Using the concept of ratio and Pythagoras theorem, the length of the diagonal is 22.95 in
What is RatioA ratio is a way of comparing two or more quantities. It is a mathematical expression that shows the relationship between two or more numbers. The ratio can be written in different ways, such as 4:3, 4/3 or 4 to 3.
In this problem, we have the ratio of width to the height of the screen and we can use Pythagoras theorem to determine the length of the diagonal.
width = 20 in
ratio = 16 : 9
width = (16 / 25) * x
20 = 16/ 25 * x
Total length = 31.25
The height of the screen can be calculated as;
height = 9 / 25 * 31.25
height = 11.25
Using Pythagoras theorem, the length of the diagonal is
d² = 20² + 11.25²
d = 22.95in
The length of diagonal is 22.95 in
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1/5 of a crate of 30 eggs is bad.
What fraction is good?
(ii) Which is more?
Answer:
If 1/5 of 30 eggs is bad, then 4/5 of 30 eggs is good.
4/5 of 30 = 4*6/5*6 = 24/30
24 eggs are good
4/5 of the eggs are good
Step-by-step explanation:
A truck with 22-In.-diameter wheels Is traveling at 55 mph.
How many revolutions per minute do the wheels make?
What is the angular speed of the wheels In radians/min?
To calculate the number of revolutions per minute (RPM) that the wheels of the truck make, we can use the formula:
RPM = (Speed in miles per hour) / (Wheel circumference in inches) x (12 inches/foot) x (1 minute/60 seconds) x (1 foot/5280 miles)
The wheel circumference can be calculated by using the formula C = 2πr, where C is the circumference, π is pi (approximately 3.14), and r is the radius of the wheel (half the diameter).
So first we need to find the radius of the wheel:
r = 22 inches / 2 = 11 inches
Now we can calculate the wheel circumference:
C = 2πr = 2 * 3.14 * 11 inches = 69.96 inches
Now we can calculate the RPM:
RPM = (55 mph) / (69.96 inches) x (12 inches/foot) x (1 minute/60 seconds) x (1 foot/5280 miles)
RPM = 814.85
The wheels of the truck make approximately 814.85 revolutions per minute.
To calculate the angular speed of the wheels in radians per minute, we can use the formula:
ω = (RPM x 2π) / 60
ω = (814.85 x 2π) / 60 = 51.64 rad/min
The angular speed of the wheels is 51.64 radians per minute.
Javier bought a microwave for 105$. The cost was 30% off the original price. What was the price of the microwave before sale
Answer:
$136.50
Step-by-step explanation:
105$ is 100%, To find out what 30% is you must first find out 10% which is $10.50. Multiply that by 3 to get 30%. Add to 105$.
Twice Martina's age decreased by
Mario's age is 6. Three times Martina's
age increased by twice Mario's is 23.
What are their ages?
Answer:
Martina is 5 and Mario is 4
Step-by-step explanation:
2x -y = 6 multiply through by 2 4x -2y = 12
3x + 2y = 23
Add the two numbers together
4x - 2y = 12
3x + 2y = 23
7x = 35 Divide both sides by 7
x = 5 Marina's age
2x - y = 6 Substitute 5 for x and solve for y
2(5) -y = 6
10 -y = 6 Subtract 10 from both sides
-y = -4 Multiply both sides by -1
y = 4 Mario is 4.
15.
(17x-8)
(10r - 1)*
Answer:
Step-by-step explanation: 69
Answer:
170rx−80r−17x+8
If this is simplifying!
Step-by-step explanation:
FOIL
11yrd 7yrd 18yrd is it a right triangle
The sides → 11 yards, 7 yards, 18 yards, do not represent a right angled triangle.
What is a right angled triangle?A right-angled triangle is a type of triangle that has one of its angles equal to 90 degrees. The other two angles sum up to 90 degreesFor a right angled triangle, using the Pythagoras theorem, we can write that → (hypotenuse)² = (base)² + (perpendicular)²Given are the three sides of a triangle as shown -
11 yards, 7 yards, 18 yards.
In order to be the given triangle as a right angled triangle, we will have to prove that → (hypotenuse)² = (base)² + (perpendicular)².hypotenuse is the longest side i.e. 18 yards.18² = 11² + 7²324 = 121 + 49
324 ≠ 170
Therefore, the sides → 11 yards, 7 yards, 18 yards, do not represent a right angled triangle.
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Use the formula SA=2(lw)+2(wh)+2(lh) to find the surface area for a rectangular prism with the length l of 2.8, a width w of 1.19 yd, and a height h of 6 yd
Step-by-step explanation:
The formula for the surface area of a rectangular prism is SA = 2(lw) + 2(wh) + 2(lh), where l is the length, w is the width, and h is the height.
Given:
l = 2.8 yards
w = 1.19 yards
h = 6 yards
Plugging in the values:
SA = 2(2.8 * 1.19) + 2(1.19 * 6) + 2(2.8 * 6)
Simplifying and converting units to square yards:
SA = 2(3.32) + 2(7.14) + 2(16.8)
SA = 6.64 + 14.28 + 33.6
SA = 54.52 square yards.
The surface area of the rectangular prism is 54.52 square yards.
Arianna north borrowed $12,500 to purchase a new chilli and agreed to pay back $13,250 in 270 days what exact interest rate was she paying
Arianna North agreed to borrow $12,500 to buy a new chilli and agreed to pay back $13,250 in 270 days at an interest rate of 8.11%.
what is interest rate ?Divide this same principal by the lending rates, the duration of time, and other factors to result at simple interest. Simple return Equals principal + interest + hours is the marketing formula. This system makes it easiest to calculate interest. One of most typical technique to figuring out interest is as a portion of the principal sum. He will only pay his share of the 100% interest, for example, if he borrow $100 from with a friend and offers to return the loan with 5% interest. $100 (0.05) = $5. When you borrow money, you must pay interest, and when you give it out, you must charge interest. Interest is often determined as an indicator of the overall of the loan total. The interest on the loan is this percentage.
given
Arianna North took out a $12,500 loan
She committed to repaying $13,250 over 270 days.
If x is the interest rate she was paying,
x= 13250 - 12500
= 750
So, x= 750/ 12500 (270/ 365)
x% = 750/ 9,246.57
x% = 0.0811
x%= 8.11%
Arianna North agreed to borrow $12,500 to buy a new chilli and agreed to pay back $13,250 in 270 days at an interest rate of 8.11%.
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12 songs in 42 minutes
The duration of one song will be 3.5 minutes.
What are constant functions?Constant functions are the functions that are of the form -
y = f(x) = K
Given is that 12 songs in 42 minutes.
Now, for 12 songs, the duration is 42 minutes.
For 1 song, the duration will be - (42/12) minutes or 3.5 minutes.
We can represent it using a constant function as -
y = f(x) = 3.5
Therefore, the duration of one song will be 3.5 minutes.
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If you got 24 out of 28 what the grade in a percent
Answer:
84.71%
Step-by-step explanation:
24 out of 28:
24/28 = 0.8471
0.8471*100 = 84.71%
EASY POINTS!
A game streaming service is having an end-of-the-year sale. They are offering discounts
on everything, from new memberships for their service to gaming controllers. Suppose
that you just purchased a new membership with this service for $46.20 for the year, that
was originally $60, what percent of a decrease will this be?
A shop keeper bought 26 apples from a fruit vendor for $37.70. How much did each apple cost?
PLEASE ADD A PICTURE to HELP ME PLS!!!!!!!!
Answer:
Each apple cost $1.45.
Step-by-step explanation:
To find the cost of each apple, we need to divide the total cost of $37.70 by the number of apples, which is 26.
$37.70 ÷ 26 = $1.45
Therefore, each apple costs $1.45.
Jina borrowed a total of $21,000 from two different banks to start a business. One bank charged the equivalent of 6% simple interest, and the other charged 3.5% interest. If the total interest after 1 year was $1210, determine the amount borrowed from each bank.
Answer: hope this helps
Let x be the amount borrowed from the bank that charged 6% interest and y be the amount borrowed from the bank that charged 3.5% interest. We know that:
x + y = 21,000 (the total amount borrowed)
We also know that the total interest after 1 year was $1210. The interest charged by the first bank is 6/100x = 0.06x and the interest charged by the second bank is 3.5/100y = 0.035y.
The total interest is the sum of the interest charged by both banks:
0.06x + 0.035y = 1210
We have two equations:
x + y = 21,000
0.06x + 0.035y = 1210
To find the amount borrowed from each bank, we can use the first equation to solve for one of the variables in terms of the other. For example, we can substitute y = 21,000 - x in the second equation:
0.06x + 0.035(21,000 - x) = 1210
0.06x + 735 - 0.035x = 1210
0.025x = 485
x = 19400
Now, we can substitute this value of x back into the first equation to find the value of y:
y = 21,000 - x
y = 21,000 - 19400
y = 1600
So, Jina borrowed $19400 from the bank that charged 6% interest, and $1600 from the bank that charged 3.5% interest.Step-by-step explanation:
Simplify.
Rewrite the expression in the form bn.
6-2
64
Stuck? Review related articles/videos or use a hint.
Repor
The expression in the form of [tex]b^n[/tex] is 8².
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
64
We need to write 64 in the form of [tex]b^n[/tex]
Now,
8 x 8 = 64
So,
8² = 64
b = 8 and n = 2
Thus,
The expression is 8².
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Maxine bikes 6 miles from home. She then rests for a
short time before biking 4 more miles. After a short rest,
she bikes home. Complete the graph so it shows the
distance Maxine is from home compared to the time.
The graph will have one horizontal line for the rest and then again an inclined line.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
In discrete mathematics, and more specifically in graph theory, a graph is a structure consisting of a set of objects, some of which are "related" in some way. The objects correspond to mathematical abstractions known as vertices, and each pair of related vertices is known as an edge.
Given that Maxine bikes 6 miles from home. She then rests for a short time before biking 4 more miles. After a short rest, she bikes home.
The rest time will be a constant line and the 4 more miles will be an inclined line. The graph is attached with the answer below.
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6
Find the area of the figure.
10 in.
Exercises 4.3 > Exercise 6
The area is
10 in.
6 in.
square inches.
4 in.
Area of the figure is 124 cm²
Find the area?The size or extension of a two-dimensional shape or figure in a plane is used to calculate its area. It is the two-dimensional equivalent of a solid's three-dimensional volume and a curve's one-dimensional length. It can be compared to the amount of paint needed to completely cover a surface.
The International System of Units accepts the square metre, usually known as the m2, as the standard area unit (SI). The area of some of the most well-known simple forms can be calculated using the examples and equations given below.
Area of square = length x length
=10*10=100 cm²
Area of small rectangle = length x breadth
= 10*4=40 cm²
Area of two triangles together = 4 × 4
= 16cm²
Total area = 100 + (40 -16)
= 124 cm²
Thus, Area of the figure is 124 cm²
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Suppose the following random numbers is being used to stimulate event of a basketball player making three free throws in a row. How should the numbers be rearranged?
The list that represents the simulation of three free throws is 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978 078 433 330 333 153
What is Combination?An arrangement of objects where the order in which the objects are selected does not matter.
Given that random numbers is being used to stimulate event of a basketball player making three free throws in a row
The list is given as:
860583 785814 010122 337198 621549 034076 796495 978078 433330 333153
When rearranged, we have: 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978 078 433 330 333 153
Hence, the list that represents the simulation of three free throws is 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978 078 433 330 333 153
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PLEASE HELP ASAP!!
I'd really appreciate the help on this.. Thanks in advance.
In order to answer the questions below you will need the
speed of light: c = 299 792.458 km/s. Use proper unit conversion if necessary and answer with the correct number of significant digits. The questions can be solved using the speed – distance – time relation.
For the questions below, provide a complete solution with explanation.
1. How long does it take light to travel from
a. the Moon to the Earth? (Data: Earth-Moon distance = 384,000 km)
b. the Sun to the Earth? (Data: Earth-Sun distance = 149,600,000 km)
2. Suppose you wanted to reach Alpha Centauri in 100 years.
How fast would you have to go in km/hr? (Data: Sun-Alpha Centauri distance = 4.37 light years)
Answer:
Step-by-step explanation:
Oof, this question is long.
Alr,
1.
a) Time = Distance/ speed = 384000/299792.458 = 1.28 seconds
b) Time = Distance/speed = 149600000/299792.458 = 499.0 or 8.317 minutes.
2.
If the distance 4.37 light years, if we travel at the speed of light, we can reach there in 4.37 years.
so, Speed = Distance/time
Speed = 4.37 light years/100 years
Speed = 0.0437 light year/year
So, the speed would be 0.0437 x speed of light. or 13100 or 1.31 x 10⁴.
I HELP ON THIS ONE PLSSSSS
The given above function has neither maximum nor minimum.
What is the Cube Root Function? f(x) = x is the formula for the fundamental (parent) cube root function. After transformations, it can alternatively take the form f(x) = a (bx - h) + k. Here, the transformations are denoted by the real numbers a, b, h, and k.The basic cube root function is expressed as y=x13 and the entire cube root function is written as y=a(x-h)13 + k.A integer y such that y3 = x is known as the cube root of a number x in mathematics. All nonzero complex numbers have three different complex cube roots, while all nonzero real numbers have precisely one real cube root and two complex conjugate cube roots.Given data :
The cube root function begins in Quadrant III and ends in Quadrant I. It passes through the origin, (0,0).
Did you mean 4*∛3? or 4*x*√3? I will assume you meant the former, not the latter.
The graph of 4*∛3 looks the same as that of ∛3 except that the whole graph has been stretched vertically by a factor of 4.
This function has neither maximum nor minimum.
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1/2 divided by ? = 1/18
Answer:
9
Step-by-step explanation:
1/2 divided by x =1/18
1/2=1/18*x
18*1/2=18*1/18x
x=9
Jon is making a poster for safety awareness week. His poster has 2 sides of equal length. Which math words and numbers are important in this problem?
A.
The poster has 2 equal angles.
B.
The poster has 2 sides of equal length.
C.
The poster has 4 sides of equal length.
D.
The poster has 4 equal angles.
On solving the provided question, we can say that His poster has 2 sides of equal length. so it might be square. the poster has 4 sides of equal length.
what is a square?A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.
here,
His poster has 2 sides of equal length.
so it might be square.
he poster has 4 sides of equal length.
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The parent function f(x)=√ is transformed to g(x) = f(x + 2) - 4. Which is the graph of g?
O A.
OB.
-6 -5 -4 -3 -2 -1
DE
COD JODO
-6 -5 -4 -3 -2 -1
YA
+5
+3
F
1 2 3 4 5 6
-1
23
-2
3
4
-5
-6
+5
£3
+2
-2
9
1 2 3 4
5 6
XA
Answer:
The graph of g is B. This is because the function f(x) is shifted right by 2 units and down by 4 units, which is represented by the graph in B.
Step-by-step explanation:
The graph for function g is attached below.
What is Function?In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
The parent function is
f(x) = ∛x
This function is transformed to obtain
g(x) = ∛(x + 2) - 4.
So, +2 is a horizontal translation, that shifts the graph of the parent function to the left by 2 units.
and, -4 is a vertical translation, that shifts the graph of the parent function down by 4 units.
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1/10×9/10=
please step by step
The number is shown as a quotient in mathematics, where the numerator and denominator are split.
What is meant by fractions?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.
Fractions are used to depict the components of a whole or group of items. Two components make up a fraction. The numerator is the number that appears at the top of the line. It indicates how many equally sized pieces of the entire thing or collection were removed. The denominator is the quantity listed below the line.
Let the given equation be [tex]$$1 / 10 \times 9 / 10$$[/tex]
Follow the PEMDAS order of operations
Multiply and divide (left to right)
[tex]$$\begin{aligned}& 1 / 10=\frac{1}{10} \\& =\frac{1}{10} \times 9 / 10\end{aligned}$$[/tex]
simplifying the equation, we get
[tex]$$\begin{aligned}& \frac{1}{10} \times 9=\frac{9}{10} \\& =\frac{9}{10} / 10\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& \frac{9}{10} / 10=\frac{9}{100} \\& =\frac{9}{100}\end{aligned}$$[/tex]
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Find the next sequence.
3,9,7,21,19,57,55,165,
On solving the provided question we can say that the sequence is 3,9,7,21,19,57,55,165, next is = 210
What is Sequences?Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same. Arithmetic progression can be of two types: There are a finite number of terms in a finite geometric progression. The series' early, late, tolerance, and number of terms can be determined. Differential equations are frequently used in everyday life to compute the flow and motion of electricity, the back and forth motion of devices like pendulums, and to clarify thermodynamic principles.
here,
the sequence is
3,9,7,21,19,57,55,165,
next is = 210
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Lisa is a manager at a maid service company. She has two maids working for her, Sophia and Cameron. Sophia can clean a small house in 7 hours while Cameron can clean the same small house in 10 hours.
Part A: How long will it take Sophia and Cameron to clean the small house together? A complete answer will include an equation representing the situation and all steps in solving the equation.
Part B: The manager Lisa thinks if they work together on the small house, they can clean it in 8.5 hours. Is Lisa correct or incorrect? Explain your reasoning using complete sentences.
The time that it take Sophia and Cameron to clean the small house together is 4 2/17 hours.
b. The manager is incorrect. They'll finish in about 4 hours.
How to illustrate the fraction?From the information, Lisa is a manager at a maid service company and she has two maids working for her, Sophia and Cameron. Sophia can clean a small house in 7 hours while Cameron can clean the same small house in 10 hours.
This will be Illustrated as:
1/7 + 1/10 = 1/t
where t = time.
10/70 + 7/70 = 1/t
17 / 70 = 1/t
t = 70 / 17
t = 4 2/17 hours
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You can clean the gutters of your house in 6hours working together you and your friend can clean the gutters in 3.5 hours let x be the time in hours your friend would take to clean the gutters when working alone write and solve an equation to find how long you friend would take to clean the gutters when working alone
Your friend would take 11.6 hours to clean the gutters when working alone.
What is the work rate?
A rate is a ratio that is used for comparing two different kinds of quantities which have different units. A rate of change is a rate that describes how one quantity changes in relation to another quantity.
Here, we have
Given: You can clean the gutters of your house in 6 hours working together you and your friend can clean the gutters in 3.5 hours let x be the time in hours.
We have to determine an equation to find how long your friend would take to clean the gutters when working alone.
Your Work rate = 1/5
Your and your friend's work rate = 1/3.5
Your friend's rate = 1/3.5 - 1/5 = 3/35
t = 1/(3/35) = 35/3 = 11.6hours
Hence, your friend would take 11.6 hours to clean the gutters when working alone.
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Samir buys a house in a new neighborhood. A few months later, Carson buys a different house in the same neighborhood.
Is it independent or dependent?
Answer: It is independent.
Step-by-step explanation: The decision of Samir to buy a house in a new neighborhood and the decision of Carson to buy a different house in the same neighborhood are independent events. They are not dependent on each other and their actions do not affect the outcome of the other person's decision. The fact that they both bought houses in the same neighborhood is a coincidence and does not impact the outcome of either decision. Samir's decision to buy a house is not affected by Carson buying a house in the same neighborhood and vice versa.
Find the interior angle sum for each polygon. Round your answer to the nearest tenth if necessary.
The sum of interior angles of a polygon with {n} as the number of sides is given by S = (n - 2) x 180°.
What is a polygon?In geometry, a polygon can be defined as a flat or plane, two -dimensional closed shape bounded with straight sides. It does not have curved sides.A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.Given is a polygon.
To find the sum of interior angles of a polygon, we can use the formula -
S = (n - 2) x 180°
where -
{n} is the number of sides in a polygon.
Therefore, the sum of interior angles of a polygon with {n} as the number of sides is : S = (n - 2) x 180°.
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Graph the solution to the inequality on the number line.
|w+4|<6
The solution of the inequality is w ∈ (-10,2)
What is inequality?
A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.
Here the given inequality is
=> Iw+4I< 6
=> w+4< 6 and w+4>-6
=> w<6-4 and w>-6-4
=> w<2 and w>-10
=> w ∈ (-10,2)
Hence the solution of the inequality is w ∈(-10,2).
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Solve the equation 8y-7x=3 for y.
PLEASE HELP
Answer:y=3/8+/7/8x
Step-by-step explanation: