost at Bunny Hill for ski rental and x hours of skiing is ...
75 +10x
These costs will be equal when ...
15x + 50 = 10x + 75
Answer:
C: 15x + 50 = 10x + 75
Step-by-step explanation:
Patty deposited $650 in a savings account with two percent simple interest. If she keeps it in the account for one year, how much interest will she earn?
$15
$18
$12
$13
Answer:
$13
Step-by-step explanation:
Depost of 650.00 into a bank account paying 2% simple interest per year. You left the money in for 1 year. Find the interest earned and the amount earned in 1 year.
The interest is $13, and the amount is 663.00.
Answer:
13
Step-by-step explanation:
The plane that contains points C and T can also be named plane...
A) CUB
B) BED
C) ACE
D) ABE
Answer:
A) CUB
Step-by-step explanation:
Of the suggested planes, only CUB contains both points C and T.
___
Comments on the other answer choices
BED contains point T, but not C
ACE contains point C, but not T
ABE contains neither C nor T
Answer:
A) CUB
Step-by-step explanation:
I did this problem and I was told I did it wrong how do I fix it??
Answer:
(1/8)(cos(4x) -4cos(2x) +3)
Step-by-step explanation:
Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...
cos(x)² = (1/2)(1 +cos(2x))
In the context of this problem, using this formula gives you ...
sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))
sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)
please help:Find the coordinates of the midpoint of a segment having the given endpoints.
Q(0.3, 1.8), R(2.7, 3.9)
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{0.3}~,~\stackrel{y_1}{1.8})\qquad R(\stackrel{x_2}{2.7}~,~\stackrel{y_2}{3.9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2.7+0.3}{2}~~,~~\cfrac{3.9+1.8}{2} \right)\implies \left(\cfrac{3}{2}~,~\cfrac{5.7}{2} \right)\implies (1.5~,~2.85)[/tex]
Final answer:
The coordinates of the midpoint are (1.35, 2.85).
Explanation:
The coordinates of the midpoint of a segment can be found by averaging the x-coordinates of the endpoints and averaging the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (0 + 2.7) / 2 = 1.35, and the y-coordinate of the midpoint is (1.8 + 3.9) / 2 = 2.85. Therefore, the midpoint of the segment with endpoints Q(0.3, 1.8) and R(2.7, 3.9) is (1.35, 2.85).
Find the inverse of the function. f(x) = the cube root of quantity x divided by six. - 7
Answer:
[tex]f^{-1}(x)=6(x+7)^{3}[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\sqrt[3]{\frac{x}{6}}-7[/tex]
Let
[tex]y=f(x)\\ y=\sqrt[3]{\frac{x}{6}}-7[/tex]
Exchanges the variable x for y and y for x
[tex]x=\sqrt[3]{\frac{y}{6}}-7[/tex]
Isolate the variable y
[tex]x+7=\sqrt[3]{\frac{y}{6}}[/tex]
elevates to the cube both members
[tex](x+7)^{3}=\frac{y}{6} \\ \\y=6(x+7)^{3}[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=6(x+7)^{3}[/tex] ------> inverse function
Ms. Walker used a coordinate plane to plot her students' scores on a recent quiz. She let x represent the number of correct answers they had on their quiz and y represent the number of points earned. She then plotted the ordered pairs (17, 68), (20, 80), and (24, 96) to represent the data from three students.
What is the slope of the graph in points per question?
Answer:
Slope = 4
Step-by-step explanation:
The x-axis values to represent the number of correct answers.
The y-axis values to represent the number of points earned.
The points on the graph are: (17,68) , (20,80) and (24,96)
The slope(m) of the graph = change in y ÷ change in x
i.e [tex]\frac{80 - 68}{20 - 17}[/tex] = [tex]\frac{96 - 80}{24 - 20}[/tex] = 4
The equation of the straight line graph is;
y=4x
The slope of the graph, representing points earned per correct answer on the quiz, is 4. This is found by dividing the change in points earned by the change in correct answers between any two points on the graph.
Explanation:The slope of a graph in the coordinate plane is the ratio of the change in y (the vertical difference) to the change in x (the horizontal difference) between any two points on the line. In this case, the difference in y (points earned) for the pairs given by Ms. Walker, for example between (20, 80) and (24, 96), is 16. The difference in x (number of correct answers) in the same pairs is 4. Therefore, the slope of the graph, which represents the points per question, is 16 divided by 4: 4 points per question. This means that for each correct answer (each increase in 1 on the x-axis), the number of points earned (y) increases by 4.
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The lengths of the sides of triangle ABC are represented in terms of the variable m, where m>6 AB = m - 2 BC = m + 4 AC = m list the angles from smallest to largest.
Answer:
C, B, A
Step-by-step explanation:
From smallest to largest, the side lengths are ...
AB = c = m -2AC = b = mBC = a = m +4The shortest side is opposite the smallest angle, so the angles, smallest to largest, are C, B, A.
___
Comment on side naming
Side c is opposite vertex (and angle) C, so is between vertices A and B. Thus the names AB and c are both names for the side of the triangle opposite angle C.
Answer:
C, B, A
Step-by-step explanation:
The relationship between the yearly fee that the local YMCA charges and the fee to bring a friend is modeled by the linear function f (x) = 5x + 795, where x is the number of friends you bring with you each year. If the total fee is $855 one year, how many friends did you bring to the YMCA that year?
Answer:
12 friends
Step-by-step explanation:
Fill in the given number and solve for x.
855 = 5x +795 . . . . . the total fee was 855
60 = 5x . . . . . . . . . . . subtract 795
12 = x . . . . . . . . . . . . . divide by 5
The number of friends you brought was 12.
1. An angle in a right triangle is identified as θ. If the tangent of θ equals one, what must be true about the triangle side lengths?
A. The side adjacent to theta is half the length of the hypotenuse.
B. The side opposite to theta is longer than the adjacent side.
C. The sides opposite and adjacent to theta are the same length.
D. The side adjacent to theta is longer than the adjacent side.
Answer: Option C
"The sides opposite and adjacent to theta are the same length."
Step-by-step explanation:
By definition the tangent of an angle [tex]\theta[/tex] is written as:
[tex]tan(\theta) = \frac{opposite}{adjacent}[/tex]
Where:
"opposite" is the side opposite the [tex]\theta[/tex] angle
"adjacent" is the side that contains the angle [tex]\theta[/tex] and the angle of 90 °.
In this case we know that
[tex]tan(\theta) = \frac{opposite}{adjacent} = 1[/tex]
If [tex]\frac{opposite}{adjacent} = 1[/tex] then [tex]opposite = adjacent[/tex]
Finally the answer is the option C
"The sides opposite and adjacent to theta are the same length."
Answer:
C. The sides opposite and adjacent to theta are the same length.
Step-by-step explanation:
Given : tanθ = 1
recall tanθ = [tex]\frac{opposite}{adjacent}[/tex]
the only way for [tex]\frac{opposite}{adjacent}[/tex] to equal 1, is that the numerator is the same value as the denominator,
hence the answer is
C. The sides opposite and adjacent to theta are the same length.
The original price of a mountain bike was reduced $125 if p = the mountain bike's original price in dollars, which algebraic expression represents the reduce price?
Answer:
The answer to this question is p-125, because P is the cost of the bike, and reduce = subtract. YW :)
If p is the mountain bike's initial price in dollars, the (P- $ 125 is an algebraic equation indicates the lowered price.
What is the equation?A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.
If p is the initial price of the mountain bike in dollars, the algebraic equation (P- $ 125) reflects the reduced price.
Hence, (P- $ 125) is the correct expression.
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How many cans of paint are needed to cover an area of 2200 square units if one can of paint covers in area 400 square units
The cans of paints and areas are illustrations of equivalent ratios.
5.5 cans are needed to paint an area of 2200 units square
The given parameter is:
[tex]\mathbf{Cans : Area = 1 : 400}[/tex]
Express as fraction
[tex]\mathbf{\frac{Cans }{ Area }= \frac{1 }{ 400}}[/tex]
Multiply both sides by Area
[tex]\mathbf{Cans= \frac{1 }{ 400} \times Area}[/tex]
When the area is 2200, we have:
[tex]\mathbf{Cans= \frac{1 }{ 400} \times 2200}[/tex]
[tex]\mathbf{Cans= 5.5}[/tex]
Hence, 5.5 cans are needed to paint an area of 2200 units square
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5.5 cans of paint are required to cover an area of 2200 square units, but since you can't have half a can, you would actually need 6 cans of paint.
Explanation:This problem can be solved using simple division, which is a common concept in Mathematics. Given that one can of paint covers 400 square units, to find out how many cans of paint are needed to cover an area of 2200 square units, we need to divide the total area by the area that one can covers. So, 2200 ÷ 400 = 5.5.
However, you cannot have half a paint can, so you would need 6 cans of paint to fully cover the area. Here, we apply the mathematical principle of rounding up because you can't use half a can of paint.
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what is the measure of STY in oo below? 130 310 230 50
ANSWER
B. 310°
EXPLANATION
The sum of angles in a circle is 360°
From the diagram, the measure of arc SY is 50°
The measure of arc STY plus the measure of arc SY is 360°
To find the measure of arc STY, we subtract 50° from 360° to get:
Measure of arc STY
[tex] = 360 \degree - 50 \degree[/tex]
This simplifies to
[tex]310 \degree[/tex]The correct answer is B 310°
Answer:
The correct answer is option B. 310°
Step-by-step explanation:
From the figure we can see that, a circle with center o.
And an arc SY with central angle 50°
To find the measure of arc STY
From the figure we can write,
arc SY + arc STY = 360
measure of arc STY = 360 - measure of arc SY
= 360 - 50 - 310°
Therefore the correct answer is option B. 310°
4. Which relation is a function?
A.{(0; -9), (-9, -2), (0, -3)}
B.{(0, -9), (-9,0), (-3, -3)}
C.{(0, -9), (-2, -3), (-2, 0), (-3,-2)}
D.{0,-9, -2, -3}
Answer:
It's B.
Step-by-step explanation:
That is B because there are no duplicate x-values in the ordered pairs.
D is a set of numbers, not a function.
given T(-5,8,3) and M(-2,-1,-6) find the ordered triple that represents TM. Then find the magnitude of TM.
Answer:
TM = (3,-9,-9)
The magnitude of TM = 3√19
Step-by-step explanation:
Given T=(-5,8,3) and M = (-2,-1,-6)
TM is the difference between the vector M and the vector T
So,
TM = M - T = (-2,-1,-6) - (-5,8,3) = (-2+5 , -1-8 , -6-3) = (3,-9,-9)
The magnitude of TM = The distance of TM = [tex]\sqrt{3^2+(-9)^2+(-9)^2}=\sqrt{9+81+81}=\sqrt{171} = \sqrt{9*19} =3\sqrt{19}[/tex]
So, TM = (3,-9,-9) and |TM| = 3√19
Julian needs to spend at least seven hours each week practicing the drums. He has already practiced five and one third hours this week. He wants to split the remaining practice time evenly between the last two days of the week. Write an inequality to determine the minimum number of hours he needs to practice on each of the two days.
Final answer:
Julian needs to practice at least 8 and 1/6 hours on each of the last two days of the week.
Explanation:
To determine the minimum number of hours Julian needs to practice on each of the last two days of the week, we can use an inequality. Julian needs to spend at least seven hours each week practicing the drums, and he has already practiced five and one-third hours this week. Let's represent the minimum number of hours he needs to practice on each of the remaining two days as 'x'. The inequality can be written as:
5 1/3 + 2x ≥ 7
Now let's solve the inequality:
So, the minimum number of hours Julian needs to practice on each of the last two days of the week is 8 and 1/6 hours (or approximately 8.17 hours).
PLS HELP SHOW ALL YOUR WORKING OUT
BRAINLIEST
Raymond took out a 25-year loan for $135,000 at an APR of 3.6% compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80 % of the balance, what prepayment fee would he be charged for paying off the loan 5 years early?
A. 683.10
B 546.08
C. 695.49
D. 543.46
Answer:
D. 543.46
Step-by-step explanation:
The formula for the remaining balance on the loan is ...
A = P(1 +r)^n +p((1 -(1 +r)^n)/r)
where P is the principal, p is the monthly payment, r is the monthly interest rate, and n is the number of months.
We have P=135,000, p = TBD, r = 3.6%/12 = .003, n = 20×12 = 240.
___
The monthly payment is given by the same formula by setting A=0. In this case, n is 25 years, or 300 payments. Solving for p, we get, ...
p = Pr(1 +r)^n/((1 +r)^n -1) = Pr/(1 -(1 +r)^-n)
So, the monthly payment is ...
p = 135,000×0.003/(1 -1.003^-300) = 683.10
Using this value in the formula for remaining balance, we get ...
A = 135000(1.003^240) +683.10((1 -1.003^240)/0.003) = 37,459.20
___
80% of this balance is 29,967.36. The answer choices only make sense if we assume the interest penalty is equivalent to the interest being compounded monthly:
$29,967.36 × (1.003^6 -1) = $543.47
The closest match among answer choices is ...
D. 543.46
Suppose you had been in charge of designing the study. what sample size would be needed to construct a margin of error of 2% with 95% confidence? use the prior point estimate of p* = 0.15 for this calculation. round up to the nearest whole number. (for example, 144.1 would round to 145)
Answer:
1225
Step-by-step explanation:
hihi. So the equation for MoE is (z*) * SE. The z* for a 95% Confidence is one you should have memorized but for repeatability sake you can always just do an inverse Norm to find the z* for these types of applications. To do so, you can always type this command into your calculator: invNorm(conf + (1-conf)/2, 0, 1).
(When I say conf here I am referring to the confidence level as a decimal).
All that's left is the Standard Error or SE to be short. Since you gave a p* estimate then we can use the equation for SE when dealing with proportions/percents which is sqrt(p(1-p) / n) where p is the proportion and n is the sample size, which we are solving for. Once you have this established it's a basic multi-step solve for n which comes out to be 1225 after rounding.
A side note, the included picture is a bit messy due to my refusal to round when doing these kinds of problems. Rounding errors are more common than you think
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence and this can be determined by using the formula of margin of error.
Given :
A margin of error of 2% with 95% confidence.The prior point estimate of p* = 0.15.The following calculation can be used to determine the sample size needed to construct a margin of error of 2% with 95% confidence.
[tex]\rm MOE = z \times \sqrt{\dfrac{p(1-p)}{n}}[/tex]
[tex]0.02=1.96\times \sqrt{\dfrac{0.15\times 0.85}{n}}[/tex]
[tex]\left(\dfrac{0.02}{1.96}\right)^2= \dfrac{0.15\times 0.85}{n}[/tex]
[tex]n = \dfrac{(1.96)^2\times 0.15 \times 0.85}{(0.02)^2}[/tex]
[tex]n = 1224.51[/tex]
n = 1225 (round off)
The sample size would be 1225 needed to construct a margin of error of 2% with 95% confidence.
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Select the correct answer
What is the 10th term of the geometric sequence 3,6, 12, 24,48 ...?
A. 512
B. 3,072
C. 768
D. 1,536
Answer:
hey mate.
Step-by-step explanation:
Select the correct answer
What is the 10th term of the geometric sequence 3,6, 12, 24,48 ...?
A. 512
B. 3,072
C. 768
D. 1,536
is ... 768
Answer:
D
Step-by-step explanation:
The n th term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r is the common ratio
r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2
Using a₁ = 3 and r = 2, then
[tex]a_{10}[/tex] = 3 × [tex]2^{9}[/tex] = 3 × 512 = 1536 → D
BRAINLIEST
find the value of a^n b^n if n=3,a=100,and b=1/4
Answer:
= (100)^3(1/4)^3
= 15,625 i think im not that good at math but i passed
Step-by-step explanation:
Hi there! My name is Zalgo and I am here to help you out on this gracious day. If n=3, a=100 and b=1/4, the equation should look like "100^3 * 1/4^3". The answer would be 15625.
I hope that this helps! :D
"Stay Brainly and stay proud!" - Zalgo
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Last year, 9 employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.
The mean retirement age is 59.7
What is mean for the given sample data?The sample mean is a statistic obtained by calculating the arithmetic average of the values of a variable in a sample.
To calculate the arithmetic mean of a set of data we must first add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean (M):
M=∑ x/n
Given, the sample data of ages of 9 employees respectively are
52, 63, 67, 50, 59, 58, 65, 51, 56.
Mean of sample data
M=∑ x/n
M=(52+63+67+50+59+58+65+51+56)/9
M=537/9
M=59.667
Hence, the mean for the given sample data round to one more decimal place than is present in the original data values is 59.7
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Note- The complete question is mentioned below
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.
52, 63, 67, 50, 59, 58, 65, 51, 56.
Final answer:
To find the mean retirement age for the 9 employees, add up all ages, divide by the number of employees, yielding a mean retirement age of 71.6 years.
Explanation:
Mean Retirement Age Calculation:
Add up all the ages: 65 + 67 + 68 + 70 + 72 + 74 + 75 + 76 + 77 = 644
Count the number of ages, which is 9
Divide the total sum of ages by the number of employees to find the mean: 644 / 9 = 71.6 years
You are choosing between two health clubs. Club A offers membership for a fee of $ 17 plus a monthly fee of $22. Club B offers membership for a fee of $13 plus a monthly fee of 24. After how many months will the total cost of each health club be the same ? What will be the total cost for each club?
Answer:
2 months$61 (for two months)Step-by-step explanation:
Club B's savings of $17 - 13 = $4 in fee is eaten up at the rate of $24 -22 = $2 per month in monthly fees. It will take $4/($2/mo) = 2 mo for the total costs to be equal.
After 2 months, the amount at each club will be ...
$17 + 22×2 = $61$13 + 24×2 = $61_____
If you want to write equations, the club costs (a and b) in terms of months (m) of membership are ...
a = 17 +22m
b = 13 +24m
The difference is zero when ...
a - b = 0
(17 +22m) -(13 +24m) = 0
4 -2m = 0 . . . . . . . simplify
4 = 2m . . . . . . . . . add 2m . . . Note that 4 is 17-13; 2 is 24-22, as above.
4/2 = m = 2 . . . . . . divide by the coefficient of m
The difference in total cost will be zero after 2 months.
Please help me with this proof
5. Next time include the entire page in the photo. I'm guessing it's U at the top right and O at the bottom right.
First box.
SE ≅ SU
Given
Second box
angle 1 ≅ angle 2
Those are vertical angles, which are always congruent
Third box
angle E = angle U
Given
Next box, three arrows in.
triangle MES ≅ triangle OUS
Angle - Side - Angle
Last box:
MS ≅ SO
Corresponding parts of congruent triangles.
-----------
6.
First box:
angle E ≅ angle U
Given
Second box:
NS ≅ NS
reflexivity (aka it's the same segment)
Third box:
angle 1 = angle 2
Definition of angle bisector
Next box:
triangle WNS ≅ triangle ENS
Angle - Side - Angle
Next:
WN ≅ EN
Corresponding parts of congruent triangles.
Answer:
5. Next time include the entire page in the photo. I'm guessing it's U at the top right and O at the bottom right.First box. SE ≅ SUGivenSecond boxangle 1 ≅ angle 2Those are vertical angles, which are always congruentThird boxangle E = angle UGivenNext box, three arrows in.triangle MES ≅ triangle OUSAngle - Side - AngleLast box:MS ≅ SOCorresponding parts of congruent triangles.-----------6.First box:angle E ≅ angle UGivenSecond box:NS ≅ NSreflexivity (aka it's the same segment)Third box:angle 1 = angle 2 Definition of angle bisectorNext box:triangle WNS ≅ triangle ENSAngle - Side - AngleNext: WN ≅ ENCorresponding parts of congruent triangles
Yesterday, Pablo had 4 4/9 quarts of iced tea, and Rosa had 3 5/12 quarts of iced tea.
How much more iced tea did Pablo have than Rosa?
Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
1. How much more iced tea did Pablo have than Rosa?
= 4 4/9 - 3 5/12 = 40/9 - 41/12 = 40/9 - 41/12 = (40 × 4)/(9 × 4) - (41 × 3)/(12 × 3) = 160/36 - 123/36= 37/36= 37/36 = 1 1/36Pablo has 1 1/36 quarts of ice tea more than Rosa.
2. Pablo gave Rosa 15% of his iced tea today. How much iced tea do each of them have now? Write your answer in fraction form.
Iced tea given
= 15% × 4 4/9= 15/100 × 40/9 = 600/900= 2/3Pablo iced tea
= 40/9 - 2/3 = 40/9 - (2 × 3)/(3×3) = 40/9 - 6/9= 34/9= 3 7/9Rosa iced tea
= 41/12 + 2/3 = 41/12 + (2 × 4)/(3 × 4) = 41/12 + 8/12= 49/12= 4 1/12Pablo has 3 7/9 quarts of iced tea and Rosa has 4 1/12 quarts.
Ribbon costs $0.45 per foot . A sewing project calls for 20. 5 feet of ribbon to the nearest cent that will be the cost of the ribbon for the project
To find the total cost of the ribbon, multiply the length needed (20.5 feet) by the cost per foot ($0.45), which equals $9.225. Round this to the nearest cent to get $9.23.
To calculate the cost of the ribbon needed for a sewing project, you multiply the length of the ribbon required by the cost per foot. In this case, the project calls for 20.5 feet of ribbon and the ribbon costs $0.45 per foot. The formula to use is: Total Cost = Length in Feet x Cost Per Foot. Now, let's do the math:
Total Cost = 20.5 feet x $0.45/foot = $9.225.
To round to the nearest cent, the total cost would be $9.23.
Let f(x)=14/7+2e^−0.6x . What is f(3) ? Enter your answer, rounded to the nearest tenth, in the box.
Answer:
[tex]f(3)=1.9[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\frac{14}{7+2e^{-0.6x}}[/tex]
we know that
f(3) is the value of the function for the value of x equal to 3
so
substitute the value of x=3 in the function
[tex]f(3)=\frac{14}{7+2e^{-0.6(3)}}=1.9[/tex]
Answer:
1.9
Step-by-step explanation:
fX)=14/7=2e^-0.6x = 1.9
please help Find the area of the figure.
Answer:
69.09 yd^2
Step-by-step explanation:
14.1*9.8=138.18
138.18*0.5=69.09
Answer:
69.09 square yd.
Step-by-step explanation:
Area of a triangle is
[tex]A=\dfrac{1}{2}\times base\times height[/tex]
From the given figure it is clear that height of the triangle is 9.8 yd and base of the triangle is 14.1 yd.
Substitute the given values in he above formula, to find the area of triangle.
[tex]A=\dfrac{1}{2}\times 14.1\times 9.8[/tex]
[tex]A=69.09[/tex]
Hence, the area of triangle is 69.09 square yd.
Elizabeth attempts a field goal by kicking a football from the ground with an initial vertical
velocity of 64 ft/s. How long will the football be in the air?
[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{64}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{0\qquad \textit{from the ground}}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf h(t)=-16t^2+64t+0\implies h(t)=-16t^2+64t\implies \stackrel{\textit{hits the ground}~\hfill }{0=-16t^2+64t} \\\\\\ 0=-16t(t-4)\implies t= \begin{cases} 0\\ \boxed{4} \end{cases}[/tex]
Check the picture below, it hits the ground at 0 feet, where it came from, the ground, and when it came back down.