Answers
Answer:
Priya: S=20w+50
Vanessa: S=25w+20
6 weeks
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Part aDefine the variables:
Let w be the number of weeks.Let S be the total savings (in dollars).Given that Priya starts with $50 in her bank account, the y-intercept of the linear equation modelling her savings will be 50.
If she then deposits $20 each week for 12 weeks, the slope will be 20.
Therefore, the linear equation that models Priya's savings is:
[tex]S=20w+50[/tex]Given that Vanessa starts with $20 in her bank account, the y-intercept of the linear equation modelling her savings will be 20.
If she then deposits $25 each week for 12 weeks, the slope will be 25.
Therefore, the linear equation that models Vanessa's savings is:
[tex]S=25w+20[/tex]Part bCreate a table for each linear equation from part a.
Priya Vanessa
[tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&70 \\\cline{1-2} 2& 90\\\cline{1-2} 3&110 \\\cline{1-2} 4&130 \\\cline{1-2} 5& 150\\\cline{1-2} 6&170 \\\cline{1-2} 7&190 \\\cline{1-2} 8&210 \\\cline{1-2} 9&230 \\\cline{1-2} 10&250 \\\cline{1-2} 11& 270\\\cline{1-2} 12& 290\\\cline{1-2} \end{aligned}[/tex] [tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&45 \\\cline{1-2} 2& 70\\\cline{1-2} 3& 95\\\cline{1-2} 4& 120\\\cline{1-2} 5& 145\\\cline{1-2} 6& 170\\\cline{1-2} 7& 195\\\cline{1-2} 8& 220\\\cline{1-2} 9& 245\\\cline{1-2} 10& 270\\\cline{1-2} 11& 295\\\cline{1-2} 12&320 \\\cline{1-2} \end{aligned}[/tex]
Create a graph for each linear equation (see attachment).
Part cThe week in which Priya and Vanessa will have the same amount of savings is the week where the S-values in the tables are the same, and the point of intersection of the graphed lines.
Therefore, from inspection of the tables and graphs from part b, Priya and Vanessa will have the same amount of savings in week 6.
Related Questions
Are the whole numbers closed under subtraction justify with example?
Answers
The whole numbers are closed under subtraction only by distributive property else they are not closed under subtraction.
Whole numbers constitute natural numbers including zero. The subset is given by {0, 1, 2, 3, 4, 5, …}, the set does not include fractions, decimals, and negative integers. The set of whole numbers is represented by ‘W’={0, 1, 2, 3, 4, 5, …...}
To check if the whole numbers are closed under subtraction or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.
Let us consider each property one by one -
1. The closure property-
let's take two whole numbers say 5 and 2.
now 5-2=3, but 2-5= -3 which is not a whole number.
Thus, whole numbers are not closed under subtraction by closure property.
2. The commutative property-
let's take two whole numbers say 5 and 2.
now 5-2=3 and 2-5=-3
hence, we get 2-5 ≠ 5-2.
Thus, whole numbers are not closed under subtraction by commutative property.
3. The associative property-
let's take three whole numbers say 5, 3, and 2.
now (5-3)-2 = 0 and 5-(3-2)= 4
hence, we get (5-3)-2 ≠ 5-(3-2).
Thus, whole numbers are not closed under subtraction by associative property.
4. The distributive property-
let's take three whole numbers say 20, 6, and 5.
now, 20 × ( 6 – 5 ) = 20 × 6 – 20 × 5 = 20
and 20 × ( 6 – 5 ) = 20 × 1 = 20
Hence, 20=20.
Thus, whole numbers are closed under subtraction only by distributive property.
Hence, we can conclude that whole numbers are closed under subtraction only by distributive property.
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A unicorn daycare center requires there to be 222 supervisors for every 181818 baby unicorns. Write an equation that shows the relationship between nnn, the number of supervisors, and uuu, the number of baby unicorns. Please note that this is a magical daycare center, so fractional supervisors are allowed.
Answers
The number of supervisors for baby unicorns is 9 times the number of unicorns.
Let 'n' be the number of supervisors.
Let there be u number of unicorns.
A unicorn daycare center needs two supervisors for every 18 unicorns, according to the question.
As a result, mathematically, it is stated as
9/u = 2/18
9n = u
As a result, the relationship between the number of supervisors and unicorns was established.
Hence, there are nine times as many supervisors as unicorns.
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The graph of y=f(x) is graphed below. What is the end behavior of f(x)?
Answers
The graph of y = f(x) has end behavior as x ⇒ ∞, y ⇒ - ∞ and
as x ⇒ - ∞, y ⇒ ∞.
What is the end behavior of a polynomial?A polynomial function's final behavior is how its graph behaves as x gets closer to positive or negative infinity.
The graph's final behavior is determined by a polynomial function's degree and leading coefficient.
The given function f(x) has end behavior as x approaches infinity y approaches negative infinity and as x approaches negative infinity y approaches infinity.
As when x value is positive y value is negative and when y value is negative x value is positive.
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The function y = 6.25x describes the amount of
money y Peter gets paid after x hours. Graph the
function. Use the graph to estimate how much
money Peter gets paid after 7 hours.
Answers
The money that Peter gets paid after 7 hours is 43.75
What are Functions?
A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).
Solution:
The question given is quite straight forward.
Sinec, we are given with the function y = 6.25x
where x is the hours and y is the pay
To find the pay for 7 hrs
we need to replace x by 7
y = 6.25 * 7
y = 43.75 units
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1st question ,easy answer
Answers
Answer:
a
Step-by-step explanation:
Answer:
The answer is: A. Hope it helps.
find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative.) f(x)
Answers
The given function is x² - 7x + 5 and the most general antiderivative of the function is F(x) = x³/3 - 7x²/2 + 5x + c.
The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;
F(x) = ∫f(x)dx
From the question, f(x) = x² - 7x + 5
Therefore,
F(x) = ∫x² - 7x + 5
F(x) = x³/3 - 7x²/2 + 5x + c
Where c is the constant of the integration (antiderivative).
The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.
Therefore, F(x) = x³/3 - 7x²/2 + 5x + c is the most general antiderivative of the function.
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55% prefer oda over port drink. Of thoe who prefer port drink, 61% alo prefer coffee over tea, while 51% who enjoy oda prefer tea over coffee. What percentage of all cutomer prefer port drink and tea
Answers
The percentage of all customers prefer port drink and tea is 17.55%. The result is obtained by multiplying the two percentages of the data.
How to calculate the percentage?We have a number of customers.
55% prefer soda over port drink.61 % who prefer port drink also prefer coffee over tea.51% who prefer soda also prefer tea over coffee.Of all customers, find the percentage that they prefer port drink and tea!
If 55% prefer soda over port drink, then the ones who prefer port drink is
100% - 55% = 45%
Of the customers who prefer port drink, 61% prefer coffee over tea. So, the ones who prefer tea is
100% - 61% = 39%
From that information, we can get the ones who prefer port drink and tea. Let's say pt = port drink and tea.
pt = 39% × 45%
pt = 0.39 × 0.45
pt = 0.1755
pt = 17.55%
Hence, of all customers, the percentage who prefer port drink and tea is 17.55%.
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What is the simplified form of the following expression? assume x greater-than-or-equal-to 0 and y greater-than-or-equal-to 0.
Answers
The simplified form would be 338√x -72√2y.
If a fraction's top and bottom share only one additional common factor, it is said to be in its simplest form. In other words, the top and bottom cannot be divided further and remain full numbers.
The simplest form is also referred to as "lowest words."
the given expression is :
2(4√16x) - 2(4√2y) + 34√81x - 4(4√32y)
⇒ 8(√16x) - 8(√2y) + 34√81x - 16√32y
⇒8×4√x - 8√2y + 34×9√x - 16√16×2y [∵ √16 = 4 and √81 = 9]
⇒32√x - 8√2y + 306√x - 16×4√2y
⇒(32√x + 306√x) - 8√2y - 16×4√2y
⇒338√x -72√2y
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Evaluate the function graphically.
Answers
By evaluating the function graphically , f (4) = -4
What is a function ?An expression, rule, or law in mathematics that establishes the relationship between an independent variable and a dependent variable (the dependent variable).
How to represent Function Graphically ?The x-axis is indicated with the input values. The vertical displacement from the x-axis is the appropriate output value for any input value. For instance, the output is identical to f when x = a. (a).
According to the Given information
f( x ) = y
where x is an input and y is an output
We need to find the value for f(4)
f( 4 ) = y
For x = 4 we have a corresponding value at y axis as -4 in fourth quadrant
f (4) = -4
By evaluating the function graphically , f (4) = -4
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what is the vaule expression of m4 - 11 when m = 3
Answers
Answer:
m4 - 11 = 1
Step-by-step explanation:
Given information,
→ m4 - 11
→ m = 3
Now the value of expression is,
→ m4 - 11
→ (3)4 - 11
→ 12 - 11 = 1
Hence, value of expression is 1.
(3x4)-11
12-11
=1
Hope this helps
Help with this substitution problem
3x-3y=-12
y=2x-9
Answers
Triangles a b c and d b c share common side b c. sides a c and c d are congruent. in order to prove △abc ≅ △dbc by sas, what additional information must be given? ∠abc ≅ ∠dbc ab ≅ db ∠acb ≅ ∠dcb bc ≅ bc
Answers
Answer:
(c) ∠acb ≅ ∠dcb
Step-by-step explanation:
You want to know what additional information is required to show ∆abc ≅ ∆dbc by SAS, given ac ≅ dc.
SASThis postulate tells you triangles are congruent if two corresponding sides are congruent, and the angles between them are congruent.
In the given geometry, the corresponding sides are given as congruent, so the additional information required is that the angles between them are congruent.
The angle between sides ac and bc is ∠acb.
The angle between sides dc and bc is ∠dbc.
The additional information required is ...
∠acb ≅ ∠dcb . . . . . matches choice C
<95141404393>
Help me on this please and thank you
Answers
Answer:
The probability for the green one is 6/10
and for the next one, it is 4/10
Step-by-step explanation:
a student believes that the average grade on the final examination in statistics is at least 85. she plans on taking a sample to test her belief. the correct set of hypotheses is
Answers
By using testing of hypothesis, it can be concluded that-
The correct set of hypotheses is
[tex]H_0 : \mu \geq 85[/tex]
[tex]H_a : \mu < 85[/tex]
What is testing of hypothesis?
Suppose there is a data at hand and there is a hypothesis to be tested. Testing of hypothesis determines whether the given hypothesis can be supported with the data at hand.
A student believes that the average grade on the final examination in statistics is at least 85.
The null hypothesis is [tex]\mu \geq 85[/tex]
The alternative hypothesis is [tex]\mu < 85[/tex]
So, the correct set of hypotheses is
[tex]H_0 : \mu \geq 85[/tex]
[tex]H_a : \mu < 85[/tex]
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Ty get spends 25 mins studying mathematics 35 minutes study science and 20 mins studying history
Answers
Answer:
1 hour and 20 minutes I think
Step-by-step explanation:
add all of them up then divide by 60
A function has a degree of 8. It has two x-intercepts, one of multiplicity 1 and one of multiplicity 3. How many imaginary zeros does the function have?
Answers
Answer:
two or four
Step-by-step explanation:
Any degree-X polynomial can have up to 8 zeros (some of them can have multiciplity higher than 1).
The polynomial can be written as:
f(x) = (x-a)(x-b)(x-c)(x-d)(x-e)(x-f)(x-g)(x-h)
and we're already told that there are 2 x-intercepts, one with multiplicity 1. Let's assign those x-intercepts a and b=c=d (multiplicity 3).
We're left with (x-e)(x-f)(x-g)(x-h), where e, f, g and h need to be non-real complex numbers (otherwise they'd provide x-intercepts).
The complex zeros (more accurate term than imaginary) must come in pairs - if a number c is a zero of the function, its conjugate is a zero too. That means that we need to have an even number of complex zeros.
We can either have 4 distinct complex zeros, or 2 complex zeros, each with multiplicity of 2.
A kangaroo hops 9 kilometers in 3 minutes. At this rate: How far does the kangaroo to travel in 1 minute?
Answers
Answer:
3 km
Step-by-step explanation:
Dividing by 3, the kangaroo travels 3 km in 1 min.
To indirectly measure the distance across a river, Carson stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Carson draws the diagram below to show the lengths and angles that he measured. Find P R PR, the distance across the river. Round your answer to the nearest foot.
Answers
Using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.
What is a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
ABC refers to a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
So, the triangles PRE and POC appear to be comparable triangles in the diagram.
Utilizing the similarity theorem:
PR/RE = PR+RO/OC
x/135 = (x+140)/230
By cross-multiply:
230x = 135(x+ 140)
230x = 135x + 18,900
230x - 135x = 18,900
95x = 18900
x =18900/95
x = 198.94
Therefore, using the given triangle shown in the image, we know that the PR, the distance across the river is 198.94ft.
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Correct question:
To indirectly measure the distance across a river, Nolan stands on one side of the river and uses sight lines to a landmark on the opposite bank. Nolan draws the diagram below to show the lengths and angles that he measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.
The equation for line q is 3x + 5y 10, Line r is parallel to line q and passes through the
point (5,-4).
Write the equation for line r in slope-intercept form.
Answers
The equation of line r which is parallel to line q and passes through point (5,-4) is y = (-3/5)x - 1.
What is the equation for line r in slope-intercept form?The slope-intercept form is expressed as;
y = mx + b
The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Given the data in the question;
Equation of line q : 3x + 5y = 10Point: (5,-4)Equation line r = ?First, determine the slope of the line q using the slope intercept-form.
y = mx + b
3x + 5y = 10
5y = -3x + 10
y = (-3/5)x + 10/5
y = (-3/5)x + 2
Hence;
Slope of line q m = -3/5
Since, line r is parallel to line q, they both have the same slope.
Therefore, slope of line r will be m = -3/5
Now, plug the point (5,-4) and and slope m = -3/5 into the point slope formula and solve for y.
y - y₁ = m( x - x₁ )
y - (-4) = (-3/5)( x - 5 )
y + 4 = (-3/5)x + 3
y = (-3/5)x + 3 - 4
y = (-3/5)x - 1
Therefore, the equation of line r is y = (-3/5)x - 1.
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Quadrilateral GHIJ is similar to quadrilateral
KLMN. Find the measure of side MN. Round
your answer to the nearest tenth if necessary.
Answers
Based on the definition of similar quadrilaterals, the measure of side MN is: 14.1 units.
What are Similar Quadrilaterals?If two quadrilaterals are similar to each other, then the measure of their corresponding sides will have a ratio that is equal. This means they will have proportional side measures.
Since we are told that quadrilaterals GHIJ and KLMN are similar to each other, then their corresponding sides will have measures that are proportional to each other.
Therefore:
IJ/MN = GJ/KN
IJ = 35
MN = ?
GJ = 52
KN = 21
Substitute:
35/MN = 52/21
Cross multiply:
MN(52) = (35)(21)
MN(52) = 735
MN = 735/52
MN = 14.1 units
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The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards. Enter the function f(x) that describes the area, in square yards, as a function of the width, x.
f(x) = _____
Answers
f(x) = Area = (length)(width)
width = x
The length is 16 yards greater than 3 times x
length = 3x+16
f(x) = (3x+16)(x) = 3x^2 + 16x
Answer:
f(x) = 3x² + 16xStep-by-step explanation:
We have been given that -- The length of a rectangular parking lot is 16 yards greater than 3 times its width, x, in yards
Length of parking lot is 16 + 3x
Width of parking lot is x
We have to write the function f(x) that describes the area, in square yards, as a function of the width, x
Area of rectangle is Length × width
[tex] \sf Area = f(x) [/tex]
put value of length and width here,
[tex] \sf f(x) = (16 + 3x)(x )[/tex]
[tex] \sf f(x) = 3x^2 + 16x [/tex]
Therefore, f(x) = 3x² + 16x
Which numbers are less than –8/3? Select all that apply.
Answers
The number which is less than that of -2.67 are -2.8, -2.9, -3.0.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
Which numbers are less than –8/3 = -2.67
So given in the option which is less than -2.67
Numberless -2.7 are
-2.8, -2.9, -3.0.
Hence the number is less than that of -2.67 are -2.8, -2.9, -3.0.
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Complete Question.
Which numbers are less than-8/3 Select all that apply.
A. -2.6 (repeating)
B.-2.76
C.-2 1/4
D. -11/4
E. -2
Show y=2x-7 on a graph
Answers
Answer:
Step-by-step explanation:
you could do is buy 2x on the x-axis
What is the slope perpendicular to Y =- 7?
Answers
The slope of a line perpendicular to Y =-7 is 7. We may use this as a substitution in the inverse slope formula because the slope of Y = -7 is -1.
To find the slope of a line perpendicular to Y = -7, we need to use the inverse slope formula.
The inverse slope formula is m = -1/m1
where m1 represents the original line's slope.
We may use this as a substitution in the inverse slope formula because the slope of Y = -7 is -1.
m = -1/-1
This simplifies to m = 1.
As a result, a line's slope that is perpendicular to Y = -7 is 7.
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- A game show host has developed a new game called "Grab All Can." Here's how it works: a contestant reaches his dominant hand (i.e. right hand for right-handed people) into a jar of $10 bills and grabs as many as he can in one handful. Then he does the same thing with his non-dominant hand in a jar of $20 bills. Research with many volunteers has determined that the mean number of $10 bills drawn is 68 with a standard deviation of 9.5, and the mean number of $20 dollar bills is 58, with a standard deviation of 7.8.
(a) If D-the amount of money, in dollars, that a randomly-selected contestant grabs from the "$10 grab,"
find the mean and standard deviation of D.
Please help. I’m so confused
Answers
The mean and the standard deviation of D are given as follows:
Mean: $680.Standard deviation: $95.How to obtain the mean and the standard deviation of D?Variable D is the average amount of money earned, and the number of $10 bills grabbed has the distribution with mean and standard deviation given as follows:
Mean of 68.Standard deviation of 9.5.(as stated in the problem).
We want now the mean and the distribution for the total amount of money, meaning that the entire distribution is multiplied by 10, and thus:
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The point (5,4) is not a solution to the inequality. Why? Explain your reasoning using the graph and using algebra
Answers
By using algebra (5, 4) is not a solution of the inequality.
Boundary does not contain in the given graph this is the error was made when graphed.
What is inequality?
In mathematics, inequalities describe the relationship between two values that are not equal. Equal means to be equal, not. The "not equal symbol (≠)" is typically used to indicate that two values are not equal. But different inequalities are used to compare the values to determine whether they are less than or greater than.
Consider, the given inequality
x + 2y ≤ 12
Here the inequality contain ≤ .
Since, if there is ≤ sign then graph must contain boundary line.
The boundary line is solid line need to use in the graph.
But in the given graph the boundary line is dotted.
Boundary does not contain in the graph.
Hence, this is the error was made when graphed.
Also from graph we can see that the point (5, 4) is not contain in the graph.
Hence, (5, 4) is not a solution of the inequality.
Now prove by using algebra.
Plug x = 5, y = 4 in the given inequality
⇒ 5 + 2(4) ≤ 12
5 + 8 ≤ 12
13 ≤ 12
It is not possible that 13 ≤ 12.
Hence, (5, 4) is not a solution of the inequality.
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please help, answers only!!
Answers
Answer:
Step-by-step explanation:
slope=-5/4
b=5
y=-5/4x+5
(4+6)x5x5-2 (four plus six)times 5 times 5 subtracted by 2
Answers
Answer: 248
Step-by-step explanation: First, you add 4 + 6 to get 10, then you multiply that by 5 to get 50. Then you multiply 50 by 5 to get 250, so 250-2 = 248. I hoped this solved your problem.
Answer:
248
Step-by-step explanation:
(4+6)x5x5-2
10x5x5-2
50x5-2
250-2
248
(if wrong sorry)
which graph best represents the equation y=1.5x-2?
Answers
The graph is given below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = 1.5x - 2
We can have the following coordinates on the graph.
x = 1, y = 1.5 - 2 = -0.5
(1, -0.5)
x = 2, y = 3 - 2 = 1
(2, 1)
x = 3, y = 4.5 - 2 = 2.5
(3, 2.5)
x = 4, y = 6 - 2 = 4
(4, 4)
And so on.
The graph of y = 1.5x - 2 is given below.
Thus,
Some of the coordinates on the graph are:
(1, -0.5), (2, 1), (3, 25), (4, 4), and so on.
The graph is given below.
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what is the slope of line perpendicular to the line whose equation is y=-2/3x-5
Answers
Answer: 3/2
Step-by-step explanation:
Let's start with what we know. For a slope to be perpendicular it is the - reciprocal. So:
-2/3's negative reciprocal is
3/2