The addition is:
[tex]=\dfrac{513}{16}\ in.[/tex] or [tex]32\frac{1}{16}\ in.[/tex]
Step-by-step explanation:We are asked to add the expression :
[tex]21\frac{1}{2}\ in.[/tex] and [tex]10\frac{9}{16}\ in.[/tex]
both the numbers are in mixed fraction .
We will first change both the numbers into simple fraction as follows:
[tex]21\frac{1}{2}=\dfrac{21\times 2+1}{2}\\\\\\21\frac{1}{2}=\dfrac{43}{2}\ in.[/tex]
and
[tex]10\frac{9}{16}=\dfrac{10\times 16+9}{16}\\\\10\frac{9}{16}=\dfrac{169}{16}\ in.[/tex]
Hence, the addition of the two numbers is calculated as follows:
[tex]\dfrac{43}{2}+\dfrac{169}{16}\\\\\\=\dfrac{43\times 8+169}{16}[/tex]
( Since, on taking lcm of 2 and 16)
Hence, we get:
[tex]=\dfrac{513}{16}\ in.[/tex]
which in mixed fraction is:
[tex]32\frac{1}{16}\ in.[/tex]
How to write 7 95/125 as a decimal?
In order to apply the law of sines to find the length of the side of a triangle, it is enough to know which of the following?
A. Two angles and a side
B. All three angles
C. Two sides and one angle
D. The area of the triangle ...?
Answer:
We must have two angles and a side.
A is the correct option.
Step-by-step explanation:
For any triangle ABC, the law of sine is given by
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
From this formula it is clear that in order to find the length of the side of the triangle, we must have two angles and a side.
Let us understand this by assuming that we need to find a (length of the side). From the formula, we have
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}\\\\a=\frac{b\sin A}{\sin B}[/tex]
Thus, to find the length a, we must have b, sin A and sin B.
Hence, o find the length of the side of the triangle, we must have two angles and a side.
write the area A of a square as a function of its perimeter P. ...?
Final answer:
The area of a square as a function of its perimeter is A = (P/4)².
Explanation:
The area of a square can be represented as a function of its perimeter. Let's say the side length of the square is a. The perimeter of the square is given by P = 4a. So, to write the area A as a function of the perimeter P, we can use the formula:
A = (P/4)²
1.There are 10 kids running a race. How many ways are there for them to come in first, second, and third place?
2.In a drawing, a jar holds the numbers 1 to 8. If you draw three numbers to form a three-digit number (without replacement), what is the probability you will draw 135?
Answer:
1: 720
2: [tex]\frac{1}{336}[/tex]
Step-by-step explanation:
1: There are 10 kids in a race so the number of ways such that they come first , second and third=10×9×8
=720
(since the first place is occupied by any one of the ten students i.e. we have ten choices after occupying first position there are only 9 students left for second position and after occupying second for the third position only 8 choices are left)
2: We have to find the probability such that there is no replacement such that we draw 135.
for the first position we have to find the probability([tex]P_{1}[/tex]) that '1' comes out of 8 numbers=[tex]\frac{1}{8}[/tex]
similarly for second choice we could not take 1 as there is no replacement
so probability that 3 comes([tex]P_{2}[/tex]) =[tex]\frac{1}{7}[/tex]
similarly probability that 5 comes at third position([tex]P_{3}[/tex]) = [tex]\frac{1}{6}[/tex]
hence, probability that 135 is drawn= [tex]\frac{1}{8}\times\frac{1}{7}\times\frac{1}{6}=\frac{1}{336}[/tex]
Jeans costs $15 each and shirts costs $9 each. You have at most $90 to spend clothing. You must purchase at least 3 pairs of jeans. Let x be the amount of jeans purchased and y be the amount of shirts purchased. What is a possible solution?
(4,-5)
(4, 5)
(4,2)
(2,4)
Answer: 4,2 is the correct answer
Step-by-step explanation:
A science experiment calls for mixing 3 2/3 cups of distilled water with 1 3/4 cups of vinegar and 2/3 cups of liquid detergent. How much liquid, in all, in cups, is needed?
Answer:
D) 6 1/12
Have a good day.
Answer:
D. It’s right
Step-by-step explanation:
expand and simplify (2t-3)^2
Find an equation in standard form for the hyperbola with vertices at (0, ±2) and foci at (0, ±7).
To find the standard form equation of a hyperbola with given vertices and foci, calculate the values of a and b using distances from the origin, and then insert into the standard form equation (y²/a²) - (x²/b²) = 1. The final equation for the hyperbola with vertices at (0, ±2) and foci at (0, ±7) is 45y² - 4x² = 180.
To find the equation of a hyperbola in standard form, we need the vertices and the foci. Given that the vertices are at (0, ±2), we know that the hyperbola is vertical, and the distance between the vertex and the center, which is the origin, is 2 units, so a=2. Since the foci are at (0, ±7), the distance from the center to a focus is 7 units, which means c=7.
With these values, we can calculate b by using the relationship c² = a² + b². Plugging in the known values gives us 7² = 2² + b², so b² = 49 - 4 = 45. Therefore, b = √45.
The standard form equation of a vertical hyperbola with a center at the origin is (y²/a²) - (x²/b²) = 1. Replacing a and b with the found values, the equation becomes (y²/4) - (x²/45) = 1. Multiplying through by 180, which is the least common multiple of 4 and 45, we get the equation in standard form: 45y² - 4x² = 180.
What number is 32% of 75?
Which of the following equations could be used to solve the problem?
n = 0.32(75)
0.32n = 75
n = 75 ÷ 0.32
How many different strings can be made from the letters in MISSISSIPPI, using all the letters and having no consecutive S's? ...?
Which transformations map the strip pattern onto itself?
dP dP dP d
a horizontal translation and a 180° rotation
a horizontal translation and a reflection across a vertical line
a horizontal translation and a glide reflection
a horizontal translation only
Answer:
a horizontal translation and a glide reflection
Step-by-step explanation:
What is the point in the middle of a circle called?
A. Radius
B. Center
C. Circumference
D. Epicenter
Answer:
center
Step-by-step explanation:
The point in the middle of a circle called, B. Center
What are the circumference and diameter of a circle?The circumference of a circle is the distance around the circle which is 2πr.
The diameter of a circle is the largest chord that passes through the center of a circle it is 2r.
We know, The largest chord that passes through the center of a circle is called a diameter.
All the other line segments that can be drawn with endpoints touching the circumference of a circle are called chords.
The radius is half the length of the largest chord(diameter).
A circle is defined as if we fix a point and mark points in a plane such that each point is equidistant from that fixed point a circle will be formed.
That fixed point is called the center of a circle.
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The perimeter of a square is equal to the perimeter of an equilateral triangle. The length of a side of the square is given by x, and the length of a side of the equilateral triangle is given by x=1. Which equation can be used to find the value of x?
To solve for x, given that the perimeter of a square is equal to the perimeter of an equilateral triangle, the equation 4x = 3(x + 1) can be used.
Explanation:To find the value of x when the perimeter of a square is equal to the perimeter of an equilateral triangle, we set up an equation. Since the side of the square is given by x, and the perimeter of a square is 4 times the length of a side, the perimeter of the square is 4x. The length of a side of the equilateral triangle is given by x + 1, and since the perimeter of the equilateral triangle is 3 times the length of a side, its perimeter is 3(x + 1). Setting these two perimeters equal to each other gives us the equation 4x = 3(x + 1).
Each figure represents a Real Number and no denominators are zero. Choose the
correct statement and briefly explain why the others are not correct.
A) a/b+ c/d= a+c/bd
B) a/b+c/d= a+c/b+d
C) a/b+c/d= ad+bc/bd
What is the solution to 4n-6=10n?
write a fraction with a denominater of 6 that is greater than 4/2
4.5 3.9 4.258 3.75 4.256 from least to greatest
Determine whether the graphs of the given equations are parallel, perpendicular, or neither
y=x+11
y=-x+2
A.Parallel
B.Perpendicular
C.Neither
Keywords
parallel, perpendicular, graphing, linear equation, slope, lines
we know that
If two lines are perpendicular, then the product of their slope is equal to minus one
so
[tex]m1*m2=-1[/tex]
If two lines are parallel, then their slope are equal
[tex]m1=m2[/tex]
In this problem we have
[tex]y=x+11[/tex] --------> linear equation A
the slope is [tex]m1=1[/tex]
[tex]y=-x+2[/tex] --------> linear equation B
the slope is [tex]m2=-1[/tex]
Find the product
[tex]m1*m2=-1[/tex] ---------> the lines are perpendicular
therefore
the answer is the option B
Perpendicular
using a graphing tool
see the attached figure
Answer:
Perpendicular
Step-by-step explanation:
Given are two equations as
[tex]y=x+11\\y=-x+2[/tex]
We have to find whether these two are parallel or perpendicular or neither
For this first we have to find the slope of these two lines
I line slope = 1
II line slope =-1
Since slopes are not equal, the lines are not parallel.
Let us check product of these slopes. IF product =-1 the lines are perpendicular
We find that product = [tex]1*-1=-1[/tex]
Hence two lines are perpendicular
A kite is flying on the end of a 300-ft string. The kite string makes a 65 degree angle with the ground. How far above the ground the kite?
Which is greater 0.12 or 1.2?
Which of the following is an inequality that represents the following scenario: Peter is at a local burger shop. He wants to purchase burgers and fries from the store. The cashier tells him that burgers are $5 each and fries are $2 each. Peter has only $15 to spend on food. Let y represent the number of fries purchased and let x represent the number of burgers purchased
5x+2y >/= 5
Answer: 2 burgers and 2 fries if he has only $15
Burgers=$5 each
Fries=$2 each
5+5=10
2+2=4
which comes out to $14 so the max he can get is 2 each
Probability with Huntington's disease?
Huntington disease is a rare degenerative human disease determined by a dominant allele, HD. The disorder is usually manifested after the age of 45. A young man has learned that his father has developed the disease; his mother does not have the disease (and does not carry to HD disease allele).
What is the probability that the young man will later develop the disease?
If the young man has a child with a woman who does not carry the HD disease allele, what is the probability that their first child will be affected by Huntington disease as ...?
The young man has a 50% chance of developing Huntington's disease, as he can inherit the HD allele from his father. Similarly, if he carries the HD allele and has a child with a woman who does not carry the HD allele, their child has a 50% risk of inheriting and developing the disease.
Explanation:Huntington's disease is associated with genetics and can be passed from parents to offspring. If this young man's father suffers from the condition due to a dominant allele, HD, and his mother does not carry the HD allele, he has a 50% chance of inheriting and later developing the disease. This probability arises because the offspring inherits one allele from each parent.
If the young man has a child with a woman who does not carry the HD disease allele, the child's risk of developing the condition depends on whether the father carries the HD allele. If the father does not carry the HD allele, the probability that their first child would be affected by Huntington's disease is 0%. If the father does carry the HD allele, the risk would be 50% as the child will inherit one allele from the each parent (one from the father who might have HD and one from the mother who does not carry the HD allele).
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The price p of a pizza is $6.95 plus $.95 for each topping t on the pizza
The following bar graph shows the amount of time Latisha participated in an exercise program over a four-week period. If Latisha wants to make the increase over time appear larger, what could she do to the graph?
a. use a smaller range on the vertical scale
b. use a larger range on the vertical scale
c. use different colored bars
Answer:
The bar graph is given ,which shows the amount of time Latisha participated in an exercise program over a four-week period.
If amount of exercising , that is increase over time appear larger
She must use a larger range on the vertical scale.There will be no change in width of bar graph, as coloring the bar graph with different color will make no sense.
Pictorial representation of this problem is depicted below:
Option (B) is true.Use a larger range on the vertical scale.
This answer is correct in the sense that , if time of exercise increases,
Otherwise, if you increase the width between two whole numbers, the graph will appear larger.That is between if width between 0 to 1 is 1 cm than increase it by 1.5 cm or 2 cm, that will make the bar graph larger.
The main tank has a radius of 70 feet. What is the volume of the quarter-sphered sized tank? Round your answer to the nearest whole number.
Is the relation a function? {(14, 9), (15, 8), (8, 7), (1, 9), (15, 2)}
Write an equation in point-slope form for the line with the given slope
that contains the given point.
slope 3; (4, 2)
Answer:
[tex]y-2=3(x-4)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given that a line has a slope (m) of 3 and passes through (4, 2). We want to write this equation in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point.
SolvingWe can substitute what we know into the equation.
First, substitute 3 as m.
[tex]y-y_1=3(x-x_1)[/tex]
Now, substitute 4 as [tex]x_1[/tex] and 2 as [tex]y_1[/tex].
[tex]y-2=3(x-4)[/tex]
which ordered pair is a solution of y=-6x-7
What is the solution to the following of equations {5x-3y=34 x-2y=4?
Why would you want to solve a literal equation for a variable when you could simply plug in known values and then solve the resulting linear equation?
Solving literal equations for a variable is beneficial for finding general solutions that apply to multiple situations, saves time by avoiding repetitive calculations, and reduces potential errors when working with complex numbers.
Why Solve Literal Equations for a Variable
Solving a literal equation for a variable is fundamental in mathematics because it allows one to find a general solution that can apply to various situations. Instead of replacing a variable with a given number each time, which can be time-consuming and error-prone especially when dealing with long decimals and complex fractions, working with no numbers—just variables—simplifies the process. Having found the values that make the equation true, one can easily convert words to an algebraic expression or equation that best models a given problem. This results in the ability to find a solution more swiftly and with less room for error.
For example, in computer programs, solutions to equations are frequently required for multiple sets of input values. Algebraically solving an equation provides a general form that can easily be reused with different inputs, saving substantial time and resources. Additionally, in complex problems involving multiple unknowns, solving for one variable in terms of others can lead to a simplified equation, making it easier to solve the problem.