Answers
Using mathematical operations we can conclude that the area of the given figure is 40 units².
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. A mathematical action is called an operation. Mathematical operations include addition, subtraction, multiplication, division, and finding the root.So, the area of the figure:
Where x = 4, so the expression will become:
x² + x² + x + xNow, do the mathematical operations to get the area of the figure as follows:
x² + x² + x + x4² + 4² + 4 + 416 + 16 + 840'
Therefore, using mathematical operations we can conclude that the area of the given figure is 40 units².
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Related Questions
1. A clock has a minute hand that is 6 inches long. How fast is the tip of the minute hand moving?
Give your answer in inches/minute.
Answers
The tip of the minute hand moves in a circle of radius exists 6 in. In 25 minutes, the tip of the minute hand moves 15.7 in
What is meant by length of an arc?The arc length of a circle can be estimated with the radius and central angle utilizing the arc length formula, Length of an Arc = θ × r, where θ is in radian. Length of an Arc = θ × (π/180) × r, where θ exists in degree.
The tip of the minute hand moves in a circle of radius R = 6in.
We will find that for each case, 15 minutes and 25 minutes, the distance traveled is 9.42 in and 15.7 in correspondingly.
Remember that the length of an arc is defined by an angle θ in a circle of radius R is given by:
L = (θ/360°) × 2 × pi × R
We know that R = 6in.
To find how much the tip of the minute hand moves in 15 minutes.
Then we need to find the angle θ that the tip moves in these 15 minutes.
Remember that a complete rotation in the clock has 60 minutes.
This means that there exists an equivalence:
60 min = 360°
1 = (360°/60 min)
15 min = (15 min) × (360°/60 min) = 90°
Then, in 15 minutes, the tip of the minute hand moves:
L = (90°/360°) × 2 × 3.14 × 6in = 9.42 in
For the case of 25 minutes the procedure is the same:
25 min = (25 min) × (360°/60 min) = 150°
Then, in 25 minutes, the tip of the minute hand moves:
L = (150°/360°) × 2 × 3.14 × 6in = 15.7 in
Therefore, the correct answer is 15.7 in.
The complete question is:
The minute hand of a clock is 6 inches long. how far does the tip of the minute hand move in 15 minutes? how far does it move in 25 minutes? round answers to two decimal places.
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the event containing the outcomes belonging to a or b or both is the __________ of a and b.
Answers
The event containing the outcomes belonging to a or b or both is the union of a and b.
Let us consider two sets a and b, and say events or the elements in set a are: (x, y, z), and the elements in set b are: (o, p, q)
The union of these two sets will give:
aUb=(x, y, z, o, p, q)
Now, a union of two sets (denoted by U), for our case a and b, is the set or event containing the elements belonging to a or b or both the elements in a and b altogether.
Thus, the even containing the outcomes belonging to a or b or both in a and b altogether is the union of a and b.
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Bridge math sails.....
Answers
The volume of the waffle of come is 44.7735 inches².
How to calculate the volume?The volume of a cone is calculated as:
= 1/3 πr²h
where π = 3.142
r = radius = Diameter / 2 = 3/2 = 1.5
h = height = 19
The volume will now be:
V = 1/3 πr²h
V = 1/3 × 3.142 × 1.5² × 19
V = 44.7735 inches²
The volume is 44.7735 inches².
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Grace gave her sister a riddle.
I have a number x. I add 15 to twice of x to obtain A. I subtract 4 from x to obtain B. I multiply B by 3 to obtain C. A is equal to C.
Graces sister said the riddle cannot be solved but Grace thought otherwise. Who is right?
Answers
Answer:
27, Grace
Step-by-step explanation:
2x + 15 = A x-4 = B 3B = C C= 3x-12 3x-12 = 2x + 15
+12 +12
3x=2x+27
x=27
Grace is right
A cone with volume 448 m^3 is dilated by a scale factor of 1/4.The volume of the resulting cone is ___ cubic meters.
Answers
EXPLANATION
If the volume of the cone is of V=448m^3 and it is dilated by a scale factor of 1/4, the resulting volume would be as shown as follows:
[tex]\text{Volume}_{\text{dilated}}=448\cdot1\frac{1}{4}=560m^3[/tex]6. The scale on a map of a wilderness area shows that 2 cm represents 3 km. The camp store is
20 cm from the beach on the map.
a) What is the scale factor between the map and the wilderness area?
Answers
The scale factor between the map and the wilderness area is :
1:7500
Given, the scale on a map of a wilderness area shows that 2 cm represent 3 km.
Whereas the camp store is 20 cm from the beach on the map.
Calculating scale factor
From the question, we are to determine what the scale factor from the map to the wilderness area is:
we know that, the scale on a map of a wilderness area shows that 2 cm represent 3 km.
so, convert km to cm.
2cm = 3 km
1 cm = 3 km/ 2 cm
cm = 3×100000/2
cm = 3×50000
cm = 150000
= 150000 cm
scale factor between the map and the wilderness area :
⇒ 20 cm : 150000 cm
⇒ 2 : 15000
⇒ 1 : 7500
Hence the scale factor between the map and the wilderness area
is 1:7500
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pllllllllllllllllllls help plllllllls i beg you
Answers
Answer:
135 cookies
Step-by-step explanation:
If the baker starts with 1382 cookies and uses 302 of them then they'll have 1080 left because 1382-302=1080. Then, if she wants to make cookies with 8 chocolate chips each, then she can make 135 cookies because 1080/8=135.
What is the correct way to solve this problem? I cannot for the life of me figure this out.
180-x=x
????
Answers
Answer:
x = 90
basically this is just finding the half of the number. so you can verify this by adding 90 + 90 = 180. Lmk If you get a good grade on this.
Given the graphs of y = f(x) and y = g(x), what is the value of f(x)-g(x) where the two graphs intersect?
Answers
Answer:
0
Step-by-step explanation:
If they want the values of where the graphs intersect, that means the values are both = to each other, meaning subtracting the same value by the same value is 0
PLEASE HELP!!!
Is x = 3 a solution to the inequality: −8 ≤ 4x − 7?
Answers
Answer:
yes
Step-by-step explanation:
−8 ≤ 4(3)− 7
−8 ≤ 12-7
−8 ≤ 5 it works
write an expression you could use to convert 2.5 gallons to quarts
Answers
After the conversion of units, 2.5 gallons to quarts is 12 quarts.
What is the conversion of the unit?Unit is a standard measure that is used to express any amount. For example, a unit of length is a meter, unit of volume is a liter.The process of changing from one unit to another is called the conversion of a unit.Conversion of units is a very important tool for doing mathematical calculations in maths, physics, and even in chemistry.Multiply to change from a larger to a smaller unit. Divide to change from a smaller unit to a larger one.The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.So, 1 gallon = 4.8 quarts:
Now,
4.8 × 2.5 quarts= 12 quartsTherefore, after the conversion of units, 2.5 gallons to quarts is 12 quarts.
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For a card trick, Barry is using 14 cards from a deck. If each suit he uses has 5 numbered cards and c face cards, which expression shows how many suits he is using?
A. 14 ÷ (5 + c)
B. 14 x 5 + c
C. 14 ÷ 5 + c
D. 14 x (5 + c)
Answers
The correct answer is option A. 14 ÷ (5 + c).
Barry exists spreading the cards among the suits, then he needs enough suits to hold the total of 14 cards he has. Hence, we need to divide the total number of cards by the total number of cards,
What is meant by expression ?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.
A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression. Two expressions joined by an equal sign form an equation.
If we assume Barry exists spreading the cards among the suits, then he needs enough suits to hold the total of 14 cards he has. Hence, we need to divide the total number of cards by the total number of cards.
Therefore, the correct answer is option A. 14 ÷ (5 + c)
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3x+y=10
y=-3x+10
Use substitution
Answers
Answer:
Infinitely many solutions
Step-by-step explanation:
substituting [tex]y=-3x+10[/tex] into [tex]3x+y=10[/tex] we get:
[tex]3x-3x+10=10\\\\0+10=10\\\\0=0[/tex]
Since it is equal to itself there are infinitely may solutions to this problem
A monument is 120 feet tall. How many inches is this? First fill in the blank on the left side of the equation using one of the ratios. Then write your answer on the right side of the equation.
Answers
The length of the building is equal to 1440 inches
Conversion of Metric UnitTo solve this problem, we simply need to convert the length from feet to inches.
So, to convert a measurement in feet to inches, all you need to do is multiply the number by 12. This is an exact number and this will make it easy on our question since its a significant figure.
From metric units;
1 feet is equal to 12 inches
To convert 120 feet to inches, we simply have to multiply 120 by 12 to get the value in inches.
Let the value of the unknown be represented by x
[tex]1ft = 12in\\120ft = x\\x = 120 * 12 \\x = 1440in[/tex]
The length of the monument is equal to 1440 inches.
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5000 people were expected to run and lose 700000 calories. some didnt run and only 4.2x10^6 calories were lost. how many participants did not run
Please show work
Answers
The number of participants that didn't take part is 2000.
How to calculate the number?Let the number of people that take part in the race be x.
From the information, 5000 people were expected to run and lose 7000000 calories. some didnt run and only 4.2x10^6 calories were lost. It should take about 4.2x10^6 = 4200000.
This will be illustrated as:
x/5000 = 4200000 / 7000000
x = (5000 × 4200000) / 7000000
x = 3000
Therefore, 3000 took part. Those that didn't take part will be:
= 5000 - 3000.
= 2000
Therefore, 2000 people didn't take part.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use inverse operations to solve each equation. Explain each step and identify the property used to reach step.
19
=
h
3
−
8
Answers
Using inverse operations, the value of h in the given equation is: 81.
What is an Inverse Operation?An inverse operation can be defined as a mathematical process that involves the use of one operation to cancel the action of the other operation.
For example, if we have a + b = c, using inverse operation to solve for a, we can cancel b on the left by subtracting b from both sides of the equation:
a + b - b = c - b [subtraction property of equality]
a = c - b.
Another example:
ab = c, to solve for a, divide both sides by b:
ab/b = c/b [division property of equality]
a = c/b.
Therefore, given the equation:
19 = h/3 - 8
Add 8 to both sides of the equation
19 + 8 = h/3 - 8 + 8 [addition property of equality]
27 = h/3
Multiply both sides by 3:
27(3) = h/3(3) [multiplication property of equality]
81 = h
h = 81
The value of h in the equation is determined as: 81.
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Can 2015473 in expanded form be written like 2,000,000+15,000+400+70+3 ?
Answers
The most appropriate choice for expanded form of a number will be given by-
We can expand 2015473, as 2015473 can be written as 200000 + 15000 + 400 + 70 + 3
And every integers can be written in expanded form.
What is expanded form of a number?
At first it is important to know about integers.
A number with no fractional parts is called integer. Integers can be positive, negative and zero is also an integer.
Expanded form of a number is equal to the sum of place value of its digit.
For example, for 423, place value of 4 = 400, place value of 2 = 20, place value of 3 = 3
423 = [tex]400 + 20 + 3[/tex]
Here,
2015473 can be written as 200000 + 15000 + 400 + 70 + 3
every integer can be written in expanded form.
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Question 14>If 3000 dollars is invested in an account for 10 years. Find the value of the investment at the end of10 years if the interest is:(a) 6.2% compounded monthly: $(b) 6.2% compounded daily (ignore leap years): ¢
Answers
Given:
Principal amount, P = $3000
Time, t = 10 years
Let's solve for the following:
• (a). Find the value of the investment if the interest is 6.2% compounded monthly.
Apply the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where:
• P is the principal = $3000
,• r is the interest rate = 6.2% = 0.062
,• n is the number of times compounded = monthly = 12 months a year
,• t is the time in years = 10 years
Plug in these values and solve for the value, A:
[tex]\begin{gathered} A=3000(1+\frac{0.062}{12})^{12*10} \\ \\ A=3000(1+0.00516667)^{120} \\ \\ A=3000(1.00516667)^{120} \\ \\ A=3000(1.855963241) \\ \\ A=5567.89 \end{gathered}[/tex]Therefore, if it is compounded monthly, the value at the end of 10 years is $5567.89
• (b). 6.2% compounded daily
In this case, the number of times compounded will be:
n = 365 times a year.
Thus, we have:
[tex]\begin{gathered} A=3000(1+\frac{0.062}{365})^{365\times10} \\ \\ A=3000(1.000169863)^{3650} \\ \\ A=3000(1.858830169) \\ \\ A=5576.49 \end{gathered}[/tex]If it is compounded daily, the value at the end of 10 years will be $5576.49
ANSWER:
(a). $5567.89
(b).
A packet of sweets contains only purple and orange sweets. The ratio of
purple to orange sweets in the packet is 4: 1.
If there are 15 sweets in total, how many orange sweets are there?
Answers
There were three orange sweets in the given packet.
What is ratio and how can it be assessed?
A ratio is the comparative or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".
Given, the ratio of purple to orange sweets = 4 : 1
Total number of sweets including both purple and orange = 15 -(i)
Let x be the ratio constant for the given ratio.
Therefore, number of purple sweets = 4x -(ii)
Also, the number of orange sweets = 1x = x -(iii)
From (i), (ii) and (iii), we get, 4x + x = 15 ⇒ 5x = 15 ⇒ x = 3
Putting the value of x in (ii), we get number of purple sweets = 4x = 12
Putting the value of x in (iii), we get number of orange sweets = x = 3
Thus, there were three orange sweets in the given packet.
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Find the radio said the circle given the central angle in the area of the shaded sector
Answers
The formula for the area of sector is,
[tex]A=\frac{\theta}{360}\times\pi(r)^2[/tex]Detemine the radius of the circle.
[tex]\begin{gathered} 60\pi=\frac{24}{360}\times\pi(r)^2 \\ r^2=\frac{60\cdot360}{24} \\ =900 \\ r=\sqrt[]{900} \\ =\sqrt[]{3\cdot3\cdot10\cdot10} \\ =30 \end{gathered}[/tex]Thus, radius of the circle is 30 units.
After working a summer job, you have $1,000 to put into a bank account. You need to decide which bank is a better investment: Elite Bank or Bankify.
Elite Bank is offering a monthly interest rate of 1%. Which equation models how much money you'd have in an Elite Bank account after (x) months?
A. g(x) = 1000/x + 1.01
B. g(x) = 1000(1.01)^x
C. g(x) = 1000 + 1.01x
D. g(x) = 1000 (1.1)^x
Answers
Answer:
A because you need to divide that $1000 into the x amount of months that you have.
An alloy contains 15% manganese and 85% iron. 37.5 kg of manganese is used to make the alloy.
a.) How much alloy is produced?
b.) How much iron is used?
Answers
An alloy contains 15% manganese and 85% iron.
manganese/ iron = 15/85= 3/17.
manganese = 37.5 kg.
iron = 37.5 x 17/ 3= 212.5 kg
alloy = manganese + iron = 37.5 +212.5 = 250kg
250kg alloy is produced from 37.5 kg manganese and 212.5 kg Iron.
What is a alloy ?A metal alloy is a substance that combines multiple metals or combines metals with non-metallic elements. Brass, for example, is an alloy of two metals: copper and zinc. Steel is a metallic element (iron) alloyed with a small amount (up to 2%) of a non-metallic element (carbon)Alloy steel is steel that contains approximately 5% alloying elements. Manganese, chromium, vanadium, nickel, and tungsten are examples of alloying elements. Alloying elements improve overall machinability and corrosion resistance.here,
An alloy contains 15% manganese and 85% iron.
manganese/ iron = 15/85= 3/17.
manganese = 37.5 kg.
iron = 37.5 x 17/ 3= 212.5 kg
alloy = manganese + iron = 37.5 +212.5 = 250kg
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4-5 Isosceles and Equilateral Triangles
What is the value of x?
(5x)°
-(3x + 28)°
Answers
Answer:
?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿?¿
What is the Standard Form of the line with x-intercept of 6 and y-intercept of 5?
5x + 6y = 30
5x + 6y = 11
6x + 5y = 30
6x + 5y = 11
Answers
The standard form of the line with x-intercept of 6 and y-intercept of 5 is
5x + 6y = 30
How to write equation in standard form?The equation in standard form can be represented as follows:
Ax + By = C
Where
A, B and C are constantTherefore, let's find the standard form of the equation with x -intercept of 6 and y-intercept of 5.
The x-intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.
Therefore,
(6, 0)(0, 5)
using the form y = mx + b
where
m = slopeb = y-interceptm = 5 - 0 / 0 - 6
m = - 5 / 6
Therefore,
y = - 5 / 6 x + 5
5 /6 x + y = 5
multiply through by 6
Therefore,
5x + 6y = 30
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1. Write a variable expression for the product between a number y and 2.
y. 3
y 2
2+y
2-y
Answers
Answer:
it'd be "the product OF a number y and 2." Answer: 2y.
Step-by-step explanation:
which equations represent exponential growth? which equations represent exponential decay? drag the choices into the boxes to complete the table. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. exponential growth exponential decay
Answers
1. isn't an exponential function
2. growths
3. growths
4. decay
5. growths
The exponential operations have the subsequent formula: y = K1 × [tex]K2^{(k3*t)}[/tex], where K3, K2, and K1 are constants and K2 is more distinguished than zero.
Exponential operation graphs either decrease or always increase.
To determine whether the operation increases or declines, just consider it at two points, for example, t = 0 and t = 1, and compare the consequences.
1. y = 100 × [tex](1 - 12)^x[/tex] = 100 × [tex](-11)^x[/tex]
Because (-11) is a negative number, y is not an exponential function.
2. y(0) = 0.1 × [tex](1.25)^0[/tex] = 0.1
y(1) = 0.1 × (1.25) = 0.125
y(1) > y(0) → growths
3. y(0) =((1−0.03) × 12)² × (0) = 1
y(0) =((1 − 0.03) × 12)²= 135.4896
y(1) > y(0) → growths
4. y(0) = 426 × [tex](0.98)^0[/tex] = 426
y(1) = 426 × [tex](0.98)^1[/tex] = 417.48
y(1) < y(0) → decay
5. y(0) = 2050 × [tex](12)^{0}[/tex] = 2050
y(1) = 2050 × 12 = 24600
y(1) > y(0) → growths
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The question is -
Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth Decay
y=100(1−12)^ty=0.1(1.25)^ty=((1−0.03)12)^2ty=426(0.98)^ty=2050(12)^tPLease help meeeeeeeeeee
Answers
Answer:
1)
1/2 does not belong to the set
All other numbers belong to the Integers (Z).
2)
√7 does not belong to the set.
All other numbers are rational numbers (Q).
Ella has a collection of bracelets. out of the 6 brackets, she gave her Sister 1 and her mother 3. What fraction of bracets did Ella's sister receive?
Answers
Answer:
1/6
Step-by-step explanation:
just use the total amount of bracelets as the denominator and the amount of bracelets her sister received as the numerator
Which pair of angles are corresponding angles?
Answers
Answer:
3 and 7
Step-by-step explanation:
They are in the same relative position as each other
an insurance company offers its policyholders a number of different premium payment options. for a randomly selected policyholder, let x be the number of months between successive payments. the cumulative distribution function of x is
Answers
The cumulative distribution function of x is 0.60.
Here X has discrete probability distribution.
[tex]$$\begin{aligned}&\mathrm{P}(\mathrm{X}=1)=0.30 \\&P(X=3)=F(3)-F(1)=0.40-0.30=0.10 \\&P(X=4)=F(4)-F(3)=0.45-0.40=0.05 \\&P(X=6)=F(6)-F(4)=0.60-0.45=0.15 \\&P(X=12)=F(12)-F(6)=1-0.60=0.40\end{aligned}$$[/tex]
Following table shows the pmf:
X P(X=x)
1 0.3
3 0.1
4 0.05
6 0.15
12 0.4
Following is the graph of CDF is [SEE in attachement]
[tex]$P(3 \leq X \leq 6)=F(6)-F(1)=0.60-0.30=0.30$$P(X \geq 4)=1-F(3)=1-0.40=0.60$[/tex]
The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, evaluated at x. It is employed to describe a table's random variables' probability distribution.
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