find the unit rate of $36 : 1/2 hour
Answer:
$72 / hr
Step-by-step explanation:
$36 / (1/2 hr ) = $72 per hour
sophie's favorite number is a two-digit number. if she reverses the digits, the result is $45$ less than her favorite number. the sum of the digits in her favorite number is $11$. what is sophie's favorite number?
Sophie's favorite number is 83
We have that;
A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.
To get Sophie's favorite number, we need to assume the case as;
Let,
⇒10x + y = 10y + x + 45
x + y = 11
y = 11-x
⇒10x + 11 - x = 10(11 - x) + x + 45
10x + 11 - x = 110 - 10x + x + 45
9x + 11 = 155 - 9x
18x + 11 = 155
18x = 144
x = 8
Therefore, y = 11 - 8
y = 3
Sum = x + y = 8 + 3 = 11
Hence, the given condition is satisfied.
Sophie's favorite number is 83.
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Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15. If
each bottle costs the same amount, how much is 8 bottles of juice?
As per the unitary method, the cost of 8 bottles is $6.48
Unitary Method:
Unitary method is the way of solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
Hawa buys 15 bottles of apple juice at the corner store for a total cost of $12.15.
Here we need to find the if each bottle costs the same amount, how much is 8 bottles of juice.
Let x be the cost of one bottle.
so, based on the unitary method we can written the situation as,
15 bottles = costs $12.15
Therefore, the cost of one bottle is.
x = 12.15/15
x = 0.81
So, the cost of 8 bottle is calculated by multiplying the cost of one bottle with 8,
Then we get,
=> 8 x 0.81
=> 6.48
Therefore, the cost of 8 bottles is $6.48
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help
If T=5n+2, which term will have a value of 52?
Answer:
T = 52
Step-by-step explanation:
The area of a rectangle is 110 square units. It’s length measures 11 units. Find the length of diagonal
The diagonal of the rectangle is 14.87 units.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Area of rectangle = 110 square units
Length = 11 units
Area of a rectangle = Length x Wide.
110 square units = Length x Wide
110 = 11 x Wide
Wide = 110/11
Wide = 10
Now,
The diagonal of a rectangle.
Using the Pythagorean theorem we get,
Diagonal² = Wide² + Length²
Diagonal² = 10² + 11²
Diagonal² = 100 + 121
Diagonal² = 221
Diagonal = √221
Diagonal = 14.87 units.
Thus,
The diagonal of the rectangle is 14.87 units.
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The ____ of 12 is -12.
Answer; the Negative of 12 is -12
Step-by-step explanation: first of all the reciprocal of 12 is 1 over 12. so that's not it. The absolute value of 12 is still 12 so that's not it. So the only thing that it can be is the Negative of 12 is -12
Helpppppppssssss ejejnee
Answer:
Step-by-step explanation:
Arithmetic Sequence
Answer:
(a) Arithmetic Sequence
Step-by-step explanation:
You want to know if the graph of a straight line represent an arithmetic, geometric, or neither sequence.
Arithmetic sequenceAn arithmetic sequence is characterized by a common difference between terms that are 1 unit apart. A graph of an arithmetic sequence is points that lie on a straight line.
The graph shows an Arithmetic Sequence.
__
Additional comment
A graph of a geometric sequence would show points that lie on an exponential curve.
a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus. she wants to know if anxiety levels were higher in the fearful stimulus condition. if the same participants are observed in each group, then what type of statistical design is appropriate for this study? group of answer choices a one-way between-subjects anova a one-way within-subjects anova an independent t-test a dependent t-test
Using the theories of statistical design, we got that both related sample t test and one-way within-subjects ANOVA is the appropriate statistical design for the study in which a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus.
Statistical design of experiments and the response surface methodology has become a standard tool for the medium development. There are several applications reported in literature, such as the production of antibiotics, secondary metabolites, and enzymes.
Applications of statistical design of experiment shown in the Table 1 and several other studies use exclusively of the response surface method with quadratic polynomial models and the central composite design with on average 20–30 experiments. In most cases, the important components were identified by fractional factorial design or by the Plackett–Burman design with 10–15 experiments. Methods for narrowing optimal variable range are only infrequently applied.
Hence, when a researcher measures anxiety levels among participants in the presence and absence of a fearful stimulus and wants to know if anxiety levels were higher in the fearful stimulus condition and if the same participants are observed in each group, then the appropriate statistical design is that both related sample t test and one-way within-subjects ANOVA .
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A town has a population of 2.25 x 104 and grows at a rate of 5.1% every year. Which
equation represents the town's population after 2 years
Answer:
P=(2.25 x 10^4)(1 + 0.051)(1 +0.051)
Step-by-step explanation:
which equations are true when k = - 50? Select two correct answers.
1.5 - k/5 = 11.5
-2k + 78 = -22
-4k + 80 = -120
6k - 150 = -150
K/10 -3 = -8
30 POINTS IF YOU ANSWER!!
There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.
Given,
The equations;
1.5 - k/5 = 11.5-2k + 78 = -22-4k + 80 = -1206k - 150 = -150K/10 -3 = -8The value of k = -50
We have to solve the given equations using k as -50 and find the true ones;
Lets check;
1.5 - k/5 = 11.51.5 - (-50/5) = 11.5
1.5 - (-10) = 11.5
1.5 + 10 = 11.5
11.5 = 11.5
This equation is true.
-2k + 78 = -22(-2 x -50) + 78 = -22
100 + 78 = -22
178 ≠ -22
This equation is false
-4k + 80 = -120(-4 x -50) + 80 = -120
200 + 80 = -120
280 ≠ -120
This equation is false
6k - 150 = -150(6 x -50) - 150 = -150
-300 - 150 = -150
-450 ≠ -150
This equation is false
k/10 -3 = -8(-50/10) - 3 = -8
-5 - 3 = -8
-8 = -8
This equation is true.
That is,
There are two equations which are true. They are 1.5 - k/5 = 11.5 and K/10 -3 = -8.
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Select the correct answer. Which expression is equivalent to , if x ≠ 0 and y ≠ 0? A. B. C. D.
see image below:
The expression similar to [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.
A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]
What are the laws of indices?According to some of the laws of indices, we have;
[tex]\dfrac{1}{x^n} =x^{-n}[/tex]
[tex]x^m \cdot x^n = x^{m+n}[/tex]
[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]
The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]
Simplifying the above expression gives;
[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]
[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]
Collecting terms with an index of a multiple of 3 gives;
[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]
[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]
The expression that is equivalent to [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.
A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]
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What is the radical form of each of the given expressions? Drag the answer into the box to correctly match each expression.
2 2/3 -
3 1/3 -
3 3/2 -
2 1/2 -
The radical form of each of the given expressions are;
1) 2^(2/3) = ∛(2²)
2) 3^(1/3) = ∛3
3) 3^(3/2) = √3³
4) 2^(1/2) = √2
What is the radical form of the exponent form?The radical form of the expression [tex]a^{\frac{x}{y} }[/tex] is; [tex]\sqrt[y]{a^{x} }[/tex]
Thus, we can solve each of the given expressions;
1) We are given the expression as 2^(2/3).
Thus;
x = 2 and y = 3 and we have; ∛(2²)
2) We are given the expression as 3^(1/3).
Thus, x = 1 and y = 3 and so we have;
∛3
3) We are given the expression as 3^(3/2). Thus;
x = 3 and y = 2 and so we now have; √3³
4) We are given the expression as 2^(1/2). Thus;
x = 1 and y = 2 and so we now have; √2
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If you add a prime number to itself, is the sum composite or prime?
Answer: The sum of two prime numbers is always even (which is composite).
Hope this helped :)
The first side of a triangle is 2 feet longer than
the second. The third side is 5 feet shorter than
twice the second. The perimeter is 49 feet. Find
the length of each side.
The length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.
According to the question,
We have the following information:
The first side of a triangle is 2 feet longer than the second. The third side is 5 feet shorter than twice the second. The perimeter is 49 feet.
Let's take the second side to be x feet.
So, we have the following sides:
First side = (x+2) feet
Third side = (2x-5) feet
Perimeter = 49
x+x+2+2x-5 = 49
4x-3 = 49
Adding 3 on both the sides:
4x = 49+3
4x = 52
Dividing by 4 on both the sides:
x = 52/4
x = 13 feet
First side = 2+13
First side = 15 feet
Third side = 2*13-5
Third side = 26-5
Third side = 21 feet
Hence, the length of the first side of the triangle is 15 feet, the length of the second side of the triangle is 13 feet and the third side is 21 feet.
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Find the value of x in the triangle below:
The value of x in the given triangle is x = 12 .
Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .
In the question ,
a triangular figure is given
in which , the measure of angle A is (6x - 19)°
the measure of angle B is [tex]=[/tex] 84°
the measure of angle C is [tex]=[/tex] (3x + 7)°
So , By Angle sum property ,
we get
∠A + ∠B + ∠C [tex]=[/tex] 180°
substituting the values of angle A, B and C ,
we get
(6x - 19)° [tex]+[/tex] 84° + (3x + 7)° [tex]=[/tex] 180°
6x - 19 [tex]+[/tex] 84 [tex]+[/tex] 3x + 7 [tex]=[/tex] 180
9x + 72 = 180
9x = 180 - 72
9x = 108
x = 108/9
x = 12
Therefore , the value of x is [tex]=[/tex] 12
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If the average daily sales in a store for the past 5 days was (2.3q + 1.4) dollars, express the total sales amount for the past 5 days as an algebraic expression.
The algebraic expression is C(5) =2.5 * 5 + 1.4 and the total cost is $13.9
How to determine the total sales amount?From the question, the equation of the total sales amount is given as
Equation = 2.3q + 1.4
Where q represents the number of days
Rewrite as
Cost = 2.3q + 1.4
Express the equation as a cost function
So, we have the following representations
C(q) = 2.3q + 1.4
When the number of days is 5, we have
q = 5
Substitute the known values in the above equation So, we have the following equation
C(5) =2.5 * 5 + 1.4
Evaluate the products
C(5) = 12.5+ 1.4
Evaluate the sum
C(5) = 13.9
Hence, the total cost for the 5 days is $13.9
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y
y< 2x-3
How would I graph this ?
The graph of the inequality is attached below.
We are given an inequality. The inequality is linear in nature. An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. The inequality is given below.
y < 2x - 3
We need to graph the inequality. The first step is to find out the corresponding equation of the straight line. The equation is found by replacing the greater-than or less-than sign with the equal-to sign. The equation is given below.
y = 2x - 3
We plot this equation on the graph with a dotted line. Now we shade the area that satisfies the given inequality. The graph is given below.
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Ben bowled 151 and 183 in his first two games. What must he bowl in his third game to have an average of at least 1702
Answer:
1368
Step-by-step explanation:
let 3rd game be x
151+183+x=1702
334+x=1702
x=1702-334
x=1368
please help, I will really appricaite it :)
Step-by-step explanation:
uploading the picture is an excellent way to make sure we get the original problem definition.
but I just answered this (even without the picture). so, you need it again ?
from a group of 12 students, we want to select a random sample of 5 students to serve on a university committee. how many combinations of random samples of 5 students can be selected?
The number of combinations of random samples of 5 students can be 792.
Given, 12 groups of students
We have to select random samples of 5 students,
Here we will use the combination formula,
Cₙ,ₓ = n! / x! (n - x)!
Here n=12 and x=5
Cₙ,ₓ = 12! / 5! (7!)
Cₙ,ₓ = 479,001,600 / (120) × (5040)
Cₙ,ₓ = 792
Therefore the possible ways of selecting the random samples of 5 students are 792.
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verify by drawing a diagram if the median and altitude of an isosceles triangle can be the same
The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram
The statement is
"The median and altitude of an isosceles triangle can be same"
Draw an isosceles triangle ABC with BD = CD,
Draw a line segment AD perpendicular to the side BD
Here AD is the height of the triangle which is the altitude of the triangle
From the figure we can see that the length of BD = length of CD
Where D is the mid point of the line BD.
Therefore the line AD is the median of the triangle
Hence, The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram
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room attendants at your hotel typically clean one room every 20 minutes. one-fifth of the rooms take 40% longer to clean due to various issues. how much time will it take to clean 175 rooms?
Draw the straight line y=2x-3
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The table is
x 0 1 2
y -3 -1 1
The graph of the line is given below.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
Equation of a line:
y = 2x - 3
y = 2 x 0 - 3 = -3
y = 2 - 3 = -1
y = 2 x 2 - 3 = 4 - 3 = 1
Table
x 0 1 2
y -3 -1 1
The graph of the straight line is given below.
Thus,
The table is
x 0 1 2
y -3 -1 1
The graph of the line is given below.
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estion 11 of 42
What is the equation of a line with a slope of 6 and a y-intercept of -2
O A. y = -2x + 6
OB. y = 6x + 2
OC. y = 6x-2
OD. y = 2x+6
Use the following sequence to complete the parts: 8, 5, 2, -1,...
Is this arithmetic or geometric? (Type A or G)
What are the NEXT 3 terms?
What is the equation? t(n) =
What would be the 100th term?
n+
Is-345 a part of the sequence? (Type Y or N)
The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289.
What is a sequence?
A sequence is a function from natural numbers to the set of real numbers. it maps the set of number numbers on the set of real numbers.
We are given a sequence 8, 5,2, -1,.....
Now the first term of the sequence is 8 and common difference is -3.
As the difference between 2 consecutive terms is same, the given sequence is arithmetic.
now substituting this in the standard equation
we get,
t(n) = a+ (n-1)d
t(n)= 8+(n-1)(-3)
t(n) = 8-3n+3
t(n) = 11-3n (1)
Now we have to find the 5th, 6th, 7th term of the sequence
We substitute n=5, n=6, n=6 in equation 1
We get
t(5) = 11-3(5)
t(5) = 11-15
t(5) = -4
And,
t(6) = 11-3(6)
t(6) = 11-18
t(6) = -7
And,
t(7) = 11-3(7)
t(7) = 11-21
t(7) = -10
Hence the next three terms are -4, -7, -10.
The equation is t(n) = 11-3n
The 100th term would be given as
t(100) = 11-3(100)
t(100) = 11-300
t(100) = -289
Hence, The given sequence is arithmetic sequence. The next three terms of the sequence are -4,-7,-10. the equation can be given as 11-3n. the 100th term of the sequence is -289
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Select all ordered pairs that are a solution to -5x + 3y > 12
options:
(3, 9)
(-5, 5)
(3, -6)
(-2, -5)
(2, 8)
(-6, 0)
The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:
(-5, 5)(2, 8)(-6, 0)How to determine the solution?In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;
For ordered pair (3, 9), we have:
-5x + 3y > 12
-5(3) + 3(9) > 12
-15 + 27 > 12
12 > 12 (False).
For ordered pair (-5, 5), we have:
-5x + 3y > 12
-5(-5) + 3(5) > 12
25 + 15 > 12
40 > 12 (True).
For ordered pair (3, -6), we have:
-5x + 3y > 12
-5(3) + 3(-6) > 12
-15 - 18 > 12
-33 > 12 (False).
For ordered pair (-2, -5), we have:
-5x + 3y > 12
-5(-2) + 3(-5) > 12
10 - 15 > 12
-5 > 12 (False).
For ordered pair (2, 8), we have:
-5x + 3y > 12
-5(2) + 3(8) > 12
-10 + 24 > 12
14 > 12 (True).
For ordered pair (-6, 0), we have:
-5x + 3y > 12
-5(-6) + 3(0) > 12
30 + 0 > 12
30-5 > 12 (True).
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x represents the number
of comic books Priya buys
at the store, all at the same
price, and y represents the
amount of money (in
dollars) Priya has after
buying the comic books.
By using the concept of equation of line in slope intercept form, it can be obtained that
a) x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
y- intercept is 20
This means, Priya had $20 before buying any comics
b) Slope = -4
This means Priya's money has been decreasing by $4 after buying one comics
c) Equation of line
y = -4x + 20
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
x represents the number of comic books Priya buys at the store
y represents the amount of money (in dollars) Priya has after buying the comic books.
a)From the figure, it is clear that x- intercept is 5
This means, Priya has exhausted all her money by buying 5 comics
From the figure, it is clear that y- intercept is 20
This means, Priya had $20 before buying any comics
b) The line passes through (5, 0) and (0, 20)
Slope = [tex]\frac{20 - 0}{0 -5}[/tex] = -4
This means Priya's money has been decreasing by $4 after buying
one comics
c) Equation of line
y - 0 = -4(x - 5)
y = -4x + 20
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Complete Question
The figure has been attached-
Given a point (5,-6) and slope m = -2
Write the Point-Slope Equation of the line.
Please give me a great explanation and explain like your talking to a baby please. Thanks :)
Answer:
y+6 =-2(x-5)
Step-by-step explanation:
The question is asking for the equation of the line
The equation for point-slope form is always written as y-y₁=m(x-x₁)
y₁ and x₁ are the points given to you in this order (x₁, y₁)
so x₁=5 and y₁=-6
Now you plug in all the numbers you have into the point slope form
y- (-6)= -2(x-5)
When you subtract a negative (a double negative you get a positive)
y+6=-2(x-5)
Point-Slope form is usually the easiest form of a line to write since you do not need to solve for any intercepts or other points. You have y on one side of the equation, usually the left to make it easier to read, and x on the other, usually the right.You subtract the point that you are given from the y and the x. Multiply everything that is on the same side of the equation of the x by the slope (m).
Notes:
For y₁ and x₁, they could be any point on the line. For example, (1,2) is also on this line. So the equation would be
y-2=-2(x-1)
The equation of line k is y+2=-6(x-7).line l includes the point (-6,8) and is perpendicular to line k. What is the equation of line l?
The equation of line [L] would be y = (1/6)x + 9.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
We have a equation of line [k] is y + 2 = -6(x - 7). Line [L] includes the point (-6,8) and is perpendicular to line k.
We have the equation of line [K] as -
y + 2 = - 6(x - 7)
y = - 6(x - 7) - 2
y = - 6x + 42 - 2
y = - 6x + 40
Slope of line [L] will be -
m[L] = 1/6
Assume the equation to be -
y = (1/6)x + c
Line [L] includes the point (-6, 8), so we can write -
8 = (1/6) x (- 6) + c
8 + 1 = c
c = 9
So, the equation will be -
y = (1/6)x + 9
Therefore, the equation of line [L] would be y = (1/6)x + 9.
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lee went shopping with $60.50 . he bought 5 boxes of blue berries and 3 watermelons and had $16.50 left each watermelon cost $8.30
Assuming the question is : "how much does 1 box of blueberries cost?"
After he bought 5 boxes of blueberries and 3 watermelons, he was left with $16.50
Therefore, 5 boxes of blueberries and 3 watermelons cost $60.50 - $16.50 = $44
We are given the cost of 1 watermelon is $8.30
Therefore, 3 watermelons cost $8.30 x 3 = $24.90.
-> 5 boxes of blueberries cost $44 - $24.90 = $19.10
-> 1 box of blueberries cost $19.10 : 5 = $3.82
Answer:
If your trying to find the total of the 5 boxes of blue berries the answer is
$19.10
Step-by-step explanation:
60.50 - 16.50 = 44$ meaning he spent that much.
8.30 x 3 = 24.9
19.10 + 24.9 = 44
hope this helps