The equation in terms of x, which represents the amount of money left on the gift card of Aaliyah upon buying a cup of coffee is; A = 30 - 2x dollars.
Define the term equation?A single mathematical phrase is referred to as a term. It could be a single number (negatively or positively), a single variable (a letter), or a combination of variables multiplied but still never added or eliminated. Variables with such a number ahead of them are used in some words. A coefficient is the number that appears ahead of a phrase.The original value of the gift card was $30.
Coffee costs $2 per cup.
Let 'x' be the number of cup of coffee purchased by Aaliyah.
Total cost be 'A' be paid by her.
Thus, the equation in terms of x, which represents the amount of money left on the gift card upon buying a cup of coffee is;
A = 30 - 2x dollars.
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2015
The ratio of boys to girls in a class is 4:3. There are 35 students in the class. How many
students are boys?
Hannah swims in a swimming pool of 25 metres long.
How many laps does she need to complete for a total distance of 0.5 kilometre?
She needs to complete 20 laps for a total distance of 0.5 kilometer.
1 kilometers = 1000 meters
0.5 kilometers = 500 meters
Length of swimming pool = 25 meters
That means, she covers 25 meters in 1 lap.
Laps to cover 500 meters = 500/25
= 20
Hence, she needs to do 20 laps.
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Point O is the center of this circle. What is mzBCA?
A. 56
B. 62
C. 72
D.76
Answer:
B
Step-by-step explanation:
∠ ADB and ∠ AOB sum to 180° , that is
56° + ∠ AOB = 180° ( subtract 56° from both sides )
∠ AOB = 124°
An angle on the circle is half the central angle subtended on the same arc , so
∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°
Translate the sentence into an equation.
Seven more than the quotient of a number and 6 is equal to 2.
Use the variable x for the unknown number.
Answer:
Step-by-step explanation:
Let's break down the problem:
Quotient = result obtained by dividing one quantity by another
So its division of x (a number implying variable) by 6
Then it says equal to 2 so we can piece together an equation like this
x/6 = 2
Then we use algebra to solve it
6(x/6)= (2)6
x = 12
So 12 is the unknown number
,
Admission to the art museum is $3 per person. When the museum opened this
there was $150 on hand in the ticket booth. At closing time, there was $1254. How many
people paid admission today?
Had:
Tickets:
Total:
Step-by-step explanation:
so the ticket booth had $150 so $1254 -$150=$1104
so $1104 ÷ by $3 each person = to 368 people paid the admission
Had: $150
Tickets :368
Total :$1254
the distribution of results from a cholesterol test has a mean of 180 and a standard deviation of 20. a sample size of 40 is drawn randomly. find the probability that the sum of the 40 values is greater than 7,450. (round your answer to four decimal places.)
The probability that the sum of the 40 values is greater than 7,450 is 0.0239
Define Normal Distribution.
A normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known.Formula of Normal Distribution isZ = (x - μ ) / (σ / √n )
We have given following info,
mean μ = 180
Standard deviation σ = 20
n = 40
σ(mean of x) = σ / √ n
= 20 / √40
= 3.16
Sample average (mean of x) = 7450 / 40
= 186.25
P(x > 186.25) = 1 - P(x < 186.25)
= 1 - P( (x - μ ) / σ(mean of x) ) < ( [186.25 - 180] / 3.16) )
= 1 - P( Z < 1.98)
Using Normal distribution table,
= 1 - 0.9761
P(x > 186.25) = 0.0239
Therefore,the probability that the sum of the 40 values is greater than 7,450 is 0.0239
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this is geometry, finding the rules for sequences of congruence transformations
The rules for the rotation and translation for the rectangle RSTU is:
Rotation: (x,y) ↔ (-y,x)
Translation : (x,y) ↔ (x+k , y)
Given,
we have rectangle R'S'T'U' which is the image of the rectangle RSTU under a rotation 90° counterclockwise about the origin followed by a translation.
we are asked to determine the rule of rotation and translation.
Rotation :
Our point A(x,y) becomes A' when a point is rotated 90 degrees counterclockwise about the origin (-y,x).
so the rule is:
Rotation: (x,y) ↔ (-y,x)
Translation:
When the shape is moved towards the right by k units, then replace x with x + k.
let's check:
R(-6,3) ↔ 90° counterclockwise rotation ↔ (-3,-6) ↔ translation↔R'(-3+9,-6) → R'(6,-6)
S(-4,7) ↔ 90° counterclockwise rotation ↔ (-7,-4) ↔ translation↔S'(-7+9,-4) → R'(2,-4)
Hence we get the required rules for sequences of congruence transformations.
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The school art club at a large high school is in charge of designing school T-shirts and getting them printed this year. A local business charges $35 to set up their T-shirt printing machine with the design and $4.25 in materials per T-shirt to print.
1). Create an equation to represent the average cost C(x), in dollars, per T-shirt if x T-shirts are printed by this business.
2). what is the average cost per shirt to print 25 shirts? 100 shirts?
3). what is the cheapest the average cost per T-shirt will get? Explain or show your reasoning.
Total cost includes initial charge for printer set up and material cost.
C(x) = 4.25x + 35 represents the total cost, where C(x) is the cost of x T- shirts.Part 1Average cost per T-shirt is
C(x)/ x = (4.25x + 35)/x = 4.25 + 35/xPart 2Average cost to print 25 T-shirts
4.25 + 35/25 = $5.65Average cost to print 100 T-shirts
4.25 + 35/100 = $4.60Part 3The average cost 4.25 + 35/x depends on the number of T-shirts printed.
The larger the x, the smaller is 35/x. It will be closer to but greater than $4.25.
Quadrilateral TEAM is rotated-180° about the origin.
Draw the image of this rotation.
The area of the quadrilateral is determined as follows if the diagonal and the length of the perpendiculars from the vertices are known: The formula for calculating the area of a quadrilateral is (12) diagonal length the sum of the lengths of the perpendiculars drawn from the other two vertices.
Explain about the Quadrilateral?A polygon with four sides, four angles, and four vertices is called a quadrilateral. The Latin words Quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral. A quadrilateral is shown in the above image as an example. quadrilateral pieces.
Quadrilaterals with four congruent sides, four right angles, and two sets of parallel sides are called squares. Quadrilaterals having two sets of parallel sides are known as parallelograms. All squares are parallelograms because squares must have quadrilaterals with two sets of parallel sides.
Four sides and four angles make up a quadrilateral. Any convex polygon's exterior angles (i.e., no interior angle is less than 180 degrees) sum up to 360 degrees ( 4 right angles).
In the quadrilateral, each point's coordinates change as follows:
(x, y) → (-x, -y)
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Help!! Can someone state all the statements and reasons to prove that triangle WXY is congruent to triangle WZY!! It’s geometry proofs.
Whoever gives me the answer I’ll give them 20!
It is true that WXY ≅ WZY.
What is a congruent?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Properties of Congruence
Reflexive Property: An angle is congruent to itself.
Symmetric Property: The order of congruence does not matter.
Transitive Property: If two angles are both congruent to a third angle, then the first two angles are also congruent.
Here, It is given that
Angle ZWY is congruent to angle XWY
Segment WZ is congruent to Segment WX
Segment WY is congruent to Segment WY - Reflexive Property of Congruence (which states that one thing is congruent to itself.
Hence, Triangle WXY is congruent to Triangle WZY because of Side Angle Side (SAS) postulate.
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when 1515 is appended to a list of integers, the mean is increased by 22. when 11 is appended to the enlarged list, the mean of the enlarged list is decreased by 11. how many integers were in the original list?
In the initial list, there were 4 integers.
We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:
m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).
The initial equation is x = mn.
Therefore, changing x in the other two equations:
m + 2 = (mn + 15) / (n + 1) ..............(1)
m + 1 = (mn + 16) / (n + 2)...............(2)
Based on equation (1):
(m + 2)(n + 1) = mn + 15
mn + m + 2n + 2 = mn + 15
m + 2n + 2 = 15
m + 2n = 13
m = 13 - 2n.
Now change m in equation (2) to:
13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)
14 - 2n = (13n - 2n^2 + 16) / (n + 2) Through-multiplication by n + 2:
(14 - 2n)(n + 2) = 13n - 2n^2 + 16
14n + 28 - 2n^2 - 4n = 13n - 2n^2 + 16
10n + 28 = 13n + 16
12 = 3n
n = 4.
Hence, there were 4 integers in the original list.
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Determine the quadratic function of the form f(x)= a(x - h)² + k whose graph is given on the
right.
The quadratic function will be f(x) = 2[tex]x^{2}[/tex] + 4x + 15
General equation of quadratic is
f(x) = a[tex]x^{2}[/tex] + bx + c
and Standard form is
f(x) =a [tex](x-h)^{2}[/tex] + k
where h , k are coordinates of vertex
and x , y represent some point on the graph.
By replacing f(x) with y in standard equation we get
y = a[tex](x-h)^{2}[/tex] + k
Put value of x , y , h , k from the graph.
h = -2
k = 7
x = 0
y = 9
9 = a (4) + 7
a = 2
Now put value of a in standard equation
f(x) = 2 [tex](x + 2)^{2}[/tex] + 7
f(x) = 2[tex]x^{2}[/tex] + 4x + 15
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Some doctors recommend that men drink 3 liters of water every day. there are approximately 29.6 milliliters in 1 fluid ounce. which measurement is closest to the number of fluid ounces in 3 liters? responses 89 fl oz 89 fl oz 10 fl oz 10 fl oz 101 fl oz 101 fl oz 33 fl oz 33 fl oz
The measurement closest to the number of fluid ounces there are in 3 liters is 101 fl oz.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
If there are approximately 29.6 milliliters in 1 fluid ounce, then divide 3 liters by 29.6 milliliters to get the amount of fluid ounces it has.
29.6 milliliters = 1 fluid ounce
3 liters = 3000 milliliters
3000 milliliters / 29.6 milliliters = 101 fluid ounce
Hence, 3 liters ≈ 101 fluid ounces.
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4. Use the rules of measurement to add:
12.32 L +251 L +4225 L
In the football club, 36 footballer are Latvian, while there are 4 time le footballer of other nationalitie. How many total athlete doe the football club have?
The total number of athletes, the football club has is 180.
Given, In the football club, 36 footballers are Latvian, while there are 4 times the footballers of other nationalities.
as, footballers that are Latvian = 36
now, footballers of other nationalities = 4×36
footballers of other nationalities = 144
so the total number of footballers = 144 + 36 = 180
Therefore, the total number of athletes, the football club has is 180.
Hence, the total number of athletes, the football club has is 180.
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What would a, b, c be??
The values of a, b and c from the given polynomial are a = -1 , b = 2 and, c= -35.
We are given the expression:-
[tex]x^2+2x-35[/tex]
We know that, the general form of a quadratic expression is :-
[tex]ax^2+bx+c[/tex]
We can rewrite the given expression as:-
[tex]-1x^2+2x+(-35)[/tex]
Comparing it with the given equation, we get:-
a = -1 , b = 2 , c= -35
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).
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How do you use distributive property to express the expression as the multiple of a sum of two whole numbers with no common factor? 27 + 99, 99+36, 3+33, 33+27, 10+50
if the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at . is this the case for the residual plot?
Yes. The residuals' distribution pattern resembles a haphazard dispersion around the horizontal line at 0.
The horizontal plot in this instance comprises points that are unstructured and randomly dispersed around the horizontal mean line.
These are also points below the mean above the mean. This shows that some points in the distribution of data points are above and some are below the least square line, which crosses through the distribution.
The least-square line model would not produce adequate results if, in a residual plot, the majority of the data points are located roughly in a straight line or on either side of the horizontal line.
A residual plot must have data points randomly distributed on both sides of the horizontal mean line in order to produce good results.
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COMPLETE QUESTION:
if the least-squares line provides a reasonable model for the data, the pattern of points in the plot will seem random and unstructured about the horizontal line at 0. is this the case for the residual plot?
1 . 10. A life insurance company found that among its last 200 claims, there were six dozen smokers. What is the ratio of smokers to nonsmokers in this group of claimants? Write in lowest terms
2. A woman threw 60 darts and hit the target a dozen times. What is her ratio of hits to misses? Write in lowest terms
3. . While watching television for one week, a consumer group counted 1240 acts of violence and 40 acts of kindness. What is the violence to kindness ratio for television, according to this group. Write in lowest terms
Answer for No.2
Answer: 1/4
Step-by-step explanation:
Hits = 12
Misses = 60-12 = 48
Ratio of hits to misses = 12/48 = ¼
So the answer is 1/4.
Can I get some help with this
The final velocity of a vehicle with a mass of 800kg is 20000 m/s.
What is velocity?The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity.The speed at which an object goes in one direction is known as its velocity. Speed may be used to calculate both the speed of the car traveling north on the major highway and the speed of the rocket bursting into space.So, calculate the final velocity as:
Formula: v = √u² + 2asWhere u is initial velocity, a is acceleration and s is displacement.Now, we know that:
u = 108 km/ha = 4 km/s²s = 50 kmInsert values in the formula and calculate as follows:
v = √u² + 2asv = √108² + 2(4)(50)v = √11,664 + 400v = √12,064v = 20000.022499991 m/sRounding off: v = 20000 m/s
Therefore, the final velocity of a vehicle with a mass of 800kg is 20000 m/s.
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(100 POINTS) HELP ASAP
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
y to the three fourths power, all over y to the one half power
the eighth root of y to the third power
the square root of y to the three fourths power
the fourth root of y
the square root of y
Answer:
[tex]^4\sqrt{2}[/tex]
Answer: Option C
Step-by-step explanation: just took the test.
An artist connects stained glass pieces with lead strips. In this rectangular window, the strips
are cut so that FH = 22 in. Find JG.
An artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
What is a rectangle?
A plane shape, as opposed to a square, with four straight sides and four right angles, particularly one with uneven neighboring sides.
Here, we have
FH ≅ GH
FH = EG = 22in
If diagonals bisect each other then, an artist connects stained glass pieces with lead strips
1/2(EG) = JG
1/2 (22) = JG
11 = JG
Hence, an artist connects stained glass pieces with lead strips and cut the strips so that FH = 22 in and JG = 11 in.
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Carrie visited two different pet adoption centers. At the first adoption center, the ratio of dogs to birds was 4:24. The ratio of dogs to birds at the second adoption center was equivalent.
Which is the ratio of dogs to birds at the second adoption center?
The ratio of dogs to birds at the second adoption center that are equivalent is 2:12.
What is a ratio?Ratio demonstrates how many times one number can fit into another number. They contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).
At the first adoption center, the ratio of dogs to birds was 4:24. The ratio will be:
= 4 / 24
= 1/6
= 1:6
Since the ratio of dogs to birds at the second adoption center is equivalent, this can be 2 to 12. This will be:
= 2/12.
= 1/6
= 1:6
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I need help like asap !!!
only numbers and decimal points
The value of c is 20.35 (approx).
What is Pythagorean Theorem?The Pythagorean Theorem states that the hypotenuse, or side opposite the right angle, of a right triangle, which is represented by the square, is equal to the sum of the squares on the legs of the triangle (or, in popular algebraic notation, a2 + b2 = c2).
Where is the Pythagorean theorem used?The following are some significant applications of the Pythagorean theorem in daily life: used in architecture and building, used to determine the shortest distance in two-dimensional navigation. used to measure how steep a mountain's or hill's slope is.
Let the other 2 sides of the triangle be named a and b
Given:- a = 15.5ft
b = 13.2ft
According to the Pythagorean Theorem, We know that
[tex]a^{2}+b^{2}=c^{2}[/tex]
By substituting the values of a and b we get
[tex]15.5^{2}+13.2^{2}=c^{2}[/tex]
[tex]c^{2}= 414.5\\c=\sqrt{414.5}\\ c=20.35[/tex]
c is the hypotenuse of the triangle.
Hence the value of c is 20.35
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5
The equation of a line is y=-x+9.
8
(a) What is the slope of a line parallel to it?
(b) What is the slope of a line perpendicular to it?
(a) The slope of a line parallel to it is. (Simplify your answer.)
(b) The slope of a line perpendicular to it is
(Simplify your answer.)
a. The slope of the line that is parallel to y = 5/8x + 9 is: 5/8.
b. The slope of the line that is perpendicular to y = 5/8x + 9 is: -8/5.
What is the Slope of Parallel and Perpendicular Lines?When two lines are parallel to each other, the lines will have the same slope value (m). However, if both lines are perpendicular to each other, they would have slope values that are negative reciprocals, meaning the product of their slope would be -1.
a. Given the equation, y = 5/8x + 9, the slope (m) of the line is 5/8.
Therefore, it implies that the line that is parallel to y = 5/8x + 9 will have a slope that is the same as 5/8.
Thus, the slope of the parallel line to the equation, y = 5/8x + 9, is: 5/8.
b. The negative reciprocal of 5/8 is -8/5.
Therefore, the slope of the line that is perpendicular to y = 5/8x + 9 would be: -8/5.
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M3L3
As Long, As Wide
David's kitchen has an area of 60 square feet. The kitchen is 6 times as many square feet as
David's pantry. If the pantry is 2 feet wide, what is the length of the pantry? ")
First find the area of the pantry.
Solve on paper and check you answer on Zearn. -->
The area of the pantry is square ft.
8
9
Enter ✓
The area of the David's pantry = 10 square feet.
The length of the pantry = 5 feet.
Define the term area of the rectangle?The territory inhabited by a rectangle inside its 4 sides or limits is known as its area. The area of such a rectangle is determined by its sides. Essentially, the formula calculating area is equivalent to the product of the rectangle's length and breadth.For the given question.
David's kitchen is 60 square feet in size. The kitchen is six times the size of the living room.Thus,
Area of kitchen = 6 x area of the pantry
60 = 6 x area of the pantry
area of the pantry = 60 / 6 = 10 square feet.
Area of the pantry = length x breadth
10 = length x 2
length = 10/2 = 5 feet.
Thus, the length of the pantry is found as the 5 feet.
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A golf ball is manufactured so that if it is dropped from A feet above the ground onto a hard surface, the maximum height of each bounce will be one half of the height of the previous bounce.
a. Find an exponential equation that gives the height h the ball will attain during the nth bounce.
h =
b. If the ball is dropped from 13 feet above the ground onto hard a surface, how high will it bounce on the 5th
bounce?
On the 5th bounce, the ball will reach a height of ____feet.
The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.
What is an exponent?Let a be the initial value and x be the power of the exponent function and b be the increasing factor.
The exponent is given as
y = a(b)ˣ
A golf ball is fabricated so that assuming it is dropped from A feet over the ground onto a hard surface, the most extreme level of each skip will be one portion of the level of the past bob.
Then the equation is given as,
h = a (1/2)ˣ
Where 'a' is the initial height.
The exponential equation that gives the height h the ball will attain during the nth bounce will be given as,
h = a (1/2)ⁿ
If the ball is dropped from 13 feet above the ground onto hard a surface. Then the height on the 5th bounce will be given as,
h = 13 (1/2)⁵
h = 13 x 1 / 32
h = 0.40625 feet
The height of the ball after the nth and 5th bounce will be a (1/2)ⁿ and 0.40625 feet, respectively.
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How many zeros are in the graph for x^3+8x^2+11x-20? How you know they are the zeros? What does this tell us about the graph?
Answer:
There are 2 zeros. You know they are zeros because they are the only two points that intercept the x-axis. There is one touch zero and one bounce zero, meaning there are both even and odd multiplicities in the graph.
a large animal preserve has noticed that an albino panther is born unpredictably once every 8 years; and that can happen at any time of the year. a) what are the expected value and standard deviation of the number of albino panthers which will be born in the next 40 years?
The expected value of the number of albino panthers is 5
The standard deviation of the number of albino panthers is 2.09
Given that albino panther is born once every 8 years, probability p, of one albino to be born in 8 years is 1/8
Expected value=n*p, where n is 40 years, and p=1/8
=40*1/8
=5 albino panthers
Hence, the expected value is 5 albino panthers
Standard deviation=(Expected value*(1-p))^1/2
=(5*(1-1/8))^1/2
=4.375^1/2
=2.09
Hence, standard deviation is 2.09
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Write the equation of the graph shown below in factored form.
a graph that starts at the top left and continues down through the x axis at negative one to a minimum around y equals negative twelve point two five and goes up to touch the x axis at two and the goes back down to a minimum around y equals negative one half and goes back up through the x axis at two.
f(x) = (x − 2)2(x + 1)(x − 3)
f(x) = (x + 2)2(x − 1)(x + 3)
f(x) = (x + 2)2(x + 1)(x + 3)
f(x) = (x − 2)2(x − 1)(x − 3)
The answer is
f(x) = (x - 1) 2(x +1)(x - 3 ).
Given equation
f(x) = (x − 2)2(x + 1)(x − 3)
f(x) = (x + 2)2(x − 1)(x + 3)
f(x) = (x + 2)2(x + 1)(x + 3)
f(x) = (x − 2)2(x − 1)(x − 3)
Factored form is a product of stayed and linear elements.
by checking of the red line cross the x-axis.it will give you the zero.
it passes at -1, touches at 1, and crosses again at 3.
This implies that the zeroes are -1, 1 and 3.
The factors 2(x+1), (x - 3), and (x - 1) must be evaluated.
Therefore the answer is
f(x) = (x - 1) 2(x +1)(x - 3 ).
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