The solution to the system is the area where shadings from both inequalities overlap one another
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
Consider
x-2y ≤ -2
Find y
=> x +2 ≤ 2y
=> x/2 + 1 ≤ y
=> (x+2)/2 ≤ y
Or
y ≥(x+2)/2 --------(1)
Consider 3x + y > -1
Find y
=> y > -3x -1---------(2)
By considering the equations with equal sign in place of inequality signs, find y values corresponding to the random x values
plot the points in (x,y) form, we get the 2 lines
For <, shade the region below the line
For >, shade the region above the line
If the inequality is "<" or ">" then connect the two points with a dotted line. The dotted line is analogous to the open circle on the number line. Otherwise, connect the two points with a solid line.
The solution to the system is the area where shadings from both inequalities overlap one another
To learn more about the inequality from the given link
https://brainly.com/question/25275758
#SPJ1
Josiah invested $96,000 in an account paying an interest rate of 3. 5% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest year, for the value of the account to reach $153,400?
Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, the value of the account will reach $153,400 after 9 years.
How long would it take, to the nearest year, for the value of the account to reach $153,400?To calculate this, we can use the formula for the future value of a single sum invested with an inverted interest rate compounded continuously.
Future Value = Present Value × (1 + r)n
Where:
Present Value = 96,000r = 3.5% expressed as a decimal, 0.035n = number of yearsWe can solve for n to find out how many years it will take to reach $153,400.
153,400 = 96,000 × (1 + 0.035)n
153,400/96,000 = (1 + 0.035)n
Taking the natural log of both sides and simplifying:
ln(153,400/96,000) = n × ln(1.035)
n = ln(153,400/96,000)/ln(1.035)
n ≈ 8.99
To the nearest year, it will take 9 years for the value of the account to reach $153,400.
More information about the future value here: https://brainly.com/question/24703884
#SPJ11
Please tell me if this is correct
No,Sarah would have 16 small stones and 14 large stones on the sixth day, since it's +4 small stones and +3 large stones per day. You must show your working if you want the marks. Best of luck!
The side of a cube is multiplied by a factor of 10 . By what factor does the volume of the cube change?
The new volume of the cube is 1000 times the original volume. This means that the volume has increased by a factor of 1000.
What is volume?Volume is a measure of the amount of space that a three-dimensional object occupies. It is a property of a solid shape, and is usually expressed in units of cubic units, such as cubic meters [tex](m^3[/tex]), cubic centimeters [tex](cm^3[/tex]), or cubic feet [tex](ft^3)[/tex].
The volume of a cube is given by the formula [tex]V = s^3[/tex] cube is multiplied by a factor of 10, then the new side length becomes 10s.
The new volume of the cube can be calculated as follows:
V' = [tex](10s)^3[/tex]
= [tex]10^3[/tex] * [tex]s^3[/tex]
= 1000 *[tex]s^3[/tex]
To know more about volume, visit:
brainly.com/question/463363
#SPJ1
The cube's new volume is 1000 times larger than its old volume. This indicates that the capacity has multiplied by 1000.
Describe volume?
The quantity of space a three-dimensional object takes up is measured by its volume. It is a characteristic of solid shapes and is frequently stated in cubic unit measurements like cubic meters, cubic centimeters, or cubic feet.
The method for calculating a cube's volume is cube times a factor of 10, where the new side length is 10s.
The new volume of the cube can be calculated as follows:
V' = [tex]s^{3}[/tex]
= [tex](10s)^{3}[/tex]
[tex]V'=1000 s^{3}[/tex]
To know more about cube visit:
brainly.com/question/30962206
#SPJ1
What is 125% as a fraction?
The fraction of the value given as 125% can be expressed by the term of 125% = 5/4.
A ratio in which the total value is always 100 is a ratio, and a percentage is a portion of that ratio.
To represent a portion of a whole, we utilise fractions. Now, we must translate a percentage to a fraction.
Use the instructions below to convert 125% to a fraction:
First, add the percent sign.
Divide the supplied percentage by 100 to express it as a fraction.
As a result, we can write as 125/100.
To simplify the fraction, divide the numerator and denominator by their respective HCFs.
Now, 125 percent can be expressed as 125/100.
When the given fraction is simplified, we obtain
[Dividing the numerator and denominator by their HCF, which is 25]: 125/100 = 5/ 4
Hence, the fraction of 125% is 5/4.
Using a percent to fraction calculator is another way to confirm.
Hence, the fraction of 125% is 5/4.
Learn more about Fractions:
https://brainly.com/question/28675194
#SPJ4
How to convert 95kg in lbs?
95 kg is approximately equal to 209.4390 pounds ( rounded to four decimal places )
The conversion factor to convert kg to lbs is 2.20462
1 kg = 2.20462 pounds
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
The mass in lbs = The mass in kg × conversion factor
Substitute the values in the equation
1 kg = 2.20462 pounds
95 kg = 95 × 2.20462
Multiply the numbers
= 209.4390 pounds ( rounded to four decimal places )
Therefore, 95 kg is 209.4390 pounds
Learn more about conversion factor here
brainly.com/question/5056146
#SPJ4
Directions: Solve for.x. Round all answers to the nearest tenth.
11
X
31°
X =
The solution is, The value of x is 21.4.
What is right-angle triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
here, we have,
The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x.
The measure of the angle opposite to height is 31°.
The sine of an angle is the ratio of height to the hypotenuse.
Therefore,
sin 31° = height/hypotenuse
sin 31° = 11/x
Multiply x with both sides:
x sin 31° = 11
Divide sin 31° with both sides:
x = 11/ sin 31°
x = 21.35
x ≈ 21.4 units
To learn more about trigonometry ratio, click on the below link:
brainly.com/question/29758394
#SPJ1
Please help!!!!!!!!!!!
Answer:
A
Step-by-step explanation:
P = 4 pi I r^2 solve for I Divide both sides by 4 pi r^2
to get
I = P / (4 pi r^2)
Answer the questions below.
(a) From the 12 albums released by a musician, the recording company wishes to release 9 in a boxed set. How many different boxed sets are possible?
(b) There are 14 European cities that Rashid would eventually like to visit. On his next vacation, though, he only has time to visit 3 of the cities: one on Monday, one on Tuesday, and one on Wednesday. He is now trying to make a schedule of which city he'll visit on which day. How many different schedules are possible? (Assume that he will not visit a city more than once.)
(a) There are 220 different boxed sets possible.
(b) here are 2184 different schedules possible for Rashid's vacation.
(a)
To calculate the number of different boxed sets possible, use the combination formula. In this case, choose 9 albums out of 12, and the order of the albums in the boxed set doesn't matter.
The number of combinations of n items taken r at a time is given by the formula:
C(n, r) = n! / (r! × (n - r)!)
In this case, to find C(12, 9):
C(12, 9) = 12! / (9! × (12 - 9)!)
C(12, 9) = 12! / (9! × 3!)
C(12, 9) = (12 × 11 × 10) / (3 × 2 × 1)
C(12, 9) = 220
(b)
To calculate the number of different schedules Rashid can make for his vacation, count the number of ways chosen 3 cities out of 14 for each day of the week.
For Monday, choose one city out of 14.
For Tuesday, choose one city out of the remaining 13 .
For Wednesday, choose one city out of the remaining 12 .
Total number of schedules = 14 × 13 × 12 = 2184
So, there are 220 different boxed sets possible and there are 2184 different schedules possible for Rashid's vacation.
Learn more about Combination here:
https://brainly.com/question/31586670
#SPJ4
The fraction n/8 is between and 4/5 Write down all the possible values of n
The fraction n/8 is between 4/5 and 1. To calculate all the possible values of n, use the following equation: n = (4/5)*8 = 6.4
Since n is a fraction, the possible values are 6, 6.4, 6.8, 7.2, 7.6, 8, and 8.4.
The possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.
To find the possible values of n, we can cross-multiply and compare the fractions.
1/2 < n/8 < 4/5
Cross-multiplying gives us:
8 < 2n < 32
Dividing by 2 gives us:
4 < n < 16
The possible values of n are the integers between 4 and 16, which are 5, 6, and 7.
Therefore, the possible values of n for the fraction n/8 to be between 1/2 and 4/5 are 5, 6, and 7.
Learn more about fraction here: https://brainly.com/question/78672
#SPJ11
Which function is not graphed correctly? Help needed ASAP!!
Answer:
Step-by-step explanation:
A is not graphed correctly. The graph is turned upside down from what it should be.
Complete the ratio table.
82 19
164 38
57
328 76
410
To complete a ratio table, we need to find the missing values that would make the ratios equivalent. 82 19 4:1 164 38 4:1 57 13.5 4:1
328 76 4:1 410 95 4:1
Completing a Ratio TableTo complete the given ratio table, we need to find the missing values that would make the ratios equivalent. Ratios are used to compare two or more quantities and are expressed in the form of a fraction, with the numerator representing one quantity and the denominator representing another.
Starting with the first row of the table, we can see that the ratio of the first two values is 82:19. To find the missing value in this row, we need to determine what value multiplied by 19 would give us 82. Using basic algebra, we can set up the equation
19x = 82
And solve for x, which gives us
x = 82/19.
= 4.32
This value is approximately 4.32. Therefore, the missing value in the first row is 82:19:4.32.
Moving on to the second row, we can see that the ratio of the first two values is 164:38. Similar to the first row, we can find the missing value by determining what value multiplied by 38 would give us 164.
Solving the equation
38x = 164
x = 164/38,
= 4.32.
Therefore, the missing value in the second row is 164:38:4.32.
In the third row, only one value is given, which means we need to determine the other value that would make the ratio equivalent to the previous rows.
Since the missing value in the first two rows is 4.32, we can set up the equation
57: x = 82/19
And solve for x.
This gives us x = 57 * (82/19), which is approximately 244.42. Therefore, the ratio in the third row is 57:244.42.
In the fourth row, we can use the same approach as the previous rows to find the missing value. Setting up the equation
76x = 328
x = 328/76,
which is approximately 4.32. Therefore, the missing value in the fourth row is 328:76:4.32.
Finally, in the last row, we are asked to explain the process of completing a ratio table. To complete a ratio table, we need to determine the missing values that would make the ratios equivalent. This involves setting up equations based on the given ratios and solving for the missing values. Once we have found the missing values, we can add them to the table and ensure that the ratios are equivalent across all rows
To know more about ratios,
visit:https://brainly.com/question/13419413
#SPJ1
Find the missing output value (y)
for the given input value (x).
(3,y)
y=x-5
y = [?]
Enter
The corresponding output value is y = -2 when x = 3 in the equation y = x - 5.
What is the missing output value (y)?Given the equation in the question;
y = x - 5
Input value x = 3
Output value y = ?
The equation given is y = x - 5.
This equation is in the form y = f(x), which means that given an input value x, we can find the corresponding output value y.
In this case, we are given an input value of x = 3 and we need to find the corresponding output value y.
To do this, we simply substitute x = 3 into the equation and solve for y:
y = x - 5
Plug in x = 3
y = 3 - 5
y = -2
Therefore, when x = 3, the corresponding output value is y = -2.
Learn more about algebraic expressions here:
brainly.com/question/4344214
#SPJ1
jimmy and amanda are on an archery team . jimmy hits 3 bullseyes in every 20 shots . amanda hits a bull-eye 0n 18 percent of her shots how hit more bull's-eyes more often explain
Answer:
Jimmy hits 3 bullseyes in every 20 shots, which can be written as a fraction: 3/20.
To compare this to Amanda's performance, we need to find out what fraction of Amanda's shots result in a bullseye. We know that Amanda hits a bullseye on 18 percent of her shots, which can be written as a fraction: 18/100 or 9/50.
To determine who hits more bullseyes more often, we can compare the two fractions. We can find a common denominator of 100 to make the comparison easier:
3/20 = 15/100
9/50 = 18/100
Now we can see that Amanda hits a bullseye more often than Jimmy, as 18/100 is a larger fraction than 15/100. In other words, if both Jimmy and Amanda shoot 100 arrows, Amanda is expected to hit more bullseyes than Jimmy.
Answer:
Jimmy
Step-by-step explanation:
To compare who hits more bull's-eyes more often, we need to calculate the probability of hitting a bull's-eye for each person.
Jimmy hits 3 bullseyes in every 20 shots, so the probability of hitting a bull's-eye for Jimmy is:
3/20 = 0.15 or 15%
Amanda hits a bull's-eye on 18 percent of her shots, so the probability of hitting a bull's-eye for Amanda is:
18% = 0.18
Comparing these probabilities, we can see that [Jimmy hits more bull's-eyes more often,] since his probability of hitting a bull's-eye (15%) is greater than Amanda's probability (18%).
It's important to note that this comparison is based solely on the given information about hitting bull's-eyes, and does not necessarily reflect overall performance or skill as an archer. Other factors, such as accuracy, consistency, and technique, may also play a role in determining an archer's success.
Members of a softball team raised $1353 to go to a tournament. They rented a bus for $943.50 and budgeted $31.50 per player for meals. Write and solve an equation which can be used to determine
�
x, the number of players the team can bring to the tournament.
Equation:
Answer:
�
x =
Answer:
13
Step-by-step explanation:
943.50 + 31.50x = 1353
This is in the form y=mx+b.
To isolate for x, move 943.50 to the other side and subtract it from 1353.
31.50x = 409.50
now, divide by 31.50 to get x by itself.
x =13
The team can bring 13 players to the tournament.
Find the surface area of the curved surfaces
Answer:
155.744
Step-by-step explanation:
Which describes the cross section of a square prism that passes through vertices A, B, and C?
The cross-section from any side in a square prism is always square.
What is cross-section?A cross-section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections.
Cross-section of a square prism :-
The cross-section of a square prism is a square. Since a square prism has its faces shaped in square and all the edges of the square prism are equal in length.
Therefore, when we cut the cube by a plane, we get a square shape.
Hence, the cross-section from any side in a square prism is always square.
Learn more about cross-sections, click;
https://brainly.com/question/15541891
#SPJ9
Calculate the standard deviation of a set of seventeen numbers described by Σx=272 Σx² = 11849
The standard deviation of a set of seventeen numbers described by Σx=272 Σx² = 11849 is 21.
What is Standard deviation?The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
We have Σx=272 and Σx² = 11849.
n= 17
So, the Variance of the Data
= Σx²/n - (Σx/ n)²
= 11849 / 17 - (272/17)²
= 697 - 256
= 441
Then, the Standard deviation is
= √Variance
= √441
= 21
Learn more about Standard deviation here:
https://brainly.com/question/30409387
#SPJ9
Once Triangle Similarity is established, which of the following corresponding parts are also established?
The corresponding parts are as follows;
Angle ATS = Angle ABC
side AS = side AC
Angle SAT = Angle CAB
Angle AST = Angle ACB
Side AT = Side AB
What is SAS similarity theorem?ΔABC ~ ΔDEF only if ratio of two sides of ΔABC and corresponding two sides of ΔDEF is equal and the angle included in both sides are congruent.
Suppose the two sides of ΔABC are AB and BC, and that of DEF be DE and EF.
For two similar figures, the pair by pair similar angles of those two similar figures are called corresponding angles. They are of same measurement.
We are given the similar triangles as;
ΔACB = ΔAST
Angle ATS = Angle ABC
side AS = side AC
Angle SAT = Angle CAB
Angle AST = Angle ACB
Side AT = Side AB
Learn more about triangles;
https://brainly.com/question/12413243
#SPJ1
what is 15/32 in inches?
15/32 inches is equivalent to 11.90625 mm
Unit conversion is the process of converting a quantity from one unit of measurement to another. The unit conversion method involves multiplying the original quantity by a conversion factor that expresses the relationship between the original unit and the desired unit.
1 inch = 25.4 mm
1 mm = 0.1 cm
We have 15/32 inch
Converting the fraction into decimal part, we obtain 0.46875 inch
Now, 0.46875 inch = 0.46875 * 25.4 mm
= 11.90625 mm
= 11.90625 * 0.1 cm
= 1.190625 cm
Learn more about unit conversion from the below link:
https://brainly.com/question/19420601
#SPJ4
how to convert 5,5 as a fraction?
The decimal 5.5 in simplified fraction can be expressed as 11/2 .
A Fraction is defined as a mathematical expression that represents a part of a whole or a ratio between two quantities .
The decimal 5.5 can be written as 5.5/1 ;
In order to remove the decimal, we multiply the numerator and denominator by 10, which moves the decimal point one place to the right:
⇒ 5.5/1 = 55/10
Since the numerator 55 and denominator 10 , have a common factor of 5,
So , we divide both the numerator and denominator by the common factor "5" ;
We get ;
⇒ 55/10 = 11/2 ;
Therefore, the decimal 5.5 is equivalent to the fraction 11/2 .
Learn more about Fraction here
https://brainly.com/question/2362378
#SPJ4
The given question is incomplete , the complete question is
How to convert the decimal 5.5 as a fraction ?
how to convert 5.5 cm to mm?
To convert 5.5 cm to mm, we multiplied the length in centimeters by 10, which gave us 55 mm.
Measurement is an essential concept in mathematics and science that involves determining the size, quantity, or degree of something. The metric system is a standard measurement system that is widely used worldwide, and it includes units such as centimeters and millimeters.
Now, let's move on to your question about converting 5.5 cm to mm. Centimeters and millimeters are both metric units of length, with millimeters being smaller than centimeters. Therefore, to convert from centimeters to millimeters, we need to multiply the measurement in centimeters by 10.
We know that 1 cm is equal to 10 mm. So to convert 5.5 cm to mm, we can use the formula:
5.5 cm × 10 mm/cm = 55 mm
Therefore, 5.5 cm is equivalent to 55 mm.
It's important to note that when measuring, it's essential to use the appropriate units to get accurate results. In this case, we used the millimeter unit, which is suitable for measuring small lengths, to convert the 5.5 cm to a smaller unit, millimeters.
To know more about measurement here.
https://brainly.com/question/4725561
#SPJ4
The width of a rectangle is 10 feet, and the diagonal length of the rectangle id 32.5 feet. What us the measure of the length if the rectangle in feet? round yo the nearest tenth
Answer:
about 30.9 feet
Step-by-step explanation:
Using the Pythagorean Theorem:
[tex] {l}^{2} + {10}^{2} = {32.5}^{2} [/tex]
[tex] {l}^{2} = 956.25[/tex]
[tex]l = 30.9[/tex]
what is maximum and minimum calculator online
Minimum and Maximum Calculator is an online widget that helps you find the max and min values of a function.
The maximum value is the point at which the function has the highest value of all other values, while the minimum value is the lowest value in the entire function.
The calculator returns the global maximum and minimum of the function along with a graph on the Cartesian plane as the solution. A min-max calculator is an online calculator that can be used to find the maximum and minimum values of a mathematical function.
Finding the extreme values of a function is also known as optimization. Feature optimization is a central concept in engineering, business, and machine learning.
To know more about Minimum and Maximum Calculation:
brainly.com/question/13796394
#SPJ4
Write the number below as a fraction in its simplest form
answer:
answer:1/8
answer:1/8explanation :
answer:1/8explanation :0.125 as a fraction in simplest form is 1/8
answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.
answer:1/8explanation :0.125 as a fraction in simplest form is 1/8Step 2: Find the HCF or the highest common factor of 125 and 1000.hope this helped.
Which sequences are arithmetic? Select three options.
A. –8.6, –5.0, –1.4, 2.2, 5.8, …
B. 2, –2.2, 2.42, –2.662, 2.9282, …
C. 5, 1, –3, –7, –11, …
D. –3, 3, 9, 15, 21, …
E. –6.2, –3.1, –1.55, –0.775, –0.3875, …
Answer:
A. –8.6, –5.0, –1.4, 2.2, 5.8, …
C. 5, 1, –3, –7, –11, …
D. –3, 3, 9, 15, 21, …
Step-by-step explanation:
If a sequence is an arithmetic sequence, the difference between any two terms must be the same for all terms.
This is known as the common difference
The correct choices are:
A : Common Difference = 3.6
C. Common difference = -4
D. Common difference = 6
In AQRS, q = 99 cm, r = 17 cm and s-96 cm. Find the measure of ZS to the nearest
degree.
The measure of ∠S is 75 degrees
How to find the measure of ∠S to the nearest degree?
The cosine rule is for solving triangles which are not right-angled in which two sides and the included angle are given. The following are cosine rule formula:
cos(S) = (q² + r² - s²)/2qr
where q, r and s are the lengths and Q, R and S are the angles
Using the formula:
cos(S) = (q² + r² - s²)/2qr
cos(S) = (99² + 17² - 96²)/(2*99*17)
cos(S) = 0.2597
S = cos⁻¹(0.2597)
S = 75 degrees
Learn more about cosine rule on:
brainly.com/question/3240813
#SPJ1
need help please help me fast
The area of the triangular prism is 240 mm²
Right triangular prism:A triangular prism is a prism with three rectangular faces connecting its two congruent triangular faces. It consists of 5 faces, 6 edges, and vertices.
The sum of the areas of all the triangle's faces is the surface area. By using the net of a prim we can determine the area of the prism as given below. Here we calculate the individual parts of the net to get the total area.
Here we have
A right triangular prism and its net
The area of the prism can be calculated by calculating the area of the 2 triangles and the areas of 3 rectangles in the given net
As we know Area of rectangle = Length × Width
Area of rectangle parts = [ 3 × 8 ] + [ 3 × 15 ] + [ 17 × 3 ]
= 24 mm² + 45 mm² + 51 mm²
= 120 mm²
Area of triangle parts = 2 [ 1/2 (15 × 8) ]
= 120 mm²
Total area of prism = 120 mm² + 120 mm² = 240 mm²
Therefore,
The area of the triangular prism is 240 mm²
Learn more about Triangular prism at
https://brainly.com/question/24046619
#SPJ1
The function f(x) = x + 5 represents the length of a rectangle, and the function g(x) = 7x − 2 represents the width of the rectangle. What is the area of the rectangle if x = 3? 56 27 285 152
Answer: 152
Step-by-step explanation:
Length: f(x) = x+5
Width: g(x) = 7x-2
Area: A= f(x) *g(x)
A= (x+5)(7x-2)
= 7x^2 -2x + 35x -10
= 7x^2 +33x -10 // Substitute 3 in for x
=7(3)^2 +33(3) -10
=7(9) +99 -10
=63+99-10
=152
Answer:
152
Step-by-step explanation:
took the test xx
Use the diagram to complete the statements.
The angle of depression from point R to point S is angle
.
The angle of elevation from point S to point R is angle
.
Angle 2 is the angle of elevation from
.
Angle 1 is the angle of
.
The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
What is an angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
There is an angle of elevation from point R to S. Thus point R is lie above S.
The angle of depression from point R to point S is ∠1.
The angle of elevation from point S to point R is ∠2.
∠2 is the angle of elevation from S to R.
∠1 is the angle of depression from point R to point S.
To learn more about types of angles, click on the below link:
brainly.com/question/19375538
#SPJ1
3 = blank X blank X blank = 27
fill in the blanks
Answer:
blank=9
Step-by-step explanation:
