Answer:
Step-by-step explanation:
Using the Law of Cosines,
[tex]a^{2}=b^2 + c^2 - 2bc \cos A\\\\13^{2}=14^{2}+18^{2}-2(14)(18) \cos A\\\\-351=-504 \cos A\\\\\cos A=\frac{351}{504}\\\\A=\boxed{\cos^{-1} \left(\frac{351}{504} \right)}[/tex]
The perimeter of a rectangle is 286 meters. Find the length and width if the length is an integer and the width is 5 times the next consecutive integer.
Answer:
See below
Step-by-step explanation:
Which of the following rational functions is graphed below?
Answer:
ANSWER IS B
Step-by-step explanation:
NEXT TIME USE any graph website online
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms which ones should he check
Step-by-step explanation:
please attach a picture for us to see the choices
I need help please……
Answer:
f=- 6, x=-1
f = - 6, x=-3
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
❗️URGENT❗️
Chase has won 80% of the 30 football video games he has played with his brother, Jacob. If Chase and Jacob continue to play the video game, how many more games in a row goes Chase have to win to achieve an 85% win percentage?
Answer:
10
Step-by-step explanation:
24/30 = 0.8
24+x/30+x =0.85
10=x
If you want more clarification just ask
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
We can write the total number game won by Chase as -
w = 80% of 30
w = 80/100 x 30
w = 4/5 x 30
w = 24
Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -
(24 + x)/(30 + x) = 85/100
(24 + x)/(30 + x) = 0.85
(24 + x) = 0.85(30 + x)
24 + x = 25.5 + 0.85x
0.15x = 1.5
x = 10
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
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Which of the following are true statements?
Out of 220 racers who started the marathon, 203 completed the race, 12 gave up, and 5 were disqualified. What percentage did not complete the marathon?
Question Content Area
Strait Co. manufactures office furniture. During the most productive month of the year, 3,500 desks were manufactured at a total cost of $83,800. In the month of lowest production, the company made 1,240 desks at a cost of $61,900. Using the high-low method of cost estimation, total fixed costs are
a.$21,900
b.$49,885
c.$61,900
d.$83,800
b. Total fixed cost are $49885
What is fixed cost of product ?Sometimes production of a product may increase or decrease, but the cost which do not change with the change of output is called fixed cost of the product.
What is the total fixed cost ?
Highest monthly total cost = $83800
Highest monthly production units = 3500 desks
Lowest monthly total cost = $61900
Lowset monthly production units = 1240 desks
So, variable cost per unit = (Highest cost-lower cost)/(highest production units-lowest production units)
= ($83800-$61900)/(3500-1240)
= $21900/2260
= $9.7
∴ Total fixed costs=Highest monthly total cost-(highest production units×variable cost per unit)
= $83800-(3500×$9.7)
= $83800-$33950
= $49850
Nearest value is $49885, whch is the correct one.
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A scientist studying insects start with a population of 10. the population triples every hour. how many insects wil there be after 20 minutes
The question is asking you to understand that a population which is raised by a common ratio over a certain time period follows an exponential pattern. See:
After 1 hour, the population is 3*10
After 2 hours, the population is 3*3*10
After 3 hours, the population is 3*3*3*10
.....
This can be generalised as a function of t, the time in hours:
f(t) = (3^t) * 10
Since the function determines the population at a given time, it is more prudent to replace f(t) with P, the population after time t:
P = (3^t) * 10
Since 20 minutes is equal to (1/3) hours, t can be substituted for (1/3) in order to calculate the population size after 20 minutes:
P = (3^(1/3)) * 10 = 14.4224957031 ≈ 14
Therefore the population after 20 minutes is 14.
Please help !! I will give 20 points for correct answer !!!!
If 13 metres of a uniform iron rod weights 23.4 kg then what will be the weight of 6 metres of the same rod?
Answer:
Solution:
Here,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]
Weight of 13 m of rod=23.4 kg
Weight of 1 m of rod=23.4/13 kg
[less length,less weight]
Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg
[more length,more weight]
Thus,the weight of 6 m of rod is 10.8 kg.
Alternative method:
Let,the required weight be x kg.
Then,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]
We know that,
More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).
So,using the rule of direct proportion;
i.e. Ratio of length=Ratio of weight
[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]
[tex] \rm{13x = 6 \times 23.4}[/tex]
[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]
[tex] \therefore{x = 10.8}[/tex]
Thus,the weight of 6 m long iron rod is 10.8 kg.
cho hàm số f(x) liên tục trên đoạn [a;b] và có nguyên hàm F(x) thỏa F(a)=10;F(b)=2022 Khi đó \int _a^b\: f(x) dx bằng
The result follows from the fundamental theorem of calculus.
[tex]\displaystyle \int_a^b f(x) \, dx = F(b) - F(a) = 2022 - 10 = \boxed{2012}[/tex]
Factorize: 1+4a+4a^2
Answer: (1+2a)^2 or (1+2a)(1+2a)
Step-by-step explanation:
Answer:
[tex](2a +1)( 2a + 1)[/tex]
Step-by-step explanation:
[tex]1+4a+4a^2[/tex][tex]=4a^2 +4a +1[/tex][tex]=4a^2 +2a + 2a + 1[/tex][tex]=2a(2a +1) +1( 2a + 1)[/tex][tex]=(2a +1)( 2a + 1)[/tex]identify the percentage in 15 is 25% of 60
Answer:
25%
Step-by-step explanation:
In the sentence "15 is 25% of 60.", 25% is the percentage.
15 is the partial amount and 60 is the total amount.
15/60 = .25
convert a decimal to a percentage by multiplying by 100
.25 × 100 = 25
Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.
15/60 is 25%
help please
what is
Answer:
sure how can I help you? please tell me
Jaira is completing construction of a regular hexagon inscribed in a circle, as shown below: What should be the next step in her construction?
Jaira is completing the construction of a regular hexagon inscribed in a circle, as shown below: The next step in her construction should be:
construct another pont E by placing her compass at the locus DRepeat the process to get 6 more points on the given circle then join all of them together.A closed polygon with six equal sides and six equal angles is called a regular hexagon.
Thus, the steps highlighted above will help Jaira complete her construction.
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What is the quotient of -27.375 divided by 7.5
A)–3.65
B)–0.365
C)0.365
D)3.65
Answer: A. -3.65
Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.
[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]
Knowing this, we can input it into the calculator and find the answer's sign.
[tex]-27.375/7.5=-3.65[/tex]
Therefore, the answer is A. -3.65.
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An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic charge if they worked 10 hours in one day?
$450
$400
$550
None of these choices are correct.
Answer:
$800
Step-by-step explanation:
per hour $40×10hours=$400
$400÷$50=8 times initial fee
8×$50=$400 total initial fee
$400hours fee+$400 initial fee=$800 total payment
What is another way to write the equation 7/8x3/4=-6
Another way to write the equation is 7x + 54 = 0
How to rewrite the equationGiven the equation;
[tex]\frac{7}{8}x + \frac{3}{4} = -6[/tex]
Find the LCM on the left side, which is 8
[tex]\frac{7x + 6}{8} = -6[/tex]
Cross multiply
[tex]7x + 6 = -6[/tex] × [tex]8[/tex]
[tex]7x + 6 = -48[/tex]
Collect like terms
[tex]7x = -48 - 6[/tex]
[tex]7x = -54[/tex]
Take all to one side
[tex]7x + 54 = 0[/tex]
Thus, another way to write the equation is 7x + 54 = 0
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What is the vertex of the parabola defined by the equation
(x-2)² =-12(y-2)?
A (-12, 2)
B.
(2, 2)
C. (6,2)
D. (2,-2)
Answer: B. (2,2)
Step-by-step explanation:
The vertex of the parabola in the form [tex](x-h)^2 = 4p(y-k)[/tex] is (h, k).
need help with this please
The values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
Given the equation of x as the function of t is
x= 5 cos t
similarly, the equation of y as the function of t is
y= 3 sin t
At t=3 the value of x will be
x (at t=3) = 5 cos 3= 5(-0.989)= -4.95
At t=3 the value of y will be
y (at t=3) = 3 sin 3= 3(0.141)= 0.423
The derivative of the function of x with respect to t will be
dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t
at t=3 the value of dx/dt will be
dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71
The derivative of the function of y with respect to t will be
dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t
at t=3 the value of dy/dt will be
dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97
The tangent slope is dy/dx which can be calculated by
dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t= (-3/5) cot t
at t=3 the value of tangent slope will be
dy/dx (at t=3) = (-3/5) cot 3= 4.21
The speed at t=3 will be
speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]
= √(dx/dt)²+(dy/dt)²
at t=3
= √(0.71)²+(-2.97)²
= √9.325
= 3.05 unit/sec
Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
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Use the point-slope formula to write an equation of the line that passes through (4,10) and has a slope of m= 3. Write the
answer in slope-intercept form (if possible).
The equation of the line is
How can the logarithmic expression be rewritten?
Select True or False for each statement.
Answer:
True, True, False
Step-by-step explanation:
There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does this situation represent a linear or non-linear function, and why?
Answer:
Step-by-step explanation:
It represents a linear function because there is a constant rate of change.
Step-by-step explanation:
Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.
Here, number of hours represents input value and minutes represents the output value,
Now, By the given table,
The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),
Also,
⇒ The rate of change output value with respect to input value remains constant,
Hence, It represents a linear function because there is a constant rate of change.
Determine whether or not each of the following is a partition of set N of natural numbers. (With reason)
(a) {{n | n > 5}, {n | n < 5}]
(b) [{n | n > 6}, {1, 3,5} , {2, 4}]
(c) {{n | n^2 > 11}, {n | n^2 < 11}
Only Set B is a partition of set N of natural numbers .
What are Natural Numbers ?Numbers starting from 1 to infinity comes under Natural Numbers.
It is asked in the question that to determine whether or not each of the following is a partition of set N of natural numbers
A ) {{n | n > 5}, {n | n < 5}]
It is not a set of natural numbers as it does not include 5.
B ) [{n | n ≥ 6}, {1, 3,5} , {2, 4}]
{1,3,5} {2,4}and {n|n≥6} include all the natural numbers
Therefore , it forms a partition of N.
C ) {{n | n^2 > 11}, {n | n^2 < 11}
Every natural number n must satisfy either n^2 > 11 or n^2 < 11
This cannot be possible , therefore it is not the partition of Natural Numbers.
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if 3t -7 = 5t, then 6t =
Answer:
21
Step-by-step explanation:
[tex]3t-7=5t[/tex]
subtract 3t from both sides
[tex]-7 = 2t[/tex]
multiply both sides by 3
[tex]-21 = 6t[/tex]
so 6t = -21
MATH PERCENTAGE QUESTION HELP!
1. 27400 spectators in a 40000 seat stadium percentage?
2. an archer scores 95 points out of a possible 125 points percentage?
Answer:
68.5% seats filled
76% points earned
Step-by-step explanation:
General outlineIdentify the whole and the partChange ratio into a percentageRatiosPercentages are formed when one finds a ratio of two related quantities, usually comparing the first partial quantity to the amount that "should" be there.
[tex]\text{ratio}=\dfrac {\text{the "part"}}{\text{the whole}}[/tex]
For instance, if you have a pie, and you eat half of the pie, you're in effect imagining the original pie (the whole pie) cut into two equal pieces, and you ate one of them (the "part" of a pie that you ate). To find the ratio of pie that you ate compared to the whole pie, we compare the part and the whole:
[tex]\text{ratio}=\dfrac {\text{the number of "parts" eaten}}{\text{the number of parts of the whole pie}}[/tex]
[tex]\text{ratio}=\dfrac {1}{2}[/tex]
If you had instead eaten three-quarters of the pie, you're in effect imagining the original pie cut into 4 equal pieces, and you ate 3 of them.
[tex]\text{ratio}=\dfrac {\text{the number of "parts" eaten}}{\text{the number of parts of the whole pie}}[/tex]
[tex]\text{ratio}=\dfrac {3}{4}[/tex]
There can be cases where the "part" is bigger than the whole. Suppose that you are baking pies and we want to find the ratio of the pies baked to the number that were needed, the number of pies you baked is the "part", and the number of pies needed is the whole. This could be thought of as the ratio of project completion.
If we need to bake 100 pies, and so far you have only baked 75, then our ratio is:
[tex]\text{ratio}=\dfrac {\text{the number of "parts" made}}{\text{the number of parts of the whole order}}[/tex]
[tex]\text{ratio}=\dfrac {75}{100}[/tex]
But, suppose you keep baking pies and later you have accidentally made more than the 100 total pies.... you've actually made 125 pies. Even though it's the bigger number, the number of pies you baked is still the "part" (even though it's bigger), and the number of pies needed is the whole.
[tex]\text{ratio}=\dfrac {\text{the number of "parts" made}}{\text{the number of parts of the whole order}}[/tex]
[tex]\text{ratio}=\dfrac {125}{100}[/tex]
PercentagesTo find a percentage from a ratio, there are two small steps:
Divide the two numbersMultiply that result by 100 to convert to a percentageGoing back to the pies:
When you ate half of the pie, your ratio of pie eaten was [tex]\frac{1}{2}[/tex]
Dividing the two numbers, the result is [tex]0.5[/tex]
Multiplying by 100 gives 50. So, the percentage of pie that you ate (if you ate half of the pie) is 50%
When you ate three-quarters of the pie, the ratio was [tex]\frac{3}{4}[/tex]
Dividing the two numbers, the result is 0.75
Multiplying by 100 gives 75. So, the percentage of pie that you ate (if you ate three-quarters of the pie) is 75%.
When you were making pies, and 100 pies were needed, but so far you'd only baked 75 pies, the ratio was [tex]\frac{75}{100}[/tex]
Dividing the two numbers, the result is 0.75
Multiplying by 100 gives 75. So, the percentage of the project that you've completed at that point is 75%.
Later, when you had made 125 pies, but only 100 pies were needed, the ratio was [tex]\frac{125}{100}[/tex]
Dividing the two numbers, the result is 1.25
Multiplying by 100 gives 125%. So, the percentage of pies you've made to complete the project at that point is 125%.... the number of pies that you've made is more than what you needed, so the baking project is more than 100% complete.
The questions1. 27400 spectators n a 40000 seat stadium percentage.
Here, it seems that the question is asking what percentage of the stadium is full, so the whole is the 40000 seats available, and the "part" is the 27400 spectators that have come to fill those seats.
[tex]\text{ratio}=\dfrac {\text{the number of spectators filling seats}}{\text{the total number of seats in the stadium}}[/tex]
[tex]\text{ratio}=\dfrac {27400}{40000}[/tex]
Dividing gives 0.685. Multiplying by 100 gives 68.5. So, 68.5% of the seats have been filled.
2. an archer scores 95 points out of a possible 125 points percentage
Here, it seems that the question is asking what percentage of the points possible were earned, so the whole is the 125 points possible, and the "part" is the 95 points that were earned.
[tex]\text{ratio}=\dfrac {\text{the number of points earned}}{\text{the total number of points possible}}[/tex]
[tex]\text{ratio}=\dfrac {95}{125}[/tex]
Dividing gives 0.76. Multiplying by 100 gives 76. So, 76% of points possible were earned.
How many square decimeters are in 687.1 cm²?
Answer:
6.871 decimeters
Step-by-step explanation:
687.1 square centimeters = 6.871 square decimeters
1 dm² = 100 cm²
Answer:
6.871
Step-by-step explanation:
calculator
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°. Find m∠G. Round your answer to the nearest tenth.
The value of m∠G = 48.6° .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°
m∠G = ?
well, using the law of cosines,
GH ² = 9² + 11² - 2(9)(11) cos65°
f = 10.88 ft
now, using the law of sines,
sinG/9 = sin65°/10.88
m∠G = 48.6°
Therefore the value of m∠G = 48.6° .
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For the function y= -2+5 sim {pi/12(x-2)}, what is the minimum value
The function has a local minima at ( 20 , -7 )
What is a Function ?Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.
The expression given is
y = -2 +5sin ( (π/12) (x-2))
the minima of the given expression will be when
the sine term = -1
as the lowest value sin can have is -1
y = -2 +5 * (-1)
y = -7
The sin ( (π/12) (x-2)) = -1
(π/12) (x-2) = 3π /2
On solving this
x = 20
Therefore the function has a local minima at ( 20 , -7 )
It can also be confirmed form the graph attached with the answer.
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