Answer:
BC =21.03540021
Step-by-step explanation:
We know the measure of angle B since the sum of the angles of a triangle add to 180
A + B+ C = 180
61+ B + 12 =180
B = 180 - 12 -61
B =107
Then we can use the law of sines to find BC
sin B sin A
-------- = -------------
AC BC
sin 107 sin 61
-------- = -------------
23 BC
Using cross products
BC sin 107 = 23 sin 61
BC = 23 sin 61/ sin 107
BC =21.03540021
Answer:
20.12m
Step-by-step explanation:
180 - (12 + 61) = 107° = ∡B
[tex]\frac{23}{sin(107)} = \frac{a}{sin(61)}[/tex] *Cross Multiply*
[tex]a(sin(107)) = 23(sin(61))[/tex] *Divide by sin(107)*
[tex]a = \frac{23(sin(61))}{sin(107)}[/tex] *Solve*
a = BC ≈ 20.12m
Sophia wants to take out a loan of $6,000 with interest that compounds monthly. Use the formula A = P(1 + rn)n∗t to find which of these loan terms will have the lowest total cost. A) 2 years at 4% interest B) 3 years at 3% interest C) 4 years at 1% interest D) 5 years at 2% interest
Answer:
d
Step-by-step explanation:
FV = P (1 + r/m)^mn
FV = Future value
P = Present value
R = interest rate
N = number of years
m = number of compounding
a. 6000x (1 + 0.04/12)^24 = 6498.86
b. . 6000x (1 + 0.03/12)^36 =6564.31
c. . 6000x (1 + 0.01/12)^48 = 6244.76
d. . 6000x (1 + 0.05/12)^60 =6630.47
The cosine of 55 1/2 degrees is approximately 0.566. What angle, in degrees, has a sine of approximately 0.566?
Given:
[tex]\cos (55\dfrac{1}{2})^\circ\approx 0.566[/tex]
To find:
The angle, in degrees, that has a sine of approximately 0.566.
Solution:
We know that,
[tex]\sin(90^\circ-x)=\cos x[/tex]
We have,
[tex]\cos (55\dfrac{1}{2})^\circ\approx 0.566[/tex]
Using the above trigonometric identity, it can be written as:
[tex]\sin (90-55\dfrac{1}{2})^\circ\approx 0.566[/tex]
[tex]\sin (90-\dfrac{110+1}{2})^\circ\approx 0.566[/tex]
[tex]\sin (90-\dfrac{111}{2})^\circ\approx 0.566[/tex]
Taking LCM, we get
[tex]\sin (\dfrac{180-111}{2})^\circ\approx 0.566[/tex]
[tex]\sin (\dfrac{69}{2})^\circ\approx 0.566[/tex]
[tex]\sin (34\dfrac{1}{2})^\circ\approx 0.566[/tex]
Therefore, the angle [tex]34\dfrac{1}{2}[/tex] degrees has a sine of approximately 0.566.
A club plans to sell tote bags. The club members estimate they will sell 100 tote bags when the bags are priced at $11 each. For every price increase of $1, they estimate they will sell 10 fewer bags.
What is the estimated revenue, in dollars, when the bags are priced at $13 each?
(revenue = price × number sold)
1) 1,300
2) 1,100
3) 1,040
4) 880
The estimated revenue, in dollars, that the club will generate when the bags are priced at $13 each is 3) 1,040.
What is the revenue formula?The revenue formula is the multiplication of the number of units sold and the price per unit.
To determine the total revenue, we must first ascertain the unit price and the quantity sold.
We know that market forces and the competitive environment determine the quantity sold or supplied.
The demand for tote bags at $11 = 100 units
Decrease in demand for every $1 price increase = 10 units
When the price is $13 each, the units to be sold = 80 (100 -10 x 2)
The total revenue at $13 each = $1,040 (80 x $13)
Total revenue at $12 each = $1,080 (90 x $12)
Total revenue at $11 each = $1,100 (100 x $11)
Thus, we can conclude that the club generates less revenue when it increases its price per tote bag from $11 to $13, justifying the interactions between supply, demand, and cost.
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if u answer this u are a god at math
Answer:
its 90
hope this helped
Step-by-step explanation:
Answer:90
Step-by-step explanation:
Which expression has the greatest value?
Answer:
the answer is 16^3/2
Step-by-step explanation:
I took the Iready test too ;)
if g varies inversely as the square root of h, and g = 9 when h = 121, find g when h = 81.
If g varies inversely as the square root of h, this means that the product of g and the square root of h is constant. We can represent this relationship using the equation g*sqrt(h) = k, where k is the constant value.
We are given that g = 9 when h = 121, so we can substitute these values into the equation to find the constant:
9sqrt(121) = k
Simplifying this expression gives us:
k = 911 = 99
Now that we know the value of the constant, we can use the equation to find g when h = 81:
g*sqrt(81) = 99
Solving for g gives us:
g = 99/sqrt(81) = 99/9 = 11
Therefore, when h = 81, g = 11.
How many different ID cards can be made if there are six digits on a card and no digit may be used more than once
On solving the provided question, we can say that by permutation If an ID card has six digits and each digit may only be used once, then 151,200 distinct ID cards can be created.
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.
There are 6 digits on a card ( 0 - 9 ).
10 * 9 * 8 * 7 * 6 * 5 = 151,200
If an ID card has six digits and each digit may only be used once, then 151,200 distinct ID cards can be created.
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A straight line is shown on the coordinate grid below. a) What is the y-intercept of this line? b) What is the gradient of this line? Give each of your answers as an integer or as a fraction in its simplest form. Y 8- 7- 6- 5- 4- 3- 2- 1- ܝ ܚ ܚ ܢ ܗ ܘ ܙܢ ܣ -8-7-6-5 -4 -32 -1.0 -2+ -3. -4- -8- 12 4 X
Answer:
a. 4
b. -2
Step-by-step explanation:
coordinate: (2,0), (0,4)
gradient = 4 - 0 / 0 - 2
= -2
Help me please I don’t understand any of this.....
9514 1404 393
Answer:
3. B (1, -7)
4. B x < -4
Step-by-step explanation:
3. An ordered pair is a solution to a set of equations or inequalities when putting the x and y values into each expression makes the expression true.
Here, all of the y-values offered are less than 2, so we need to look at whether the given points satisfy the second inequality.
A 0 -(-5) > 5 ⇒ 5 > 5 . . . FALSE
B 1 -(-7) > 5 ⇒ 8 > 5 . . . True
C -3 -(-4) > 5 ⇒ 1 > 5 . . . FALSE
The point (1, -7) satisfies both inequalities, so is a solution of the system.
__
4. The boundary line of an inequality is solid when the "or equal to" case is included in the solution. The symbols used for that are ≤ or ≥. When the symbol is < or >, the "or equal to" case is not included, and the boundary line is dashed.
Here, you can answer the question based simply on the < symbol. There is only one inequality shown that will have a dashed boundary line: choice B.
__
On a usual graph, x-values increase to the right, and y-values increase in the up direction. This means lesser values of x or y are to the left or down. You can determine the side of a boundary line that is shaded by considering this fact.
All you really need to do is find a variable term with a positive coefficient and look at where it stands in relation to the inequality symbol. Here, we have ...
x < (something)
This tells us the shading will be where x-values are less than (left of) those on the boundary line.
So, for x < -4, shading will be to the left of the dashed boundary line.
i really need help with this one.
Solve by factorising:
x^2+10x+21=0
Answer:
[tex]x = -7\\x = -3[/tex]
Step-by-step explanation:
The steps are in the image attached to this response.
My favorite recipe for lemonade calls for 4 cups of water to 3/4 cups sugar. How
much sugar would I need for 6 cups of water?
Hint: One way to solve this would be to find the unit rate for 1 cup of water, then
use a proportion to find 6 cups of water.
Answer and Step-by-step explanation:
To find the unit rate, divide the 4 cups of water and the [tex]\frac{3}{4}[/tex] cups sugar by 4 to get a unite rate for 1 cut of water.
4 divided by 4 equals 1.
[tex]\frac{3}{4}[/tex] divided by 4 equals [tex]\frac{3}{16}[/tex].
Now, we multiply [tex]\frac{3}{16}[/tex] by 6.
[tex]\frac{9}{8}[/tex] is how many cups of sugar that needs to be measured for 6 cups of water.
#teamtrees #PAW (Plant And Water)
options:
Reflection across the y-axis
Translation to the left
Reflection across the x-axis
90° counter clockwise Rotation
Answer: Translation to the left
Step-by-step explanation: Although it may appear at first that this graph represents a reflection across the y-axis, it actually represents a translation 7 units to the left. Every point in the object is moved in the same direction and the same distance to form the new image. If you count the number of units between A and A' or B and B' (and so on), you will find that each point has been shifted to the left 7 times.
If m<1 = 98º and m< 2 = 19°, what is m 3?
mz3 =
Answer:
umm... i cant find the answer sorry
Step-by-step explanation:
tina worked out the median of the number of points scored to be 5
a) explain why it's not possible for the median to be 5?
number of points - frequency
0 1
1 3
2 5
3 4
4 3
Answer:
Could you explain this more nicley, this is quite hard to read
Step-by-step explanation:
What is an equation of the line that passes through the points (-3, 8) and (4, 1)?
Answer:
y=mx+c
m=(8-1)÷(-3-4)
=7÷-7
=-7
8=-7(-3)+c
8=21+c
c=-13
y=-7x+c
i hope it is correct :)
is 9.2 rational or irrational?
Answer:
Rational number
Step-by-step explanation:
it's a decimal
PLZ HELP QUICK!!!
Does the data provide statistical evidence that women pay more than men for the same catalytic converter repair?
Answer:
Yes,the data provide convincing statistical evidence that at women pay more than men for the same catalytic converter repair
What is the equation to this graph above
Answer:
y = -5/2x + 1
Step-by-step explanation:
y=mx+b
m is slope
b is y intercept
Answer:
(-2, 6)
(0,1)
(2,-4)
Step-by-step explanation:
It where the line meets the graph but like where the line meets equally together with other lines
formula (x,y)
Jason took his Siberian Husky dog to the veterinarian. The dog was put on a scale and found to weigh 52 lb. Assume that the population mean weight of Siberian Huskies is 49 lb. with a standard deviation of 7. The weights of Huskies are normally distributed.
What is the approximate percentage of Huskies that weigh less than Jason's dog?
a) 67%
b) 40%
c) 33%
d) 60%
Answer:
im kinda not smart but i think its B
Step-by-step explanation:
B. find the value of the unknown variables and sides using parallelogram SAFE,given:
Answer:
answer below
Step-by-step explanation:
x=4
y=8
AE line equals 16
sf line equals 20
st line equals 10
How do I solve for the measures of the the interior angles of a polygon
Answer:
Step-by-step explanation:
To solve for the interior angles for a polygon,
subtract 2 from the number of sides then multiply with 180
i.e, (n-2)180
e.g, in the case of a triangle, (3-2)180 = 1*180 = 180
As for square, (4-2)180 = 2*180 = 360
Hope u understand.
Mark as the brainliest
Can someone find the function for this please “If f(x) = 4x - 11, find the values of f(x)
for the domain of {-3, 1,5}.”
Answer:
13,3,9
Step-by-step explanation:
f(3)=4(-3)-1
= -12-1
=13
f(1)=4(1)-1
= 4-1
= 3
f(5)=4(5)-11
= 20-11
= 9
Molly needs to classify the triangle below based on angles. Which class is correct? 60° 50° 70° A. acute triangle О B. isosceles triangle C. equilateral triangle D. obtuse triangle
Answer:
A. Actute triangle
Step-by-step explanation:
Is A because an acute triangle is a triangle where all the angles are the same.
Can not be B. because isosceles triangles have two sides that are the same which doesn't relate to angles.
Can not be C. because equilatiral triangles are triangles with sides that are all the same.
Can not be D. because for a triangle to be obtuse one of the angles needs to be greater that 90 degrees.
So it has to be A.
The cost of hiring a plumber is shown by the equation � = 100� + 75, where n is the number of hours
worked, and C is the total cost to hire the plumber. The plumber wants to earn at least $200 per job,
and will work for a maximum of 6 hours for each job.
(a) What is the minimum and maximum number of hours that the plumber will work?
Answer:
The minimum number of hours the plumer can work is 1 hour and 15 minutes and the maximum number of hours is 6.
Step-by-step explanation:
the scale on a map is 1:5000000
two towns are 7cm apart on the map
work out the actual distance between the towns
Answer:
Step-by-step explanation:
scale,= 1 : 5000000
it means 1 cm depicts 5000000cm
or 50000m else 50km
the distance between two towns in map = 7cm
so the distance between two towns = 7 *50
= 350km
What is the length of the diagonal of a poster board with dimensions 22 inches by 28 inches? round to the nearest tenth
A. 24.8 in.
B. 28.4 in
C. 35.6 in
D. 50 in
Answer:
answer is c
Step-by-step explanation:
A jar contains 3 blue cubes 3 blue spheres and 6 green cubes and 4 green spheres. If you select an object at random, what is the probability that the object is green or a cube?
Answer:
it would be around 62%
Step-by-step explanation:
since there are 10 chances for the object to be green or a cube and 16 objects in total, the fraction would be 10/16. 10/16 simplified is 10 divided by 16 = 0.62. when you turn that into a percent it would be about 62%
5. The hourly garage at BWI Airport costs $4 an hour with a maximum cost of $22 a day. The equation (ℎ)= { 4 , 0<ℎ≤1 8 , 1<ℎ≤2 12 , 2<ℎ≤3 16 , 3<ℎ≤4 20 , 4<ℎ≤5 22 , 5<ℎ≤24 represents the cost of parking for ℎ hours. a. How much does it cost to park for 45 minutes? b. How much does it cost to park for 2 hours? c. How long could you have parked if it cost you $16? d. List the domain and range for this situation.
It will cost $4 for 45 minutes and for 2 hours it will cost $8. If parked for 3 to 4 hours it will cost $16 for garage at BWI Airport.
What is the scope and domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
How are range and domain determined?Graphs can be used to determine the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis because the term "domain" refers to the set of potential input values. The possible output values that make up the range are shown on y-axis.
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Enter the length ,X of the ramp in inches (no links need answers ASAP)
Answer:
53 inches
Step-by-step explanation:
use the Pythagorean Theorem
c^2 = a^2 + b^2
x^2 = 28^2 + 45^2
x^2 = 784 + 2025
x^2 = 2809
Take the square root of both sides
x = 53