Step-by-step explanation:
the same as every other individual outcome of a roll of 2 dice : 1/6 × 1/6 = 1/36
two sheets of plywood are leaning up against one another, forming a small camping shelter. One sheet of plywood is 7 feet long and makes a 31 degree angle with the ground. The other sheet of plywood is 4 feet long. What is the approximate measure of the angle made between the two pieces of plywood.
The angle made between the two pieces of plywood found using the law of sines is approximately 85°
The law of sines states that the ratio of the sine of an angle to the length of the opposite side is the same for the three angles and sides of the triangle.
[tex]\dfrac{sin(A)}{a} = \dfrac{sin(B)}{b} = \dfrac{sin(C)}{c}[/tex]
The length of one plywood = 7 feet
The angle made by the 7 feet plywood with the ground = 31°
Length of the other sheet of plywood = 4 feet
Using the law of sines, we get;
sin(31)/4 = sin(B)/7
sin(B) = 7 × (sin(31)/4)
∠B = arcsine(7 × (sin(31)/4)) ≈ 64.33°
The angle between the two pieces of wood is therefore;
Angle = 180° - 31° - 64.33° = 85°
The measure of the angle formed between the two plywood is about 85°
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TWO PART QUESTION NEED! :)))
You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula:A = P(1 + r/n) ^nt to give:
a. The future value in 4 years.
b. The interest gained in 4 years.
Future value in four years is $1060.30 and Interest gained in four years is 560.30.
Define compound interest.Compound interest is interest that builds up over a set length of time on both principal and interest. The principal is also used to account for the interest that has accrued on a principal over time. Furthermore, the accumulated principal value is used to calculate interest for the subsequent time period. The new way of calculating interest now utilized in all international financial and commercial operations is known as compound interest. When we look at the compound interest values that have built over successive time periods, the power of compounding is clearly apparent.
Given
You decide to invest $500 into a 4-year CD that pays 2.85% interest compounded monthly
Compound interest
A = P( 1+ r/n)^nt
Interest gained in 4 years
A = 500( 1+ 0.0285/12)^(12)(4)
A = 500( 1 + 0.002375) ^48
A = 560.30
Future value in 4 years = $500 + $560.30
Future value in 4 years = $1060.30
Future value in four years is $1060.30 and Interest gained in four years is 560.30.
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The solution to an inequality is given in set-builder notation as {x l x > two-thirds}. what is another way to represent this solution set?
a. (–[infinity] , two-thirds]
b. (–[infinity] , two-thirds)
c. (two-thirds, [infinity])
d. [two-thirds, [infinity])
The solution to an inequality is given in set-builder notation as {x l x > two-thirds}.
option c. (two-thirds, [infinity]) is the correct option
What exactly is set builder notation?The set-builder notation can also be used to express sets using an interval or an equation. It is common practise for sets with an unlimited number of elements to write and represent their elements in this way. This makes use of a variable (or several) that fit under the group of typical numerical kinds, such as integers, real numbers, and natural numbers.
What is roster notation?The roster notation is a convenient way to express sets mathematically. Within the curly braces of the roster form, the elements (or members) of a set are listed in a row. In a roster notation, a comma is used to indicate the separation of every two elements when the set contains more than one element.
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Complete the similarity statement for the two quadrilaterals
given.
Enter your answer in the box.
quadrilateral PGY X ~ quadrilateral
Answer: loll ok so yes
Step-by-step explanation:
The equation c = 10.50p represents the proportional relationship between the total cost (c) and the number of pounds (p) of shrimp at a grocery store.
Which description is true, based on the equation of the proportional relationship?
A) For $0.50, you can buy 1 pound of shrimp.
B) For $1, you can buy 10.50 pounds of shrimp.
C) For $10.50, you can buy 10.50 pounds of shrimp.
D) For $10.50, you can buy 1 pound of shrimp.
The equation of the proportional relationship is For $10.50, you can buy 1 pound of shrimp.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
c = 10.50p
where total cost (c) and the number of pounds (p) of shrimp at a grocery store.
When p= 1 pounds then the cost is
c= 10.5
Hence, For $10.50, you can buy 1 pound of shrimp.
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Hi, the answer would be D...
For $10.50, you can buy 1 pound of shrimp.
have a nice day! :)
$55 is what percent of $55?
100%
Step-by-step explanation:$55 = $55. Or in other terms:
100% = 100%
$55 is the maximum number of the problem, which would be 100%. So, they are asking what the maximum is. Which is 100%.
Solution:100%
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Answer: %100
Step-by-step explanation:
55 is the number you are using and the highest number is 55 so it will be %100
PLS HELP ME NEOW PLS
The correct order of sentences to bisect the angle Q is (1) draw a line from Q to where the arc crosses (2) vertex: set the compass to any convenient width (3) from where the arc crosses lag, make an arc.. (4) place the compass point on the angle Q.
How to bisect an angle?We should know that an angle is the intersection of two or more straight lines.
In construction of angles, using the compass, the first thing is to locate a point say Q. The open the leg of the compass to a convinient radius, make an arc at another point say P. From the point P, bisect the initial arc so made then joion to the starting point Q.
Second, from the point where the arcs met on the two lines, make another two arcs above the points, then join them to the starting point Q
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Graph triangle lmn with vertices l(1,6), m(-2,4), and n (3,2) and its
image after the composition.
Rotation: 90 about the origin
Translation: (x,y) (x-3,y+2)
The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).
What is Translation of graph?
A graph can be horizontally translated by moving the base graph to the left or right in relation to the x-axis. Each point on a graph is moved by k units in order to translate it horizontally.
To graph triangle LMN and its image after the composition of a 90 degree rotation about the origin and a translation of (x, y) (x-3, y+2), we can first plot the vertices of triangle LMN on the coordinate plane.
pair L = (1,6);
pair M = (-2,4);
pair N = (3,2);
Next, we can apply the 90 degree rotation about the origin to the vertices of the triangle. The rotation matrix for a 90 degree rotation about the origin is given by:
[cos(90) -sin(90)][x] [y]
[sin(90) cos(90)][y] = [-x]
Substituting the coordinates of the vertices into the rotation matrix, we get:
[cos(90) -sin(90)][1] [6]
[sin(90) cos(90)][-2] = [4]
[3] [2]
Therefore, the image of triangle LMN after the rotation is triangle L'M'N' with vertices L'(-6,1), M'(4,-2), and N'(-2,3).
Finally, we can apply the translation of (x, y) (x-3, y+2) to the vertices of the rotated triangle to get the final image of triangle LMN. The translation matrix is given by:
[tex][1 \ 0][x] [y][-3 \ 2][y] = [x-3][/tex]
Substituting the coordinates of the rotated vertices into the translation matrix, we get:
[1 0][-6] [1]
[-3 2][4] = [-1]
[-2] [3]
Therefore, The final image of triangle LMN is triangle L''M''N'' with vertices L''(-3,-5), M''(1,-4), and N''(-1,-1).
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What is the slope of the line that passes through the points (1, -6)
and (-2, 8)? Write your answer in simplest form.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{8}-\stackrel{y1}{(-6)}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{1}}} \implies \cfrac{8 +6}{-3} \implies \cfrac{ 14 }{ -3 } \implies - \cfrac{14 }{ 3 }[/tex]
12. An antique painting is purchased in 1980 for $995. The value increases by 3.1% every
year. Determine the increase in value of the painting in the 6th year after it was pur-
(3)
chased. You must include an equation with your solution.
An antique painting is purchased in 1980 for $995. The value increases by 3.1% every year, the increase in value of the painting in the 6th year after it was purchased is: $200.02
What is increase in value?Increased Value is the amount obtained after deducting the Base Value from the current assessed value.
Given that,
An antique painting is purchased in 1980 for $995 = P
The value increases by 3.1% every = r
r = 3.1%
r = 3.1/100
r = 0.031
As we know,
Value of painting after t years: [tex]P (1+r)^t[/tex]
So, after 6 years:
f(6) = [tex]995 (1+0.031)^6[/tex]
or, f(6) = [tex]995 (1.031)^6[/tex]
or, f(6) = 1195.0197
or, f(6) = 1195.02
Now, at t = 0, f(0) = 995
Thus, value increased by, f(6) - f(0)
= [1195.02 - 995]
= 200.02
Thus, increase in price since it purchased = $200.02
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divide 4x^3 -x^2 +x - 5 by x^2 +x -1
Answer: 4x^3+1
Step-by-step explanation:
someone help me solve this
y= x-2
Answer:
See below.
Step-by-step explanation:
There is nothing to solve without some additional information. Does the problem state what is to be done, or does it contain any information on the values of x or y? For example:
1) Rearrange for x:
y= x-2
x = y+2
2) What is the value of x if y is 3?
y= x-2
(3)= x-2
x = 5
2x-6y=-18 please help me its due today
Answer:
Assuming you want to convert this to slope-intercept form.
Step-by-step explanation:
y=1/3x+3
Subtract 2x from both sides, then divide both sides by negative 6
if you want to graph it, this is what your graph should look like
** See attached photo**
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120
The number q is an odd number
The median of q consecutive integers = 120
Consider the q = 3
Then three consecutive integers will be 119, 120, 121
The largest number = 121
Substitute the value of q in each options
Option A
(q-1) / 2 + 120
Substitute the value of q
(3-1)/2 + 120
Subtract the terms
=2/2 + 120
Divide the terms
= 1 + 120
= 121
Therefore, largest of these integers is (q-1) / 2 + 120
I have answered the question in general, as the given question is incomplete
The complete question is
if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?
a) (q-1) / 2 + 120
b) q/2 + 119
c) q/2 + 120
d) (q+119)/2
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help me with this math question
Answer:
c
Step-by-step explanation:
Which is not a valid strategy to use when solving the system of equations? 4x - 3y = 8, 2x + 9y = -3
A. Multiply the first equation by 3.
B. Multiply the second equation by 2.
C. Multiply the first equation by 2 and the second equation by 4.
D. Multiply the first equation by 3 and the second equation by 2
The strategy that does not work to solve the system is the one in option D
"Multiply the first equation by 3 and the second equation by 2"
Which one is not a valid strategy?Here we have the following system of equations:
4x - 3y = 8
2x + 9y = -3
To solve it, we can take a linear combination of the two equations, for example if we do what the first option says and we multiply the first equation by 3 we get:
3*4x - 3*3y = 3*8
12x - 9y = 24
Now we can add this to the other equation to get:
(12x - 9y) + (2x + 9y) = 24 - 3
14x = 21
And the system can be solved.
Now, the option that does not help us to solve the system is the third option:
"Multiply the first equation by 3 and the second equation by 2"
If we do that we will get the equations:
12x - 9y = 24
4x + 18y = -6
If we add these two equations no variable is canceled.
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................................................
Answer:
.........................................
Step-by-step explanation:
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three sides of a triangle are 3, radical7, and 4. Is the triangle acute, right or obtuse?
Answer: To determine whether a triangle is acute, right, or obtuse, we need to compare the lengths of its sides to the measure of its angles. The triangle is acute if all three angles measure less than 90 degrees, it is right if one angle measures exactly 90 degrees, and it is obtuse if one angle measures more than 90 degrees.
In the case of a triangle with sides 3, radical7, and 4, we can use the Pythagorean theorem to find the measure of its angles. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Since we know that one side of the triangle has length 4, and another side has length radical7, we can use the theorem to find the length of the third side, which is the hypotenuse. We can write this as an equation: 4^2 + radical7^2 = x^2, where x is the length of the hypotenuse. Solving for x, we get x = 5.
Since the length of the hypotenuse is 5, and one of the other sides has length 4, we can conclude that this triangle is a right triangle. Therefore, the triangle is a right triangle and not acute or obtuse.
Determine whether the Law of Sines or Law of Cosines is the best choice to solve for
the missing dimension for the given figure. Substitute the values into the appropriate
formula and solve for x.
X
26.43
21.35
82.42
49.09
Answer:
Hi use the sine rule: answer: 26.43
Step-by-step explanation:
If p=3 and q=5 find p+q+2
Answer:
= 10
Step-by-step explanation:
p+q+2 = 3 + 5 + 2 = 10
Answer:
10
Step-by-step explanation:
3 + 5 + 2 = 10
Guadalupe has 15 cups of dough to make dumplings. If she uses 3/4 cup of dough for each dumpling, how many dumplings can Guadalupe make?
Answer: she can make 20 dumplings.
Step-by-step explanation:
15 divided by 3/4 (15/.75) = 20
Which ordered pairs lie on the graph of the exponential function ƒ(x) = 5 (1/2) ^x
What is the slope of the line that passes through the points (-1, -7)and (1, -13)? Write your answer in simplest form.
Answer:
m=-3
Step-by-step explanation:
use slope formula to solve
m=rise/over=y2-y1/x2-x1
Help me plssssssssssssssssssss
Answer:
Yes, point (2,4) satisfies the system of inequalities.
Step-by-step explanation:
The area of the graph that is the darkest contains all points that satisfy both inequalities. See the attached worksheet for further explanation of the graph and other colors.
Ms. D'Amico bought a car with a 20% down payment, which was 5,750. She will finance the rest of the car payments. What was the price of the car?
Answer:
$28,750
Step-by-step explanation:
To find the price of the car, you need to use the following formula:
price of the car = down payment / (down payment percentage / 100)
Plugging in the given values, you get:
price of the car = 5,750 / (20 / 100)
Simplifying the expression, you get:
price of the car = 5,750 / 0.2
The price of the car is therefore 28,750.
Marcy is making a hooked circle-shaped rug for her mother. The circumference of the circle-shaped rug is 69.08 inches.
What is the area of the rug? (Use 3.14 for .)
By using the formula of circumference and area of circle, it can be calculated that-
Area of the rug = 379.94 sq. inches
What is area and circumference of a circle?
Area of a circle is the total space taken by the circle.
If r is the radius of the circle, then area of the circle is calculated by the formula
Area = [tex]\pi r^2[/tex]
Circumference of a circle is the length of the boundary of a circle
If r is the radius of a circle, then circumference of a circle is calculated by the formula
Circumference = 2[tex]\pi[/tex]r
Let the radius of the rug be r inches
Circumference = [tex]2 \times \pi \times r[/tex] inches
= 2 [tex]\times[/tex] 3.14 [tex]\times[/tex] r
= 6.28 r
By the problem,
6.28 r = 69.08
r = [tex]\frac{69.08}{6.28}\\[/tex]
r = 11 inches
Area of the rug = 3.14 [tex]\times[/tex] 11 [tex]\times[/tex] 11
= 379.94 sq. inches
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To make 5 batches , jude need to use blank packages of pre mixed mortar
Answer:
the answer to your question is 20
Step-by-step explanation:
5 batches× 4 quarts
Decide whether the equation has no solution, one solution, or infinitely many
solutions. Put an X in the appropriate box in the table.
Infinitely
If you place these marbles in a bag close your eyes and choose a marble what is the probability That it will be yellow
Answer:
Step-by-step explanation: You have 14 and 5 are yellow so 5/14.
Will mark 5 stars and give thanks
Answer:
x = 14.56 units
Step-by-step explanation:
In the given figure, two secants of the circle are intersecting outside of the circle.Thus, by the 'Theorem of intersecting secants', we have:[tex]9(9+x)=8(8+19)[/tex][tex]\implies 9(9+x)=8(27)[/tex][tex]\implies 81+9x=216[/tex][tex]\implies 9x=216-81[/tex][tex]\implies 9x=131[/tex][tex]\implies x=\frac{131}{9}[/tex][tex]\implies x=14.55555..[/tex][tex]\implies x\approx14.56\: units [/tex]