Answer:
Yes, 21.23 is a rational number.
[tex]21.23=\dfrac{2123}{100}[/tex]
Step-by-step explanation:
Terminating decimal numbers are decimals that have a finite number of decimal places.
A Rational Number is the division of an integer by another integer.
Therefore, 21.23 is a terminating decimal since it has a finite number of decimal places.
Let x be the rational number.
[tex]\implies x=21.23[/tex]
Multiply both sides by 100 so that the right side is an integer:
[tex]\implies 100x=2123[/tex]
Divide both sides by 100:
[tex]\implies x=\dfrac{2123}{100}[/tex]
(This fraction cannot be reduced any further).
Therefore, we have proved that 21.23 is a rational number.
Answer:
It is a rational number.
Step-by-step explanation:
Given value,
→ 21.23
Converting into rational number,
→ (21.23/1) × (100/100)
→ (21.23 × 100)/(1 × 100)
→ 2123/100
Hence, it is a rational number.
What is the value of the Missing angle
Answer: 120
Step-by-step explanation:
All angles in a triangle add up to 180. The third angle in the triangle is 60. A straight line is always 180, and line TU intersects it. So, subtract 60 from 180 and you get 120.
Answer:
120 degrees
Step-by-step explanation:
70 + 50 = 120 (exterior angle of a triangle)
Given: m//n
Prove: m2 + m28 = 180
Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.
If m2 + m28 = 180 then we get ∠2 + ∠8 = 180°
What are the theorems for parallel lines?Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines.
Two lines are said to be parallel if a transversal and two matching angles it forms are congruent.
Verification of Parallel Lines
that which contradicts the alternate interior angles theorem.the opposite of the theorem relating comparable angles.the converse of the same-side interior angles hypothesis.alternative exterior angles theorem's opposite.When two lines are intersected by a transversal and the opposing interior angles line up, the intersected lines are said to be parallel. Two lines are said to be parallel if they are divided by a transversal such that their opposing exterior angles are equivalent.
Therefore,
Given line m is parallel to line m
Interior Angle Theorem asserts that the alternate interior angles that result when two parallel lines are cut by a transversal are equivalent.
Alternate Exterior Angles are congruent if a transversal cuts two parallel lines. When a transversal cuts two parallel lines, the resulting angles are congruent.
Therefore, ∠2 = ∠6
∠2 + ∠4 = 180° ( Sum of the angles on a straight line is 180°)
∠6 + ∠8 = 180° ( Sum of the angles on a straight line is 180°)
∵ ∠2 = ∠6
∴ ∠6 + ∠8 = 180° ⇒ ∠2 + ∠8 = 180°
∠2 + ∠8 = 180° , Hence Proved.
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A cooking for the nursing home is preparing 100 yeast rolls for dinner the dry ingredients needed include 14 1/8 cups of flour 6 3/8 cups of sugar and 3/8 cups of salt how many cups of dry ingredients are in this recipe
Given the following ingredients
Cups of flour = 14 1/8 = 113/8 cups
Cups of sugar = 6 3/8 cups = 51/8 cups
Cups of salts = 3/8 cups
Calculate the total cups of dry ingredients
[tex]Total\text{ cups}=\frac{113}{8}+\frac{51}{8}+\frac{3}{8}[/tex]Find the LCM
[tex]\begin{gathered} Total\text{ cups}=\frac{113+51+3}{8} \\ Total\text{ cups}=\frac{167}{8} \\ Total\text{ cups}=20\frac{7}{8}cups \\ Total\text{ cups}=19+1\frac{7}{8} \\ Total\text{ cups}=19+\frac{15}{8} \\ Total\text{ cups}=19\frac{15}{8}cups \end{gathered}[/tex]Therefore there are 19 15/8 cups of dry ingredients in this recipe
with a vertex of (-7,-2) and directrix of x=-1, is this a vertical or horizontal parabola?
answer step by step please
Considering a parabolic equation with a vertex of (-7,-2) and directrix of x = -1. This is a horizontal parabola
What is directrix of a parabola?The directrix of a parabola is a straight line perpendicular to the axis of symmetry of the parabola.
The directrix does not touch the parabola
How to determine if a parabola is vertical or horizontal using the directrixA parabolic equation is also called quadratic equation.
Since the directrix is perpendicular to the axis of symmetry of the parabola it means that if:
when the directrix is given at x, the directrix runs in the vertical direction and the parabola is a horizontal parabolawhen the directrix is given at y, the directrix runs in the horizontal direction and the parabola is a vertical parabolaThe axis of symmetry says if the parabola is vertical or horizontal, when the axis of symmetry is parallel:
the y direction the parabola is a vertical parabolathe x direction the parabola is a horizontal parabolaIn the given problem, the directrix is given at x, the axis of symmetry is along the x direction and hence a horizontal parabola
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PLEASE SOLVE THIS IM GIVING 40 POINTS
The coordinates of the point P lying between AB is found as (7, -2/5).
What is termed as the section formula?The Section formula is used to calculate the coordinates of a point that separates a line segment either internally or externally into a certain ratio. When a point separates a line segment in some ratio, we just use section formula to determine the coordinates of the that point.For the given question;
The two end coordinates are;
(x₁, y₁) = (8, 0)
(x₂, y₂) = (3, -2)
The ratio of the division is;
AP/PB = 1/4
OR
m:n = 1:4
The Formula for finding the coordinates of P for internally crossing is;
x = (mx₂ + nx₁)/(m + n)
y = (my₂ + ny₁)/(m + n)
Put the values;
x = (mx₂ + nx₁)/(m + n)
x = (1×3 + 4×8)/(1 + 4)
x = (3 + 32)/5
x = 7
Now for y coordinates.
y = (my₂ + ny₁)/(m + n)
y = (1×(-2) + 4×0)/(1 + 4)
y = -2/5
Thus, the coordinates of the point P lying between AB is found as (7, -2/5).
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A used car dealership is interested in the age of a used car and the price of the vehicle. The manager collects a simple random sample of vehicles as shown in the table.
The equation of the least-squares regression line is
ŷ = 19.2 – 0.868x, where ŷ is the price of the vehicle (in thousands of dollars) and x is the age (in years). Which shows the residual plot?
ANSWER: A
Answer:
The Answer is A
Step-by-step explanation: Edge
Jason has 22 strawberry scones and 55 blackberry scones. He wants to make as many identical bags of scones as possible. Each bag should have an equal number of raspberry scones and an equal number of blackberry scones. What is the greatest number of bags Jason can fill? Explain how you know.
11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.
In this question we have been given Jason has 22 raspberry scones and 55 blackberry scones.
We need to find the maximum number of bags Jason can fill with equal number of raspberry scones and blackberry scones.
We will be using Greatest common factor (GCF) for knowing the number of bags.
22 = 2 × 11
and 55 = 5 × 11
So, the greatest common factor of 22 and 55 is 11
GCF(22, 55) = 11
Therefore, 11 is the greatest number of bags that Jason can fill with equal number of raspberry and blackberry scones.
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Hey can someone help me for q2 and onwards with step by step working out on paper so that I can understand them better. Thank u!!!
Answer:
f
Step-by-step explanation:
Which relation IS a function?
Answer: B.
Step-by-step explanation: A function relates an input to an output.
The relation which is a function is: function 1.
Option A is correct.
What is Function?A function is an expression, rule, or law in mathematics that describes a relationship between one variable (the independent variable) and another variable (the dependent variable).
A relation is a function when each input have only one output.
Function 1 have one output to each corresponding output.
Function 2 have two output for input x= 2.
Function 3 have two output for input x= 3.
Function 4 have two output for input x= 1.
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Can someone help with 16,17 and 18 ! thank you !
In questions 16, 17 and 18 we have a right triangle and in the three cases you know the measues for 2 sides, except for hipotenuse.
We can use the following relation to solve the problem:
[tex]tg(x)=\frac{\text{Opposite side}}{Adjacent\text{ side}}[/tex]16)
[tex]\begin{gathered} tg(x)=\frac{\text{1}7}{7}=2.4285 \\ tg(x)=2.4285 \\ x=tg^{-1}(2.4285) \\ x=68\degree \end{gathered}[/tex]17)
[tex]\begin{gathered} tg(x)=\frac{8}{10}=0.8 \\ x=tg^{-1}(0.8) \\ x=39\degree \end{gathered}[/tex]18)
[tex]\begin{gathered} tg(x)=\frac{\text{1}1}{8}=1.375 \\ x=tg^{-1}(1.375) \\ x=54\degree \end{gathered}[/tex]Find the 12th term in the arithmetic sequence an = 3 − 6(n − 1)a. -33b. -36c. -63d. -69
Given:
[tex]a_n=3-6(n-1)[/tex]Find-: 12th term of the sequence is
Sol:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \end{gathered}[/tex]Where,
[tex]\begin{gathered} n=\text{ term.} \\ \\ n=12 \end{gathered}[/tex]Put the value then:
[tex]\begin{gathered} a_n=3-6(n-1) \\ \\ n=12 \\ \\ a_{12}=3-6(12-1) \\ \\ a_{12}=3-6(11) \\ \\ a_{12}=3-(6\times11) \\ \\ a_{12}=3-66 \\ \\ a_{12}=-63 \end{gathered}[/tex]So 12th term is -63
Answer:
-63
Step-by-step explanation:
An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 70
grams of an alloy that contains 12% copper with 90 grams of pure copper.
(a) How many grams of copper are in the resulting mixture?
(b) What percentage of the resulting mixture is copper?
a)There is 160 grams of copper are in the resulting mixture
b) There is 61.5% percentage of the resulting mixture is copper.
What are mathematics operations?
• An operation is a function in mathematics that converts zero or more input values (also known as "operands" or "arguments") to a well-defined output value.
• The operation's arity is determined by the number of operands.
• Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied operations.
• A zero-arity operation, also known as a nullary operation, is a constant.
• The mixed product is an example of an arity 3 operation, also known as a ternary operation
From the question:
a) Suppose that a certain alloy is made by mixing 70 grams of an alloy that contains 12% copper with 90 grams of pure copper.
The number of grams of copper in the resulting mixture = 70 grams + 90 grams = 160 grams
b) 70 grams of an alloy that contains 12% copper = 70 × 12%
= 70 grams × 0.12
= 8.4 grams
The number of grams of copper in the resulting mixture = 160 grams
The percentage of the resulting mixture that is copper is
=( 8.4 grams + 90 grams of pure copper/160) × 100
= 98.4/160 × 100
= 61.5%
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10) Given that a=4 b=2 and C=-1
find the value of:
1) a - b + c
11) 20
Answer:
1 is the answer
Step-by-step explanation:
a-b+c Substitute values into the equation
4-2+(-1)
2+(-1)
2-1
1 Answer
The value of: 1) a - b + c is, 1 is the solution.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
a=4 b=2 and C=-1
now,
a-b+c
Substitute values into the equation
we get,
4-2+(-1)
=2+(-1)
=2-1
=1 (Answer)
Hence, The value of: 1) a - b + c is, 1 is the solution.
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A manufacturer knows that their items have a normally distributed lifespan, with a mean of 13.3 years, and standard deviation of 1.1 years.If you randomly purchase one item, what is the probability it will last longer than 10 years?Use the normal table and round answer to four decimal places
We want to find the following probability:
[tex]P(X>10)[/tex]where X is a normal random variable with mean 13.3 and standard deviation 1.1. To find this probability let's normalize the random variable; to do this we use the z-score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]Then, in this case, we have:
[tex]P(X>10)=P(z>\frac{10-13.3}{1.1})=P(z>-3)[/tex]Using the standard normal table, we have:
[tex]P(X\gt10)=P(z\gt(10-13.3)\/1.1)=P(z\gt-3)=0.9987[/tex]Therefore, the probability of purchasing an item with a lifespan greater than 10 years is 0.9987
Does our data provide enough evidence to prove that New York police are racially biased (in terms of use of force)? Why or why not?
We want to proof for this case if there is enough evidence to conclude that the New York police are racially biased in terms of force
From the info given is possible to see that the proportion with High level of force used is higher for Black people compared to White people. A difference of 6.3-5.8% = 0.5%.
In the other hand, we can see that for the Hands up force level, there is a significant difference between the two proportions, higher for Black compared to White with a difference of 15.1-9.7%= 5.4%
And finally when we analyze the case for No force used, we can see that there is a higher percentage for White (84.4%) compared to Black (78.7%) with a difference of 5.7%.
Based on this results we can conclude that in general the New York police is partially biased since is possible to see that for any level of force used the records are in favor of the White people.
What is the measure
Here, we want to get the measure of the angle marked A
We are going to use the sides given
The trigonometric ratio that links the adjacent to the hypotenuse is the cosine
The cosine is the ratio of the adjacent to the hypotenuse
Mathematically;
[tex]\begin{gathered} \cos \text{ m}\angle CAB\text{ = }\frac{12}{15} \\ \\ m\angle CAB\text{ = }\cos ^{-1}(\frac{12}{15}) \\ \\ m\angle CAB\text{ = 36.87} \end{gathered}[/tex]On average, Adrian's salary is 1.05 times the previous year's salary.If Adrian initially has $52,000 and n denotes the number of years, which recursive equation gives Adrian's annual income, /(7), as a function ofthe year?
Given:
Adrian initially has $52,000 and n denotes the number of years
Required:
Adrian's annual income, /(7), as a function of
the year?
Explanation:
Initially has $52,000, therefore
[tex]f(1)=52,000\text{ Exclude B,D}[/tex]The salary is 1.05 times the previous year's salary.
[tex]f(n)=1.05.f(n-1),\text{ for n}\ge2[/tex]Required answer:
Option D
what is the answer of this problem ? help me to find
Given:
Total invested amount = $9000
One account = 5%
Another account = 6%
Find-:
Invested amount of each equation
Explanation-:
Let in 5% account invested amount is x
then amount in 6% account is (9000-x)
Then,
[tex]5\%\text{ of }x+6\%\text{ of }(9000-x)=510[/tex]Then the value of "x" is:
[tex]\begin{gathered} \frac{5}{100}\times x+\frac{6}{100}\times(9000-x)=510 \\ \\ 0.05x+0.06(9000-x)=510 \\ \\ 0.05x+(0.06\times9000)-0.06x=510 \end{gathered}[/tex]The "x" is:
[tex]\begin{gathered} 0.05x-0.06x+540=510 \\ \\ -0.01x=510-540 \\ \\ -0.01x=-30 \\ \\ x=\frac{-30}{-0.01} \\ \\ x=3000 \end{gathered}[/tex]The value of x is 3000 the mean amount in 5% invested amount is 3000.
6% invested amount is:
[tex]\begin{gathered} =9000-3000 \\ \\ =6000 \end{gathered}[/tex]So each account invested amount is:
[tex]\begin{gathered} 5\%\rightarrow3000 \\ \\ 6\%\rightarrow6000 \end{gathered}[/tex]8 - 5(3 + 2x)I need help
8 - 5(3 + 2x)
open the parenthesis
8 - 15 - 10x
-7 -10x
Find the perimeter and area of
the figure if each unit on the
graph measures 1 centimeter.
Round answers to the nearest
tenth, if necessary.
A(2, 1)
B(8, 6).
C(10, 1)
The figure's perimeter and area would be as follows.
Perimeter = 21.19 cm
Area = 25.501 cm²
What is coordinate system?A Cartesian coordinate system in some kind of a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates, which are the signed distances from two fixed perpendicular lines that are aligned to the point and are both measured in the same length.
According to the given data:point of the coordinates are as follows:
A(2, 1)
B(8, 6).
C(10, 1)
We know that the formula for finding for the distance is:
d=√((x2 – x1)² + (y2 – y1)²).
For Point AB:
X₁ = 2
Y₁ = 1
X₂ = 8
Y₂ = 6
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((8 – 2)² + (6 – 1)²).
d=√((6)² + (5)²).
d=√(36 + 25).
d=√(61).
AB =7.81
For Point BC:
X₁ = 8
Y₁ = 6
X₂ = 10
Y₂ = 1
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((10 – 8)² + (1 – 6)²).
d=√((2)² + (-5)²).
d=√(4 + 25).
d=√(29).
BC = 5.38
For Point CA:
X₁ = 10
Y₁ = 1
X₂ = 2
Y₂ = 1
putting the values onto formula we get:
d=√((x2 – x1)² + (y2 – y1)²).
d=√((2 – 10)² + (1 – 1)²).
d=√((-8)² + (0)²).
d=√(64 + 0).
CA = 8
The perimeter of the given figure is:
Sum of all the sides.
AB + BC + CA
7.81 + 5.38 + 8
21.19 cm
Now finding the area of the tringle we use Pythagoras formula:
H² = P² + B²
P² = H² - B²
P² = (7.81)² - (5.38)²
P = 9.4837
We know that the area of the triangle is: = 1/2(base * Hight).
= 1/2(5.38 * 9.48)
= 25.501 cm²
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Write an equation to represent , the balance in an account after years, with an initial investment of $1,000 with an interest rate of 3%, compounded each year.
The balance in the account after years of compound interest arrangement can be represented by the equation; Balance = 1,000 (1.03)^n.
Which equation represents the balance in the account after years of compound interest?It follows from the task content that the equation which represents the balance in the account after years is required to be determined.
It follows that the principal amount is; $1,000 while the interest rate is; 3%.
This indicates that after each year, the new balance is 103% of the preceding balance.
Hence, the exponential equation which correctly represents the balance at any point in time is;
Balance = 1,000 (1.03)^n.
Where n = number of years after.
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The temperature in the morning was –2º F. The temperature in the evening was 9º F higher than it was in the morning. What was the temperature in the evening?
Answer:
Step-by-step explanation:
-2f
18 is how many times more then 6
Answer: 3 times more
Step-by-step explanation:
10.Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7. 11.Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2. 12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.) 13. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0. 14. Write a quadratic equation that cannot be factored.
Explanation
Question 10
We are asked to write the quadratic eqation that has the solutions of x=3 and x =-7
To do so, we will make use of
[tex]y=x^2-(sum\text{ of roots})x+product\text{ of roots}[/tex]So we will follow the steps below
[tex]\begin{gathered} Sum\text{ of roots = 3+}-7=-4 \\ product\text{ of roots =3\lparen-7\rparen=-21} \end{gathered}[/tex]substituting the above, we will have
[tex]\begin{gathered} x^2-(-4)x+(-21)=0 \\ \\ x^2+4x-21=0 \end{gathered}[/tex]Therefore, the quadratic equation is
[tex]x^2+4x-21[/tex]How many graduates in the sample came from University A?
The number of graduates in the sample that came from University A is:
35 + 90 + 35 = 160 graduates
CRITICAL THINKING Find the values of a, b, and c so that the linear system shown has (---1. 2. --3) as its only solution. Explain your reasoning. x + 2y - Bra -r-y +z = b 2x + 3y - 2z=c enter your answer as follows: a=_,b=_,c=__without any spaces. Show Your Work
1) Let's set the system of linear equations:
x +2y -3z = a
-x -y +z = b
2x +3y -2z =c
2) Since the solution has already been given ( -1,2,-3) all that's left to do, is to plug it into each equation so that we can find a, b and c. Just like this:
x +2y - 3z = a ⇒ (-1) +2(2) -3(-3) = a ∴ a = 4
-x -y +z = b ⇒ -(-1) -(2) +(-3) = b ∴ b = 0
2x +3y -2z =c ⇒ 2(-1) +3(2) -2 (-3)=c ∴ c = -2
3) Hence, a = 4 b = 0 and c = -2
Fin tends to exaggerate. He says if he stacked all the quarters he's ever spent on gumball machines, they would reach to the moon. The distance to the moon is about [tex]3.85 \times {10}^{8} [/tex]m and the width of a quarter is about[tex]1.75 \times {10}^{ - 3} [/tex]m. If Fin's claim were true, how many quarters has he spent on gumball machines?
For this problem we were given the distance to the moon and the width of a quarter in meters. We need to determine how many quarters we would need to stack in order to reach the moon.
In order to solve this problem, we need to divide the distance from the surface of the Earth to the moon by the width of each quarter. Notice that both numbers are presented in scientific notations, therefore we need to divide the coefficients and subtract the exponents. This is done below:
[tex]\begin{gathered} n=\frac{3.85\cdot10^8}{1.75\cdot10^{-3}} \\ n=2.2\cdot10^{8-(-3)} \\ n=2.2\cdot10^{8+3} \\ b=2.2\cdot10^{11} \end{gathered}[/tex]If Fin's claim were true, he'd need to stack a total of 2.2*10^11 quarters.
Jordan looks at the line plot. He says the difference between the most capacity and the least capacity is 1/4 gallon. He says he knows the difference without subtracting. Explain Jordan’s mistake and find actual difference between measurements.
In a line plot the maximum value is the rightmost mark in the line plot; in this case the maximum capacity is 2 1/2. On the other hand the minimum value is the leftmost mark in the line plot, here the minimum is 1 1/2. Let's calculate the difference between them:
[tex]2\frac{1}{2}-1\frac{1}{2}=1[/tex]Therefore, the difference between the maxiimum and minimum capacity is 1.
The sum of the interior angles of a polygon with 10 sides can be expressed as 360n. What is the value of n? O 2 04 O 6 08
The sum of the interior angle of a polygon with 10 sides is equal to 1440°
If it can be expressed as 360n, then n is
[tex]\begin{gathered} 360n=1440 \\ \\ \text{Divide both sides by 360} \\ \frac{360n}{360}=\frac{1440}{360} \\ \frac{\cancel{360}n}{\cancel{360}}=\frac{1440}{360} \\ n=4 \\ \\ \text{Therefore, }n\text{ is equal to }4 \end{gathered}[/tex]PLEASE HELP!!!
Simplify the expression to a polynomial in
standard form:
(3x² + x − 5) (2x² + x + 3)
The standard form is 6x⁴+5x³-2x-15.
Here the term polynomial is characterized as an expression that is composed of variables, exponents, and constants, that are combined utilizing numerical operations such as subtraction, addition, division, and multiplication. the standard form of a polynomial is :
P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ +aₙ₋₂xⁿ⁻² + ………………. + a₁x + a₀
Where aₙ, aₙ₋₁, aₙ₋₂, ……………………, a₁, a₀ are the coefficients of xⁿ, xⁿ⁻¹, xⁿ⁻², ….., x and are to a real number.
The polynomial given to us is (3x² + x − 5) (2x² + x + 3)
=3x²(2x² + x + 3) + x (2x² + x + 3) − 5 (2x² + x + 3)
= 6x⁴ + 3x³+9x²+2x³+x²+3x-10x²-5x-15
= 6x⁴+3x³+2x³+9x²+x²-10x²+3x-5x-15
= 6x⁴+5x³-2x-15
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