The number √2 is an irrational number, thus, the correct options are B: irrational and F: not rational
To wich sets the number belongs?Remember what each sets are.
Natural or whole numbers are all the numbers that can be get by adding ones to one {1, 2, 3, 4, ...}
Integers are like the above ones, but also includes the zero and negative numbers.
Rationals are the ones that can be written as a quotient between two integers, and irrationals are these ones that can't be written like that.
Finally, real numbers are all the numbers.
In this case we have the square root of a prime number, √2, this is always a irrational number.
Then option B is correct.
Trivially, option F (not rational) is also true, because if the number is irrational, then it is not rational.
Then the correct options are B and F.
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A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers. Determine the expected number of the real workers in any sample of size 50. Select one: O 35 O 15 O 50 O 20 <
The expected number of the real workers in any sample of size 50 is 35
What is basic algebra ?Algebra is a branch of mathematics that facilitates the description of problems or situations into mathematical statements. It involves variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division to generate a valid mathematical statement. All branches of mathematics, such as coordinate geometry, calculus, and trigonometry, employ algebra. An elementary algebraic formula is 2x + 4 = 8. Algebraic expressions serve as the mathematical statement when operations on variables and constants, such as addition, subtraction, multiplication, division, etc., are done. Assume James and Natalie had the notion to arrange the matchsticks into numerical patterns while they were fiddling with them.
Given that : A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers.
n= 50
30 % are ghost workers
= 30% 0f 50
= 0.3×50
= 15 are ghost workers
50 - 15 = 35 are real workers
The expected number of the real workers in any sample of size 50 is 35
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Not sure how to do this question
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
he detiails of the solution are as follows:
sing the Laws of logarithm which says that:
[tex]\log _bP-\log _bQ=log_b(\frac{P}{Q})[/tex]Hence,
[tex]\log _340_{}-log_310=log_3\text{(}\frac{40}{10})=log_34[/tex]It is possible to approximate the outside temperature based on how fast crickets are chirping. Suppose on a 50 degree day, you measure 52 chirps in a minute, and on a 74 degree day, you measure 148 chirps in a minute. A. Based on this data, determine a linear equation that will output the number of chirps in a minute, n, given the temperature in degrees, t.__________B.. Use your equation to predict the temperature if you heard 96 chirps in a minute, to the nearest degree.________ degrees
Step-by-step explanation:
we have to find the equation, that's why we select the data
(t, n) = (50, 52) and (14,148)
we look as follows
n-52 = ((148-52) / (14-50)) * (t-50)
We perform the indicated operations
n-52 = (96/24) * (t-50)
n-52 = 4 (t-50)
finally we get the result
n = 4t-148
Answer:
Linear equation n = 4t-148
B)
[tex]n=96[/tex]Therefore,
[tex]\begin{gathered} 96=4t-148 \\ 4t=96+148 \\ 4t=244 \\ t=\frac{244}{4}=61^0 \end{gathered}[/tex]Hence, the answer is 61degrees.
To make Citrus Orange paint, a paint store mixes yellow, white, and red paint in the ratio of 5 to 3 to 1. How many gallons of yellow, white, and red paint does the store need to mix to make 135 gallons of Citrus Orange paint?
Answer:
yellow 75 gallons
white 45 gallons
red 15 gallons
Step-by-step explanation:
yellow (5) + white (3) + red (1) equal 9 total parts.
5/9 is yellow
3/9 is white
1/9 is read
5/9 x 135 = 75
3/9 of 135 = 45
1/9 of 135 = 15
A monument in the form of a marble cylinder has a circular base with a radius 1.5 meters. The altitude of the monument is 3.5 meters. How many cubic meters of marble does this monument contain?
A. 24.74 M 3
B. 6.19 M 3
C. 21.21 M 3
D. 7.07 M 3
If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube
The shape of the monument is cylinder
The base radius of the cylinder = 1.5 meter
The altitude of the monument = 3.5 meters
The volume of the cylinder = [tex]\pi r^{2}h[/tex]
Where r is the radius of the cylinder
h is the height of the cylinder
Substitute the values in the equation
The volume of the cylinder = [tex]\pi (1.5)^{2}(3.5)[/tex]
= 24.74 meter cube
Hence, If a monument in the form of a marble cylinder has a circular base with a radius 1.5 meters and the altitude of the monument is 3.5 meters. then the quantity of marbles contains in the monument is 24.74 meter cube
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For 15 points, label this:
Source of magnetic force - Nail
Source electric force - battery cell
What is an electromagnet?We know that the electromagnet is a type of magnet whose magnetic property depends on the interaction of the magnetic material with an electric field. We can see in the image that the nail which serves as the magnetic material is connected to a cell which is the source of the given electric current.
It the follows that the nail above is the source of the magnetic force because the coils of wire while the battery cell is the source of the electrical force.
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280Joules of work is done pushing a bike 35m. How much force was used to push the bike?
By definition, the work is given by:
[tex]W=F\cdot d\text{.}[/tex]Where W is the work in Joules (J), F is the force in Newtons (N) and d is the distance in meters (m).
In this problem we have:
• W = 280J,
,• d = 35m.
We can find the force F in terms of W and d:
[tex]F=\frac{W}{d}\text{.}[/tex]Replacing the values of W and d, we find that the force F is:
[tex]F=\frac{280J}{35m}=8\frac{J}{m}=8N\text{.}[/tex]In the last step, we used that J = N m.
Answer: The force is F = 8N.
Find the slope and the y-intercept of the graph of the linear equation 3x−4y=−16.
Answer:
the slope is 3/4
the y-intercept is 4
Step-by-step explanation:
You want the slope and y-intercept of the line defined by the equation 3x -4y = -16.
Slope-intercept formThe values of interest can be found easily from the slope-intercept form of the equation of the line. Solving for y puts the equation in that form.
3x -4y = -16 . . . . . . given
-4y = -3x -16 . . . . . subtract 3x
y = 3/4x +4 . . . . . . divide by -4
Compare this to the slope-intercept form equation:
y = mx + b . . . . . . . line with slope m and y-intercept b
We see that ...
m = 3/4, b = 4
The slope is 3/4
The y-intercept is 4
3. The graph of a polynomial function fis
shown. Which statement about the
polynomial is true?
-3
A. The degree of the polynomial is even.
B. The degree of the polynomial is odd.
C. The constant term of the polynomial is even.
D. The constant term of the polynomial is odd.
The degree of the polynomial is even.
What is polynomial ?Algebraic expressions called polynomials include indeterminates and constants. Polynomials can be considered a particular type of mathematics. In practically all areas of mathematics, including calculus, they are used to express numbers. They are also regarded as being crucial in several areas of mathematics. Examples of polynomials include 2x + 9 and [tex]x^{2}[/tex] + 3x + 11. The "=" sign is absent from all of these samples, as you may have observed.
The polynomial's degree is even since the final behavior is the same in both directions (for -x and for +x, y→∞).
The y-intercept is the fixed term. Since it is not an integer, evenness and oddness cannot be determined.
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factor and find all roots
Answer: x = 3
x = ± √3 = ± 1.7321
Step-by-step explanation:
those are 2 solutions
A soccer ball is kicked in the air. The table shows the heights y (in feet) of the ball after x seconds. Write an equation for the height of the soccer ball. Find the height of the soccer ball after 1.8 seconds.
I got my function as [tex]y=0.06x^2 +17.82x[/tex] and 32.27 feet as the height after 1.8 seconds, I want to make sure though.
The height of the soccer ball after 1.8 seconds will be 372.47 feet.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
An air kick is made with a soccer ball. The table displays the ball's height y (in feet) after x seconds.
The function is given as,
y = 0.06x² + 17.82x + 32.27
The height of the soccer ball after 1.8 seconds will be given as,
y = 0.06(18)² + 17.82(18) + 32.27
y = 19.44 + 302.76 + 32.27
y = 372.47
The height of the soccer ball after 1.8 seconds will be 372.47 feet.
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Hello, help me please )
Find the inverse of:
[tex]f(x)=(x+3)^2[/tex]a. To sketch f(x), we use the graph of the parent function
[tex]g(x)=x^2[/tex]Translated 3 units to the left:
b. The part of the function f(x) that is one-to-one and non-decreasing is in the domain [-3, ∞). Expressing in inequality notation: x ≥ -3.
c. The function f(x) can be written as:
[tex]y=(x+3)^2[/tex]Applying square root on both sides:
[tex]\pm\sqrt{y}=x+3[/tex]Solving for x:
[tex]x=\pm\sqrt{y}-3[/tex]Swapping letters:
[tex]y=\pm\sqrt{x}-3[/tex]Since we have chosen only the non-negative part of the domain for f(x), we use only the positive sign:
[tex]f^{-1}(x)=\sqrt{x}-3[/tex]Both functions, f(x) and its inverse are shown below:
mu 3.) Add six to twelve, then divide the sum by four. Divide the quotient by negative nine and then
D multiply by twenty-four. What is the result?
com
eneral
eas to
pecific
onclusi
ns.
answer:
4.) Estimate the total cost of groceries if the prices are $6.47, $14.72, $7.99, $9.40, and $2.79.
Round each to the nearest dollar and add.
1) Using order of operations, the solution to the given expression is; 12
2) The estimated cost of groceries if the prices are estimated to the nearest dollar is; $42
How to use order of operations?In mathematics , the acronym for the right order of operations is PEMDAS which denotes;
P- Parentheses
E- Exponents
M- Multiplication
D- Division
A- Addition
S- Subtraction.
3) From the given statement, we are to add 6 to 12, then divide the sum by 4. Thereafter, we divide the quotient by negative nine and then multiply by twenty-four. This is expressed as;
[(6 + 12)/4] = 18/4 = 9/2
Then divide by -9 to get;
(9/2) ÷ 9 = 1/2
Then we multiply by 24 to get;
1/2 * 24 = 12
4) Let us first estimate each cost to the nearest dollar to get;
$6.47 ≈ $6
$14.72 ≈ $15
$7.99 ≈ $8
$9.40 ≈ $9
$2.79 ≈ $3
Total estimated cost = 6 + 15 + 8 + 9 + 3 = $42
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Expand and simplify 3(2x + 1) + 2(x + 4) =
Answer:
3(2x+1)+2(x+4)
3x2x and 3x1
6x+3+2(x+4)
2xx and 2x4
6x+3+2x+8
and the like terms
6x+2x and 3+8
8x+11
Step-by-step explanation:
Answer:
8x +11
Step-by-step explanation:
3(2x+1)+2(x+4)
Use the distributive property to multiply 3 by 2x+1.
6x+3+2(x+4)
Use the distributive property to multiply 2 by x+4.
6x+3+2x+8
Combine 6x and 2x to get 8x.
8x+3+8
Add 3 and 8 to get 11.
8x+11
please help this is due today
Carlos sells coupon booklets for $5.50 apiece. He makes $60.50. Monica sells the same books for $4.75 each and makes $57. Who sells more booklets? How many more?
Answer:
Monica sells one more book (12) than Carlos (11).
Step-by-step explanation:
Carlos: $60.50/$5.50 = 11
Monica: $57.00/$4.75 = 12
Monica sells one book more than Carlos.
Each of Sean’s comedy routines lasts for 35 minutes. He tells an average of 3 jokes every minute. It takes _ comedy routines to hear 360 jokes
It takes four (4) comedy routines to hear 360 jokes
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
By applying direct proportion, we have:
1 minute = 3 jokes
X minutes = 360 jokes
Cross-multiplying, we have:
3X = 360
X = 360/3
X = 120 minutes
Now, we can determine the number of comedy routines required for 360 jokes as follows:
Number of comedy routines = 120/35
Number of comedy routines = 3.42 ≈ 4 comedy routines.
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A restaurant decides to include a 16% tip automatically in all customers’ bills. The restaurant will apply the 16% tip after applying a 5% sales tax. If the total cost of a meal is c dollars, write two different expressions that represent the total bill, including both tax and tip.
Two different expressions that represent the total bill, including both tax and tip for the meal sold by the restaurant, are:
c dollars + 5% of c dollars + 16% of c dollarsc dollars + 21% of c dollarsWhat expressions can we get for the total amount to be paid by the customer?To arrive at the amount to be paid by the customer, we first have to get the original amount that they should pay for the meal. Next, they are meant to apply the 16% tip for the total meal and this is gotten by calculating 16% of the total meal.
Next, we ought to get 5% of the sales tax which will also be applied to the total bill. When all of these are summed up, we will arrive at the total amount to be paid by the customer. Another way will be, to sum up, all of the percentages and apply them to the total bill.
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The lines intersect. Parallel lines never intersect. What must be true?
A) The lines are not parallel.
B) The lines do not intersect.
C) The lines are perpendicular.
D) The lines are parallel.
Wally's Wagons is a store that sells wagons. The store sells three sizes of wagons: small, medium, and large.
Matrix A shows the number of wagons sold at two different locations during the month of June.
50 90 30
25 50 50
A-
Each wagon must be assembled and then packaged.
Matrix B shows the number of minutes required for assembly and packaging of the three different-sized wagons.
15 5
B 20 8
-
30 12
How can these matrices be used to determine the total number of minutes spent on assembly and packaging of the wagons in June
at these two stores?
Drag a phrase or matrix to each box to correctly complete the statements.
The total number of 8780 minutes was spent on the assembly and packaging of the wagons in June at these two stores.
Matrix A shows the number of wagons sold at two different locations during the month of June.
[tex]A =\begin{bmatrix}50 & 90 & 30\\25 & 5 & 50\\\end{bmatrix}[/tex]
Matrix B shows the number of minutes required for the assembly and packaging of the three different-sized wagons.
[tex]B = \begin{bmatrix}15 & 5\\20 & 8 \\30 & 12 \end{bmatrix}[/tex]
We have to multiply Matrix A by Matrix B
[tex]AB =\begin{bmatrix}50 & 90 & 30\\25 & 5 & 50\\\end{bmatrix}\begin{bmatrix}15 & 5\\20 & 8 \\30 & 12 \end{bmatrix}[/tex]
[tex]AB =\begin{bmatrix}3450 & 1330 \\2875 & 1125 \\\end{bmatrix}[/tex]
So the time is 3450 + 1330 + 2875 + 1125 = 8780 minutes
Therefore, a total number of 8780 minutes was spent on the assembly and packaging of the wagons in June at these two stores.
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Answer:
Step-by-step explanation:
Took the quiz
Answer please number 15 only
Answer:
a) -2/9
Step-by-step explanation:
2/3 - 5/6, you would need to start by making the denominators the same, so 2/3 would become 4/6. 4/6-5/6 = -1/6.
-1/6 ÷ 3/4, use the keep change flip rule
-1/6 × 4/3 then multiply directly across:
-1×4=-4
6×3=18
-4/18 reduces to -2/9
Can someone please help me with this? Geometry by the way
Answer:
Step 1: DAB
Step 2: rotated triangle 180° using AC as center of rotation
Step 3: EAC
Step 4: now all 3 angles…
Step 5: a + b + c = 180°
Step-by-step explanation:
See question and photo please: The
Answer: 50.24ft²
Step-by-step explanation:
Total area of square = 8 * 8 = 64 ft²
Diameter of circle = 8 ft
The formula of area of circle = π r²
(4 = r)
(r² = 16)
3.14 * 16
50.24ft²
find sin(c). round to the nearest tenth if necessary a. .92b. .42c. .38d. 1.08
We have following:
The sine of the angle is given by the quotient of the opposite side and the hypotenuse
[tex]\sin C=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]replacing:
[tex]\begin{gathered} \sin C=\frac{5}{13} \\ \sin C=0.38 \end{gathered}[/tex]The answer is the option C. 0.38
A rectangle has a length six inches less than its width. If the perimiter of the rectangle is 54 inches, find the dimensions
Answer:
l=10.5 in , w=16.5 in
Step-by-step explanation:
p=2l+2w
54=2(w-6)+2(w)
54=2w-12+2w
54=4w-12
66=4w
w= 16.5
l=w-6
l=16.5-6
l=10.5 in
w=16.5 in
hope this helps
Find the surface area (in square units) of the polyhedron. i need help!!
The surface area and volume of the polyhedron are mathematically given as
SA=160 Sqr UnitsV=105 cubic unitsThis is further explained below.
What is surface area?Generally, The surface area of a three-dimensional object is equal to the total of areas of all of its faces, also known as surfaces. A cuboid has six faces that are rectangular in shape.
Add together the areas of each of the cube's six sides to get the surface area of the cube. To get the surface area of the prism, we may additionally label its length (l), width (w), and height (h), and then use the formula surface area = length (l) times width (w) times height (h).
To refresh your memory, the surface area of an item is the entire area of the exterior surfaces of the three-dimensional object or the total sum of the area of the faces of the object.
In other words, the surface area of an object is its "face area." It is expressed in terms of square units as a measurement.
In conclusion, Generally, the Surface area is mathematically given as
SA= 9+35+35+33+36+12
SA=160 Sqr Units
Generally, the equation for Volume is mathematically given as
V=(11*9)+6
V=99+6
V=105 cubic units
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CQ is attached surface area
Hope some math whiz is on pls dont answer if u dont know
Match the scenario with the law of reasoning.
Law of Contrapositive
Law of Syllogism
Law of Detachment
Not a valid conclusion
options:
1.
If Alex runs a mile in under 6 minutes, then he will have a new personal record.
Alex ran a mile in 5 minutes and 45 seconds.
Therefore, Alex set a new personal record.
2.
If you go to the water park, then you will need to bring sunscreen.
If you do not bring sun screen, then you will burn.
Therefore, when you go to the water park you will get a sunburn.
3.
If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°.
If a triangle has a 90° angle, then it is a right triangle.
Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle.
4.
If two lines are parallel, then they never intersect.
Line a and line b intersect.
Therefore, line a and line b are not parallel
1. If Alex runs a mile in under 6 minutes, then he will have a new personal record. Alex ran a mile in 5 minutes and 45 seconds. Therefore, Alex set a new personal record. - law of Detachment
2. If you go to the water park, then you will need to bring sunscreen. If you do not bring sun screen, then you will burn. Therefore, when you go to the water park you will get a sunburn. - law of contrapositive
3. If two lines are parallel, then they never intersect. Line a and line b intersect. Therefore, line a and line b are not parallel - Law of Syllogism
4. If the measures of two angles in a triangle are 30° and 60°, then the third angle is 90°. If a triangle has a 90° angle, then it is a right triangle. Therefore, if a triangle has two angles that measure 30° and 60°, then it is a right triangle. - Not a valid conclusion
How to illustrate the information?According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if the contrapositive is false. A conditional assertion that may or may not depend on another is a contrapositive.
Using deductive reasoning, a syllogism is a three-part logical argument in which two premises are joined to get a conclusion.
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Please help it’s geometry and it’s hard
Measure of the angle m ∠ RQS = 58 ° for the given circle with arc RS subtending m ∠RPS=14 x + 46 ° at the center P and m ∠ RQS = 3 x + 43 ° at Q, on the circumference.
As given in the question,
Measure of the angle is given by :
m ∠ RPS=14 x + 46 °
m ∠ RQS=3 x + 43 °
m ∠ RPS = twice m ∠RQS (angle subtended at center of the circle)
14 x +46 =2(3 x + 43)
⇒ 14x + 46 = 6x +86
⇒ 14x-6x=86-46
⇒8x=40
⇒ x=5°
m ∠ RQS = (3 x + 43) °
=[3(5) + 43 ]°
= 58°
Therefore, measure of the angle in the given circle m ∠RQS is equal to the 58 °
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Are the triangles scaled copies of each other? True or false?
Answer:
You cannot multiply or divide for 4 and 3 so no false
Step-by-step explanation:
18 Answer:
Write the verbal phrase as an algebraic expression. Use x for the
variable in your expression: Sum of 8 and a number
19 Answer:
Write the verbal phrase as an algebraic expression. Use x for the
variable in your expression: Ten less than a number
20 Answer:
Write the verbal sentence as an equation or an inequality:
The sum of three and x is ten.
21 Answer:
Write the verbal sentence as an equation or an inequality:
Four is greater than six times a number t.
22 Answer:
Write an equation or inequality to model the situation:
The distance d to school is 1 1/2 miles more than the distance p to
the park.
23 Answer:
Write an equation or inequality to model the situation:
The perimeter of a square with a side length s is greater than or equal
to seventy plus five.
The required expression is "8+x" .
When integer variables, constants, and algebraic operations are used to create an expression, it is said to be algebraic (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)
However, since they are not produced by using integer constants and algebraic operations, transcendental numbers like such and e are not algebraic.The production of is commonly stated as a geometric expression, although the definition of e requires an infinite number of algebraic operations.An expression is said to be rational if it can be reduced to an acceptable fraction using the characteristics of arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).The required expressions are:
19) 8 + x
20) x - 10
21) 3 + x = 10
22) 4 > 6t
23) d > 3/2 p
24) 4s ≥ 70 + 5
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Find the perimeter of the figure to the right.
The perimeter is
(Simplify your answer.)
4y
meters.
2y meters
7y meters
6 meters
18 meters
6y meters
Answer:
72 m
Step-by-step explanation:
We observe that 7y+6=18, and thus y=12/7.
So, the perimeter is:
[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]