The length of the diagonals of the rhombus is 3.5cm.
A rhombus's diagonals are always perpendicular to one another and always the same length. It contains four right angles, hence an acute angle of 840 is an obtuse angle. We are aware that in a rhombus, the diagonal is the hypotenuse of a right triangle, and the other two sides make up each half of the side.
Consequently, we can use the Pythagorean theorem to determine the diagonal's length:
c = √(a² + b²)
where an is the rhombus's half-length side and b is the other half, and c is the length of the diagonal. So we have:
a = (5cm) / 2 = 2.5cm
b = (5cm) / 2 = 2.5cm
c = √(2.5² + 2.5²) = √(6.25 + 6.25) = √12.5 = 3.5cm
Therefore, the length of the diagonals of the rhombus is 3.5cm.
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Zahra invested $8,800 in an account paying an interest rate of 8 5/8% compounded annually. Christopher invested $8,800 in an account paying an interest rate of 8 1/4% compounded daily. After 11 years, how much more money would Zahra have in her account than Christopher, to the nearest dollar?
After 11 years, the amount (future value) in Zahra's account will be $58 more than the amount in Christopher's.
How the future value is determined?The future value can be determined by using the FV table or formula.
We can also ascertain the future value using an online finance calculator as follows:
Zahra's Investment:N (# of periods) = 11 years
I/Y (Interest per year) = 8.625%
PV (Present Value) = $8,800
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $21,863.03
Total Interest = $13,063.03
Christopher's Investment:N (# of periods) = 4015 days (11 years x 365)
I/Y (Interest per year) = 8.25%
PV (Present Value) = $8,800
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $21,805.22
Total Interest = $13,005.22
Future Values:Zahra's = $21,863.03
Christopher's = $21,805.22
Difference = $57.81 ($21,863.03 - $21,805.22)
Thus, with a slightly higher interest rate, Zahra's account will generate $58 more in future value than Christopher's investment.
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how to simplify 8(1+5x)
Answer:
0.2
Step-by-step explanation:
1. distribute 8 to 1 and 5
2. Now its 8+40x
3. Divide on both sides
4. 40x/40 cancels out
5. 8/40=0.2
Which is the approximate percentage of total pay that fringe benefits make up?
O
O
4%
10%
15%
30%
O
The approximate percentage of total pay that fringe benefits make up is 10%
The term called percentage in math is defined as a number or ratio that can be expressed as a fraction of 100
Here we have to find the approximate percentage of total pay that fringe benefits make up.
As the total compensation offered to the workers or employees by employers in different countries can usually be bifurcated into two broad components.
Here we have to know that the first one is based on wages & salaries components and the second one is the fringe benefits component.
Here this one includes the benefits components usually consist of supplementary benefits such as gratuity, pension contribution, transportation service, accommodation facility, etc.
Here as per the report published by the Bureau of Labor Statistics, U.S. Department of Labor in 2020 said that the approximate of the total pay that the fringe benefits make up usually range from 26.1% - 37.3%.
Based on that the percentage of fringe benefits could vary from the type of industry such as the goods-producing industry or service-providing industry.
So, the increased percentage is calculated as
=> 37.3 - 26.1
=> 11.2
Therefore, the correct option is (b).
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A swim club bought a box of c swim caps to split evenly among its 20 members. Write an expression that shows how many swim caps each swimmer will get.
Answer:
20/C=X
Step-by-step explanation:
C= swim caps
X=How many swim caps each swimmer gets
Write an equation for the secant line of the function Y =X^4 on the interval [1,2]
The equation of a secant line given two points (a, b) and (c, d) is y - b = [(d - b)/(c - a)] (x - a).
How do you find the equation of a secant line over an interval?The Latin word secant, which means to cut, is used in mathematics to define a line that passes through the points P and Q of any arbitrary curve whose equation is y=f(x).
Slope is the term used to describe when one end or side of a surface is higher than the other. A Secant line is a straight line that connects two points on a function. formula for secant line slope.
A secant line's slope through two points is equal to y 2 y 1 x 2 x 1. On the secant line, locate two spots.Discover the line's slope between the two spots.To get the line's equation, enter one of your points and your slope into the point slope form of your line.
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find -|-2/5|?
-2.5
2.5
2/5
-2/5
Answer:
(2/5)
Step-by-step explanation:
(-2/5) = -(2/5)
|-(2/5)| = (2/5)
Convert 9 days into weeks. Round your answer to the nearest hundredth.
The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?
OA.
OB.
OC.
OD.
OE.
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
-
를
1/02/m
1
N/W
base area = B
h
base area = B
The ratio of the volume of the cone to the volume of a prism is equal to one.
What is volume?Three-dimensional space is quantified by volume. It is frequently measured quantitatively with SI-derived units (such the cubic metre and litre) or with a variety of imperial or US-standard units (such as the gallon, quart, cubic inch). Volume and height are related in how they are defined (cubed). The volume of a container is typically thought of as its capacity, or the amount of fluid (gas or liquid) that it could hold, as opposed to the amount of space the container occupies. Utilizing naturally occurring containers of a comparable shape and subsequently, standardized containers, volume is measured. Arithmetic formulas make it simple to determine the volume of some basic three-dimensional shapes.
We know that
The volume of the cone = area of the base. height/3
The volume of Prism = area of the base. height
Since the area of the base and height are the same hence the volume will also be . so the ratio will be 1.
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Find the volume of the solid obtained by rotating the region bounded by y=x2 , y=0, and x=1, about the y-axis.
The volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis is π/2.
We have to determine the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0 and x = 1, about the y-axis.
We will rotate the region near the y-axis using the disc method. Consequently, the curve's equation should be expressed in terms of y.
y = x^2
Taking square root on both side, we get
x = √y
We can write it as
x = y^{1/2}
The volume integral formula is
V = [tex]\pi\int_{a}^{b}R(x)^2dx[/tex]
The values of a and b are taken from the y-axis since the equation for the curve we need is expressed in terms of y.
Using the curve's equation, if x = 0, y = 0, and if x = 1, y = 1, respectively.
Thus, a = 0 and b = 1 are the values.
Now, we may use definite integral to express the volume.
V = [tex]\pi\int_{0}^{1}\left[y^{1/2}\right]^2dx[/tex]
Now simplify
V = [tex]\pi\int_{0}^{1}ydx[/tex]
Now integrating
V = [tex]\pi\left[\frac{y^2}{2}\right]_{0}^{1}[/tex]
V = [tex]\pi\left[\frac{(1)^2}{2}-\frac{(0)^2}{2}\right][/tex]
V = [tex]\pi\left[\frac{1}{2}-0}\right][/tex]
V = π/2
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the preference card calls for 0.25% marcaine and 1% lidocaine to be equally concentrated. how much marcaine will you need to draw up to equal the 1% l
4.0 mL of marcaine will be needed to draw up to equal the 1%.
Marcaine is a brand name for the medication bupivacaine, which is a local anesthetic used to numb a specific area of the body during a surgical or medical procedure.
To determine the amount of marcaine that is needed to be drawn up to equal the 1% lidocaine, we can use the following formula:
(Concentration of Lidocaine) / (Concentration of Marcaine) = (Volume of Lidocaine) / (Volume of Marcaine)
In this case, we know that the concentration of lidocaine is 1% and the concentration of marcaine is 0.25%. So we can plug these values into the formula:
1 / 0.25 = (Volume of Lidocaine) / (Volume of Marcaine)
To solve for the volume of marcaine, we can multiply both sides of the equation by the volume of lidocaine:
(Volume of Lidocaine) / (Volume of Marcaine) = 4
Therefore, 4.0 mL of marcaine will be needed to draw up to equal the 1%.
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Find the slope of the line through (-2,6) and (-5,9)
-1
Step-by-step explanation:Slope describes the rise over run for a graph.
Slope Formula
Slope is the change in y over the change in x. To find the slope of any line from two points we can use the slope formula. The slope formula is [tex]\displaystyle\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. We can plug the points we are given into this formula.
[tex]\frac{9-6}{-5-(-2)}[/tex]This equals [tex]\frac{3}{-3}[/tex] which is simply -1. The slope of the line is -1.
Counting the Change
The formula above just represents the changes in the y-values divided by the changes in the x-values. So, we can count that the y-values increase by 3. Then, the x-values decrease by 3. This creates the slope [tex]\frac{3}{-3}[/tex] (remember that increases are positive and decreases are negative). Once again this gives the slope of -1.
Match the below functions to their graphs on the right:
These are functions that almost have to be memorized but can be understood through Desmos for example:
a: W
b: Z
c: X
d: Y
e: V
Question 3 (2 points)
What translation takes the graph of f(x) = 4x - 3 to the graph of g(x) = 4x - 6 ?
Translation of 3 units down
Translation of 6 units left
Translation of 6 units down
Translation of 3 units right
Answer: The graph of g(x) = 4x - 6 is a translation of the graph of f(x) = 4x - 3.
A translation of a function results in a shift of the graph of the function, either horizontally (left or right) or vertically (up or down).
When the graph of a function is shifted down, the y-coordinates of all the points on the graph decrease. When it's shifted to the left, the x-coordinates of all the points on the graph decrease.
In this case, the graph of g(x) = 4x - 6 is a vertical translation of 3 units down from the graph of f(x) = 4x - 3.
The y-coordinates of all the points on the graph of g(x) = 4x - 6 are 3 units less than the y-coordinates of the corresponding points on the graph of f(x) = 4x - 3.
Therefore, the correct answer is:
Translation of 3 units down.
Step-by-step explanation:
Each kit to build a castle contains 235 parts.
How many parts are
in 4 of the kits?
Laura needs 139 programs for the school play on Thursday. How many boxes of programs will she need, given that each box contains 37 programs?
-2(c+2.5)-5(1.2c+4) simplify this expression
Answer: - 8c - 25
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.Use the exponent rule to remove grouping if the terms are containing exponents.Combine the like terms by addition or subtraction.Combine the constants.
Can someone please help me with this asap? I’ll give lots of points
A right triangle has 1 angle that measures 48 degrees. What is the measure of the third angle?
A: 64 degrees
B: 28 degrees
C: 42 degrees
D: 58 degrees
Step-by-step explanation:
always remember : the sum of all angles in a triangle is 180°.
so, one angle is 90° (it is a right triangle).
the second angle is 48°.
therefore,
180 = 90 + 48 + third angle
third angle = 180 - 90 - 48 = 42°
so, C is correct.
WILL GIVE BRAINLIEST
Find the average rate of change for the given function from x = −1 to x = 2
The average rate of change for the given function from x = −1 to x = 2 is -4/3
How to find the average rate of change for the given function from x = −1 to x = 2?The average rate of change of a function over an interval is a measure of how much the output of the function (y-value) changes as the input (x-value) changes over that interval. This is also the slope of the function or line.
average rate of change = (y2-y1)/(x2-x1)
From the graph, x1 = -1, y1 = 4 and x2 = 2, y2 = 0
average rate of change = (0-4)/(2-(-1)) = -4/3
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students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a
Students who successfully complete a study skills workshop will raise their grade point average by 0.2 points is best described as a hypothesis.
A hypothesis is a proposed explanation or prediction about a phenomenon, based on limited information or data. It is a tentative statement about the relationship between variables that can be tested through further investigation or experimentation.
In scientific research, a hypothesis provides a framework for designing and conducting experiments to gather evidence to support or reject the hypothesis. It acts as a starting point for scientific inquiry and helps guide the research process.
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The ratio of the perimeter of a square piece of paper to the perimeter of a rectangular piece of paper is 2 : 5. Each side of the square piece of paper is 10cm. Find A. The perimeter of the square piece of paper B. The perimeter of the rectangular piece of paper C. The length of the rectangular piece of paper if its width is 15cm ( Please answer all parts!)
The perimeter of the square piece of paper is 40 cm .The perimeter of the rectangular piece of paper is 50 cm and the length of the rectangular piece of paper is 15 cm.
A. The perimeter of the square piece of paper is 40 cm.
This is calculated by multiplying the length of each side of the square by 4.
Length of each side = 10cm
Perimeter of square = 4 x 10 cm = 40 cm
B. The perimeter of the rectangular piece of paper is 50 cm.
This is calculated by multiplying the length and width of the rectangle by 2.
Length = 15 cm
Width = 15 cm
Perimeter of rectangle = 2 x (15 + 15) cm = 2 x 30 cm = 50 cm
C. The length of the rectangular piece of paper is 15 cm.
This is given in the question.
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You are selling tickets for a high school play. Student
tickets cost $4 and general admission tickets cost $6.
You sell 31 tickets and collect $170. How many of each
type did you sell?
Answer:
sold 23 Tickets and 8 General Admission Tickets
Step-by-step explanation:
y = General Admission tickets
x = tickets
4x + 6y = 170
x + y = 31
Use the Substitution method:
4x + 6(31 - x) = 170
4x + 186 - 6x = 170
4x - 6x = -16
-2x = -16
x = 8
y = 31 - 8 = 23
Complete the statement about the model.
The model shows that there are 8 groups of
in 3.
According to the diagram, there are eight fractions of 3/8 in three.
What is a fraction?A fraction is a ratio of two numbers where the numerator and denominator are both integers that can be negative or positive. The numerator can't be zero. Proper fractions and improper fractions are the two types of fractions.A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction's numerator will be less than the denominator.We are shown a diagram of three equal parts divided into eight equal parts.
Divide 3 by 8 to get the value of the equal part.
As a result, the value of each can be given as 3/8.
Therefore There are 8 groups of 3/8 in 3 as per the given diagram.
The diagram is attached below:
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The average birth weight of a Boxer breed dog is 1.25 kilograms. What is the average birth weight in grams?The average birth weight of a Boxer breed dog is 1.25 kilograms. What is the average birth weight in grams?
Answer:
1250g
Step-by-step explanation:
1.25 kg × 1000 = 1250g
A new long-life tire has a tread depth of 3/8 inches, instead of the more typical 7/32 inches. How much deeper is the new tire?
Using the subtraction operation, the new long-life tire with 3/8 inches depth is deeper than the more typical 7/32 inches by 5/32 inches.
What is a subtraction operation?Subtraction operations involve the minuend, the subtrahend, and the result called the difference.
It is one of the four basic mathematical operations, including addition, multiplication, and division.
The depth of the new long-life tire = 3/8 inches
The depth of the old tire = 7/32 inches
The difference = 5/32 inches (3/8 - 7/32)
Thus, the depth difference between the new long-life tire and the typical tire is 5/8 inches.
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3. I have two maps. One is of the Catskill mountains. The scale is 1.5 inches : 4 miles.
The other is of the Shawangunk mountains. The scale is 2 inches : 3.5 miles.
a) Find the distance of Slide mountain in the Catskills if on the map the trail is 2.325 inches.
b) Find the distance of Gertrude's nose in the Shawangunk's is 3.8 inches on the map.
a) Distance of Slide mountain in the Catskills is 6.2 miles
b) Distance of Gertrude's nose in the Shawangunk's = 6.65 miles
How to find a distance?To find a distance on a map, you need to use a ruler or a measuring device such as a pair of compasses. Firstly, place the ruler on the two points you want to measure the distance between. If you are using a pair of compasses, adjust the legs so that the two points are inside the circle created by the compasses. Then, read the distance on the ruler or across the arc of the compasses.
If the distance is relatively short, you can also use the map scale located at the side or bottom of the map. To use the scale, line up the starting point with the scale and then measure the length of the line on the scale. This will give you the distance between the two points.
Finally, if the map has a grid system, you can count the number of squares between the two points and then refer to the grid scale to calculate the distance.
By using one of the methods described above, you should be able to easily measure distances on a map.
a) 2.325 inches * 4 miles/1.5 inches = 6.2 miles
b) 3.8 inches * 3.5 miles/2 inches = 6.65 miles
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The cost of a bicycle wheel was $62 last week. This week, the cost rose to $79 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
Answer:
the percentage increase is 27.4%
Step-by-step explanation:
To find the percentage increase, we can use the formula:
(New cost - Old cost) / Old cost x 100% = Percentage increase
(79 - 62) / 62 x 100% = 27.41%
The percentage increase is 27.41%. Rounded to the nearest tenth of a percent, the percentage increase is 27.4%
Difference of $62 and $79 is 24.1%
62 - 79/((62 + 79)/2) = 17/70.5 =
0.24113475177305 x 100 = 24.113475177305%
what is x+5=8 step by step
Answer:
x = 3
Step-by-step explanation:
x+5=8
x+5-5=8-5
X=3
Answer:
x = 3
Step-by-step explanation:
basically 2 ways
1st: Transposing
1) x + 5 = 8
2) transpose or transfer +5 to the other side
NOTE: transposing numbers and variables switches the signs (positive -> negative and vice versa)
3) x = 8 - 5
x = 3
2nd: Property of Equality (whatever u do one one side, you do the same to the other)
1) x + 5 = 8
2) x + 5 - 5 = 8 - 5
x = 3
the main focus is to isolate x, or to make it be alone in one side of the equation
A triangle has a perimeter of 9x + 6. The first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. What is the length of the third side of the triangle?
x + 13
x − 1
8x − 7
17x − 1
The length of the third side of the triangle is x + 13.
What is the length of the third side of the triangle?A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.
The perimeter of a triangle is the sum of the length of all three sides of the triangle.
Given the data in the question;
Perimeter P = 9x + 6Side A = 5xSide B = 3x - 7Side C = ?To find side C, equate the sum of all three sides of the triangle to the perimeter and simplify.
Side A + Side B + Side C = P
5x + ( 3x - 7 ) + Side C = 9x + 6
5x + 3x - 7 + Side C = 9x + 6
8x - 7 + Side C = 9x + 6
Side C = 9x + 6 - ( 8x - 7 )
Side C = 9x + 6 - 8x + 7
Side C = x + 13
Therefore, side C is x + 13.
Option A) x + 13 is the correct answer.
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Answer:
x + 13
Step-by-step explanation:
i took the test xx
5. Suppose the following table shows the number of labor hours needed to produce airplanes and automobiles in the United States and South Korea, but one of the numbers is unknown.
Number of Hours to Produce One Airplane
South Korea 2000 United States 1000
Number of Hours to Produce One Auto
?
10
a. Without knowing the number of labor hours required to produce an auto in South Korea, you can’t figure out which country has the comparative advantage in which good. Can you give an example of a number for the empty cell of the table that would give the United States the comparative advantage in the production of airplanes? What about South Korea?
b. What exact number would you have to place in the empty cell of the table for it to be impossible that trade between the United States and South Korea could benefit both
The number for an empty cell would be 20 so any number below this benefit South Korea and above this benefit the United States. This also makes it impossible for trade between these two countries.
If a country can manufacture a significant number of goods with the same resources as another country, it has an absolute advantage. If a country can manufacture a certain commodity more cheaply and with higher quality than another country, it has a comparative advantage.
In the given scenario, 1000÷10=100 autos are sacrificed by the United States to manufacture one airplane which is the opportunity cost. In comparison to the United States, South Korea requires twice (2000÷1000) as long to construct an airplane.
a) The number of hours for South Korea to produce one auto would be 2×10=20. Because of this, South Korea would benefit from any number below 20, while the US would benefit from any number above 20.
b) The empty cell value would be 20 for South Korea to have the same opportunity cost as the United States. So mutually beneficial trade cannot exist without comparative advantage.
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Gary used to make bottles of glitter glue.
Bottles Glue Glitter
1 3.8 1.9
4
How much glue and glitter would he need to make 4 bottles?
Gary would need 15.2 oz glue and 3.8 oz of glitter to make 4 bottles.
Gary would need 6.8 oz glue and 4.9 oz of glitter to make 4 bottles.
Gary would need 7.8 oz glue and 5.9 oz of glitter to make 4 bottles.
Gary would need 15.2 oz glue and 7.6 oz of glitter to make 4 bottles.
Gary would need 15.2 oz. of glue and 7.6 oz. of glitter to make 4 bottles.
The correct option is D.
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.
Given in the table,
Bottles Glue Glitter
1 3.8 1.9
Therefore
1 bottle = 3.8 oz. of glue + 1.9 oz. of glitter
Now,
Multiply 4 on both sides.
4 bottle = 4 x (3.8 oz. of glue + 1.9 oz. of glitter)
4 bottle = 15.2 oz. of glue + 7.6 oz. of glitter
Hence, 15.2 oz. of glue and 7.6 oz. of glitter is needed to make 4 bottles.
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