Final answer:
The expression for the total cost is (3 × $2.00) + (2 × $1.50). After performing the calculations, the total cost for Mark's pretzels and juice is $9.00.
Explanation:
To calculate the total cost of the pretzels and juice that Mark bought, we need to multiply the quantity of each item by its price and then add the totals for each item.
The expression for the pretzels is 3 bags × $2.00 per bag, which equals $6.00. For the juice, the expression is 2 bottles × $1.50 per bottle, which equals $3.00. The total cost is the sum of these two amounts, so we have:
Total Cost = Cost of Pretzels + Cost of Juice
= (3 × $2.00) + (2 × $1.50)
= $6.00 + $3.00
= $9.00
Therefore, the total cost for the pretzels and juice is $9.00.
Charles Stickley's gross weekly pay is $925. His earnings to date for the year total $21,045. What amount is deducted weekly for Social Security taxes, if the tax rate is 6.2%?
Final answer:
The amount deducted weekly for Social Security taxes for Charles Stickley is $57.35.
Explanation:
The student's question is regarding the calculation of Social Security taxes based on a given gross weekly pay and applying the current tax rate.
Charles Stickley's weekly Social Security tax deduction can be calculated by multiplying his gross weekly pay by the Social Security tax rate of 6.2%.
Here's how to calculate it:
Identify the gross weekly pay, which is $925 in this case.Calculate the Social Security tax deduction by multiplying $925 by the tax rate of 6.2% (or 0.062).Perform the calculation: 925 x 0.062 = $57.35.Therefore, the amount deducted weekly for Social Security taxes is $57.35.
A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm. A solid oblique pyramid has a square base with edges measuring x centimeters. The height is (x + 2) centimeters. Which expression represents the volume of the pyramid?
The expression to represent the volume of solid oblique pyramid is (x³+2x²)/3.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, a solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x+2) cm.
We know that, the volume of square base pyramid is a²h/3
Now, x²(x+2)/3
= (x³+2x²)/3
Therefore, the volume of solid oblique pyramid is (x³+2x²)/3.
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The volume of the given solid oblique pyramid with a square base of edge length x cm and height (x+2) cm can be calculated using the formula for the volume of a pyramid, 1/3 * (base area) * (height). The volume can thus be represented by the expression 1/3 * x^3 + 2/3 * x^2 cm^3.
Explanation:The question refers to a solid oblique pyramid with a square base, where the edge length of the base is x, and the height is (x+2) cm. To calculate the volume of the pyramid, you can use the formula for the volume of a pyramid: 1/3 * (base area) * (height). For the given pyramid, the base is a square with side length x, so the area of the base is x*x or x^2. Because the height of the pyramid is (x + 2), we substitute into the formula to get: 1/3 * x^2 * (x + 2). Multiplying it out, the expression representing the volume of the pyramid is: 1/3 * x^3 + 2/3 * x^2 cm^3.
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The nth harmonic number is defined non-recursively as: 1 1/2 1/3 1/4 ... 1/n. Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named harmonic that accepts an int parameters n and recursively calculates and returns the nth harmonic number.
Answer:
57
Step-by-step explanation:
Tyler ordered a pizza to eat while he watches a movie. Before the movie began, he ate 1/4 of the pizza. During the movie, he ate another 3/8 Before storing the remaining pizza, he ate a final 1/16 of the pizza. How much leftover pizza does Tyler have.
Answer:
Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.
Step-by-step explanation:
Given:
Total pizza = 1
Pizza ate at First time = [tex]\frac{1}{4}[/tex]
Pizza ate at Second time = [tex]\frac{3}{8}[/tex]
Pizza ate at Final time = [tex]\frac{1}{16}[/tex]
We need to find find the amount of pizza left.
Now to find the Amount of Pizza left is equal to Total Pizza minus Pizza ate at First time minus Pizza ate at second time minus Pizza ate at Final time.
Framing in the equation form we get;
Amount of Pizza left = [tex]1- \frac{1}{4} -\frac{3}{8} -\frac{1}{16}[/tex]
Now Taking the LCM we get;
Amount of Pizza left = [tex]\frac{1\times16}{16}- \frac{1\times4}{4\times 4} -\frac{3\times2}{8\times2} -\frac{1\times1}{16\times1}= \frac{16}{16}- \frac{4}{16} -\frac{6}{16} -\frac{1}{16}= \frac{16-4-6-1}{16}= \frac{5}{16}[/tex]
Hence Tyler has [tex]\frac{5}{16}[/tex] Left over Pizza.
8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid ____.
in full, on time, every time
in even payments each time
at least the minimum due
as much as you can when due
9. APY means ____.
annual percentage yield
annual percentage yearly
apportioned percentage yield
applied percentage yield
Answer:
8. When starting your credit history, a low-credit-limit, high-interest-rate credit card should be paid in full, on time, every time.
9. APY means annual percentage yield.
Explanation:
8. A person's credit history tells about the ability of a person to pay and repay his debts. This is very important especially when you want to avail of a credit card from a company because it reflects on how responsible you are when it comes to repaying your debts. However, when you are just starting your credit history, it is important to give a good impression, so you'd have an easier approval in the future.
Usually, for starters with low salary, a low-credit-limit with a high-interest-rate credit card is common. It is very important to pay your debts in full, on time and every time in order to avoid incurring a balance that you will be carrying from one month to the other. If you do this, you will be ending up paying lots of interest charge.
Paying in full, on time and every time will also give you the chance to have an increased credit limit in the future.
9. APY is also known as "Annual Percentage Yield." This is the actual amount (rate of return) that a person could earn while his money is being deposited in the bank in one year. Other than the deposited money, investment that earns a rate of return could also refer to bonds and stock share. APY considers the compounding interest in its computation. This means that the higher your balance, the higher the APY. The value of the asset also increases.
Hank has a board 1.75 meters long. He used 0.8 meter to build the walls of a birdhouse. He used 0.4 of what is left for the floor. He needs 0.6 meter for the roof. Dies he have enough wood for the roof? Explain
Answer:No, he doesn't have enough wood for the roof.
Step-by-step explanation:
Total length of Hank's board is 1.75 meters. He used 0.8 meter to build the walls of a birdhouse. This means that the length of the board left would be
1.75 - 0.8 = 0.95 meters
He used 0.4 of what is left for the floor. This means that the length of the board left would be
0.95 - 0.4 = 0.55 meters
He needs 0.6 meter for the roof. Since he has only 0.55 meters left, then, he doesn't have enough wood for the roof.
Kevin, Dustin, and Mike collect baseball cards. Together Dustin and Kevin have 81 cards. If Dustin and Mike combined their cards, they would total 96. The sum of Kevin's and Mike's cards is 93. How many baseball cards do they each have? Show all of your mathematical thinking below.
Answer: Kelvin has 39 cards
Dustin has 42 cards
Mike has 54 cards
Step-by-step explanation: please see attachment for explanation
Please Help! Will give Brainliest for the correct answer. Given the function f(x) = x2 and k = -3, which of the following represents a vertical shift? (An explanation would be very helpful.)
1) f(x) + k
2) f(x + k)
3) f(kx)
4) kf(x)
Answer:
1) f(x) + k
Step-by-step explanation:
1) that would result in a vertical shift as the -3, would put parabola down 3
2) that would result in horizontal shift
3) That would change the original function
4) "kf" is not a function
Answer:
1) [tex]f(x)+k[/tex]Step-by-step explanation:
Givens
[tex]f(x)=x^{2}[/tex]
[tex]k=-3[/tex]
A vertical shift of this function is represeted by the first choice: [tex]f(x)+k[/tex].
Remember, when add or subtract units to the whole function, or the dependent variable (vertical axis), we are actually shifting the function vertically. So, the first option is adding units to the dependent variable because [tex]f(x)=y[/tex].
Therefore, the right answer is 1) [tex]f(x)+k[/tex]
David made a scale drawing of a mural he is going to paint. He used a scale of 1 cm=4ft. If the actual mural will be 16 feet long, how long is the mural in David's drawing
Answer:
4 cm
Step-by-step explanation:
we know that
The scale drawing is
[tex]\frac{1}{4}\ \frac{cm}{ft}[/tex]
That means ----> 1 cm in the drawing represent 4 ft in the mural
so
To find out the dimensions in the drawing, multiply the actual dimension by the scale drawing factor
so
[tex](16\ ft)(\frac{1}{4}\ \frac{cm}{ft})=4\ cm[/tex]
In an obtuse isosceles triangle the angle measurements are, x∘, x∘, and (10x−2)=128∘. Find the measurement of one of the acute angles.
Answer:
26°
Step-by-step explanation:
An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.
An isosceles triangle is a triangle that has two equal sides and angles.
Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).
Given:
The three angles of the triangle are given to be x°, x° and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°
The sum of angles in a triangle is 180°
∴ x° + x° + 128° = 180°
2x° = 180° - 128°
2x° = 52°
x° = 52° / 2
x° = 26°
The measurement of one of the acute angles is 26°
Solve for x in the equation x squared + 2 x + 1 = 17.
A) x = negative 1 plus-or-minus StartRoot 15 EndRoot
B) x = negative 1 plus-or-minus StartRoot 17 EndRoot
C) x = negative 2 plus-or-minus 2 StartRoot 5 EndRoot
D) x = negative 1 plus-or-minus StartRoot 13 EndRoot
Answer: B) x = negative 1 plus-or-minus StartRoot 17 EndRoot
Step-by-step explanation:
The given equation is x squared + 2 x + 1 = 17. It is written as
x^2 + 2x + 1 = 17
It is a quadratic equation. The general form of a quadratic equation is ax^2 + bx + c
Rearranging the given equation, it becomes
x^2 + 2x + 1 - 17 = 0
x^2 + 2x - 16 = 0
We will apply the general formula for quadratic equation. It is expressed as
x = [-b ± √(b^2 - 4ac)]/2a
From the equation,
a = 1
b = 2
c = -16
x = [-2 ± √(2^2 - 4×1×-16)]/2×1
x = [-2 ± √(4 + 64)]/2
x = (-2 ± √68)/2
x = (-2 ± 2√17)/2
x = (-2 + 2√17)/2 or x = (-2 - 2√17)/2
x = -1 + √17 or x = -1 - √17
Answer:
B) x = negative 1 plus-or-minus StartRoot 17 EndRoot i hope this was help
Step-by-step explanation:
Determine whether the function below is an even function, an odd function, both, or neither.
f(x)=(x+5)^2
A.
neither even nor odd
B.
even function
C.
both even and odd
D.
odd function
Answer:
A. neither even nor odd
Step-by-step explanation:
The equation is that of a parabola whose line of symmetry is x=-5. Even functions are symmetrical about the line x=0, so this is not an even function. It has terms of even degree, so is not an odd function.
The function is neither even nor odd.
Answer:
Option A - neither even nor odd
Step-by-step explanation:
Given : [tex]f(x)=(x+5)^2[/tex]
To find : Determine whether the function below is an even function, an odd function, both, or neither ?
Solution :
We know that,
1) If f(-x)=f(x) it is an even function.
2) If f(-x)=-f(x) it is a odd function.
[tex]f(x)=(x+5)^2[/tex]
[tex]f(x)=x^2+10x+25[/tex]
Substitute x with -x in the function,
[tex]f(-x)=(-x+5)^2[/tex]
[tex]f(-x)=x^2-10x+25[/tex]
The function does not comply with the definitions.
The function is neither even nor odd.
Therefore, option A is correct.
Suppose the newspaper states that the probability of rain today is 65%.
What is the complement of the event "rain today"?
rain yesterday
rain tomorrow
no rain today
no rain tomorrow
What is the probability of the complement?
The complement of 'rain today' is 'no rain today'. Its probability is 1 - the probability of 'rain today', which calculates to 35%.
Explanation:In probability theory, the complement of any event A represents 'not A'. In this context, the event is 'rain today', therefore the complement of the event would be 'no rain today'.
Probability of an event and its complement always add up to 1. Therefore, you can calculate the probability of the complement by subtracting the probability of the event from 1. So, the probability of the complement of the event 'rain today' is 1 - 0.65 which equals 0.35 or 35%.
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For her birthday, Kendra received a gift card in the mail from her grandparents. The gift card was worth $50. Kendra thought, since she had just received other gifts for her birthday, she would wait a while to spend the gift card. Unfortunately, Kendra forgot all about the gift card, and the card loses $5 every month after its date of purchase if it has not been used.
If Kendra forgot the card for three months, she lost $______.
a) 9 b) 10 c) 15 d) 12
Answer:
She lost $15 on her 50 dollar credit card.
Step-by-step explanation:
Kendra received a gift card in the mail from her grandparents. The gift card was worth $50.
Kendra forgot all about the gift card, and the card loses $5 every month after its date of purchase if it has not been used.
Kendra loses $5 each month,
She forget the card for 3 months.
So, Multiply the $5 by 3 months
$5×3=$15
Hence, she lost $15.
For the following inequality, indicate whether the boundary line should be dashed or solid. x ≤ 5 dashed solid.
Answer:
Solid
Step-by-step explanation:
Rewriting for the sake of clarity:
1) For the following inequality, indicate whether the boundary line should be dashed or solid. x ≤ 5
2) Since it is a closed interval which includes the number 5 then this can also be written as:
[tex](-\infty,5][/tex]
3) Hence, we can graph it as a solid line crossing the point (5,0). For the x coordinate 5, is within the interval.
Each day valerie charges her lunch account for her lunch. If the cost of lunch is $3 then by how much has her lunch account been impacted over a period of 15 days?
Answer: the amount by which her lunch account would have been impacted is $45
Step-by-step explanation:
Each day Valerie charges her lunch account for her lunch. If the cost of lunch is $3 then, it means that Valerie charges the lunch account with $3 daily. It means that in x days, she would have charged her lunch account with 3×x = $3x
If she charged her account for a period of 15 days, it means that x = 15. Therefore, the amount by which her lunch account would have been impacted is 3×15 = $45
In a certain high school, the probability that a student drops out is 0.07 , and the probability that a dropout gets a high-school equivalency diploma (GED) is 0.25 . What is the probability that a randomly selected student gets a GED?
Using probability concepts and the information given, it is found that there is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.
The percentages given are:
7% of the students drop out, and of those, 25% get a GED.100 - 7 = 93% of the students do not drop hence, meaning of those, 0%, that is, none need to get a GED, as they will have the graduation diploma.Hence:
[tex]p = 0.07(0.25) + 0.93(0) = 0.0175[/tex]
There is a 0.0175 = 1.75% probability that a randomly selected student gets a GED.
A similar problem also involving probabilities. is given at https://brainly.com/question/14398287
The probability that a randomly selected student gets a GED is 0.0175, or 1.75%.
Explanation:To find the probability that a randomly selected student gets a GED, we need to multiply the probability of a student dropping out (0.07) by the probability of a dropout getting a GED (0.25). This can be calculated using the formula:
Probability of getting a GED = Probability of dropping out * Probability of getting a GED if dropped out = 0.07 * 0.25 = 0.0175
Therefore, the probability that a randomly selected student gets a GED is 0.0175, or 1.75%.
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If AB is the diameter of the circle with center X and C is a point on the circle such that AC = AX = 3, what is the perimeter of triangle ABC ?
Answer:
Step-by-step explanation:
The perimeter of a shape or plane figure is the distance round the shape. The diagram of the circle and the triangle ABC formed is shown in the attached photo.
To determine the length of AC, we would apply the Pythagoras theorem which is expressed as follows
Hypotenuse^2 = opposite ^2 + adjacent ^2
AC = hypotenuse
Opposite = 3
Adjacent = 3
AC^2 = 3^2 + 3^2 = 9 + 9 = 18
AC = √18 = 4.24
BX = AX = 3(they are both radii)
BC = AC = 4.24
The perimeter of triangle ABC would be
3 + 3 + 4.24 + 4.24 = 14.48
the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx
Answer:
It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx
Step-by-step explanation:
Given function is a trignometric one
y = tanx
we have tanx has values 0 for all multiples of pi.
i.e. tan x =0 whenever [tex]x = 2n\pi[/tex] for all integers n.
Also tanx has a period of pi.
It is a discontinuous graph extending in one period from -pi/2 to pi/2.
Hence the mid point of each period is the x intercept.
It is true that the x-intercepts of y=tanx are the same as the x-coordinates of the center points of y=tanx
Final answer:
The x-intercepts of the function y=tan(x) are at integer multiples of π. The concept of 'center points' for y=tan(x) is not well-defined due to the nature of the function having no central axis and being periodic.
Explanation:
The student is inquiring about the x-intercepts and center points of the function y=tan(x). The x-intercepts of the tangent function occur wherever y=0, which happens at values of x that are integer multiples of π, as the tangent function has a period of π.
On the other hand, the concept of center points is not well-defined for the tangent function since it does not have a central axis like an ellipse or a bounded pattern. The tangent function is periodic and continuous between its vertical asymptotes, which occur at odd multiples of π/2.
On a farm A 4/5 of the number of sheep are equal to 1/2 of the number of sheep on farm B. The total number of sheep on farm A and farm B is 845. How many sheep are there on farm B
Answer:
There are 520 sheep on Farm B.
Step-by-step explanation:
Let the Number of sheep on farm B be x
Given:
On a farm A 4/5 of the number of sheep are equal to 1/2 of the number of sheep on farm B.
It means Number of sheep on farm A multiplied by 4/5 is equal to 1/2 multiplied by Number of sheep on farm B.
framing the equation we get;
[tex]\frac{4}{5}\times \textrm{Number of sheep on Farm A} = \frac{1}{2} \times x[/tex]
Number of sheep on Farm A = [tex]\frac{x}{2}\times\frac{5}{4} = \frac{5x}{8}[/tex]
Now Given:
Total Number of sheep =845.
We know that Total Number of sheep is equal to sum of sheep at farm A and sheep at farm B.
Framing equation we get;
[tex]\frac{5x}{8}+x=845[/tex]
Taking L.C.M we get;
[tex]\frac{5x\times 1}{8\times1}+\frac{x\times8}{8} =845\\\\\frac{5x}{8}+\frac{x}{8} =845\\\\\frac{5x+8x}{8}=845\\\\\frac{13x}{8}= 845\\\\13x=845\times8\\\\x=\frac{845\times8}{13} = 520[/tex]
Number of sheep on Farm B = 520 sheep
Number of sheep on Farm A = [tex]\frac{5}{8}\times 520 = 325\ sheep[/tex]
Hence There are 520 sheep on Farm B.
Need help doing this question! Thanks . = )
Answer:the boat will travel about 20.62 miles
Step-by-step explanation:
Since the boat travelled from dock A to dock B without passing and stopping at dock C along the way. The number of miles travelled would be the hypotenuse of the right angle triangle shown. To determine the number of miles travelled, we would apply Pythagoras theorem which is expressed as
Hypotenuse^2 = opposite side^2 + adjacent side^2
Looking at the triangle,
Opposite side = 13 miles
Adjacent side = 16 miles
Hypotenuse^2 = 13^2 + 16^2 = 425
Hypotenuse = √425 = 20.62 miles
A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:
the median from N
the right bisector of LP
the altitude from N
Answer:
Part A) [tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) [tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) [tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]
see the attached figure to better understand the problem
Step-by-step explanation:
we have
points L(-3, 6), N(3, 2) and P(1, -8)
Part A) Find the equation of the median from N
we Know that
The median passes through point N to midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment NM
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
N(3, 2) and M(-1,-1)
substitute the values
[tex]m=\frac{-1-2}{-1-3}[/tex]
[tex]m=\frac{-3}{-4}[/tex]
[tex]m=\frac{3}{4}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex]
[tex]point\ N(3, 2)[/tex]
substitute
[tex]y-2=\frac{3}{4}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{3}{4}x-\frac{9}{4}[/tex]
[tex]y=\frac{3}{4}x-\frac{9}{4}+2[/tex]
[tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) Find the equation of the right bisector of LP
we Know that
The right bisector is perpendicular to LP and passes through midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 3
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 4
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ M(-1,-1)[/tex] ----> midpoint LP
substitute
[tex]y+1=\frac{2}{7}(x+1)[/tex]
step 5
Convert to slope intercept form
Isolate the variable y
[tex]y+1=\frac{2}{7}x+\frac{2}{7}[/tex]
[tex]y=\frac{2}{7}x+\frac{2}{7}-1[/tex]
[tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) Find the equation of the altitude from N
we Know that
The altitude is perpendicular to LP and passes through point N
step 1
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 2
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ N(3,2)[/tex]
substitute
[tex]y-2=\frac{2}{7}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{2}{7}x-\frac{6}{7}[/tex]
[tex]y=\frac{2}{7}x-\frac{6}{7}+2[/tex]
[tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]
In June, Susie buys a dozen of cans of Dog's Dinner dog food at $1.89 per can. She also buys two bags of 'Dem Bones dental chews that each cost $12.69, and a new toy for $10.25. She pays sales tax at a rate of 7.25%. What is her total cost for the month of June?
Answer:
$62.54
Step-by-step explanation:
12 cans dog food = 12 × 1.89 = $22.68
2 bags dental chews = 2 × 12.69 = 25.38
1 toy = 10.25
Subtotal = 58.31
Sales tax = 0.0725 × 58.31 = 4.23
TOTAL = $62.54
Suzie's total cost for June was $62.54.
A chemist currently has a solution of 30% hydrochloric acid and a solution of 15% hydrochloric acid. He mixes the two solutions together to create 24 oz of a 25% hydrochloric acid solution. How many ounces of the 30% hydrochloric acid solution did he use in order to obtain the 25% solution
Answer:
16 ounces of the 30% hydrochloric acid solution is used in order to obtain the 25% solution.
Step-by-step explanation:
Let amount of 30% ounces be 'x' and that of 15% ounces by 'y'.
Given:
Total amount on mixing both the solution = 24 oz
∴ [tex]x+y=24\\x=24-y------------ 1[/tex]
Also, the total acid content in the resulting 25% solution is equal to the sum of the acid contents in 30% and 15% solutions.
∴ [tex]0.30x+0.15y=0.25(24)\\0.30x+0.15y=6-------2[/tex]
Now, plug in 'x' from equation (1) into equation (2). This gives,
[tex]0.30(24-y)+0.15y=6[/tex]
[tex]7.2-0.3y+0.15y=6[/tex]
[tex]-0.3y-0.15y=6-7.2[/tex]
[tex]-0.15y=-1.2[/tex]
[tex]y=\frac{1.2}{0.15}=8[/tex] ounces
Therefore, [tex]x=24-8=16[/tex] ounces
Hence, 16 ounces of the 30% hydrochloric acid solution is used in order to obtain the 25% solution
Lisa is interested in how well people are able to detect whether another person is a "Cooperator", a "Competitor", or an "Individualist" simply by looking at a picture of the person’s face. She wants to know what kind of face can be identified most easily, and whether this varies by the race of the person in the picture. She designs a 2 x 3 within-group design where she has participants in her study look at faces from African-American and Caucasian people who are "Cooperators", "Competitors", or "Individualists." The participants identify the personality of the person in each picture and Lisa keeps track of the number of pictures accurately identified for each picture type. How many cells was each participant in?
Answer:
The answer is 6.
Step-by-step explanation:
In the question it is stated that Lisa has designed a "within-group" or "within-subject" experiment using three categories with 2 subject in each category.
Within-group / within-subject experiments mean that every participant is tested for each condition of the experiment, so everyone goes through the same process.
Considering these informations, we can calculate that each participant was in 6 cells because there are 3 categories and 2 subjects for each of the categories.
I hope this answer helps.
A store sells hardcover books for $8 and paperback books for $5. You buy 7 books, represented by the equation x+y=7, where is the number of hardcover books and y is the number of paperback books. The equation 8x+5y=41 represents the total cost. How many of each type of book did you buy?
Answer:
Total number of Hardcover books is TWO while the number of Paperback books is FIVE
Step-by-step explanation:
No. of hardcover book = x
No. of paperback book = y
Cost of one hardcover book = $8
Cost of one paperback book = $5
We are given that:
x+y=7 (Equation 1)
8x+5y=41 (Equation 2)
We can find out value of x and y by solving both equations simultaneously.
[tex]Multiplying Equation 1 by 5:\\5x+5y=35\\8x+5y=41\\Subtracting both equations\\-3x=-6\\x=2\\\\According to Equation 1:\\x+y=7\\Putting value of x=2\\2+y=7\\y=5[/tex]
Hence, Total number of Hardcover books is TWO while the number of Paperback books is FIVE
A student bought a juice pouch forn$2.50 and 3 bags of chips. The total cost was $5.05.Write and solve an equation to determine the cost of a bag of chips,c
Answer:
The cost of a bag of chips is [tex]c=\$0.85[/tex]
Step-by-step explanation:
Let
c ----> the cost of a bag of chips
we know that
The cost of a juice pouch ($2.50) plus the cost of 3 bags of chips must be equal to $5.05
The cost of 3 bags of chips is equal to multiply 3 by its cost c
so
The linear equation that represent this situation is
[tex]2.50+3c=5.05[/tex]
solve for c
Subtract 2.50 both sides
[tex]3c=5.05-2.50[/tex]
[tex]3c=2.55[/tex]
Divide by 3 both sides
[tex]c=2.55/3[/tex]
[tex]c=\$0.85[/tex]
Rewrite with only sin x and cos x.
sin 2x - cos x
2 sin x cos2x
sin x
cos x (2 sin x - 1)
2 sin x
Answer:
cos x (2 sin x − 1)
Step-by-step explanation:
sin(2x) − cos x
Use double angle formula.
2 sin x cos x − cos x
Factor.
cos x (2 sin x − 1)
Final answer:
The expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
Explanation:
Given the expression sin 2x - cos x, we can rewrite it using only sin x and cos x. Using the trigonometric identity sin 2x = 2 sin x cos x, we can substitute it into the expression:
sin 2x - cos x = 2 sin x cos x - cos x
Factoring out the common factor cos x, we get:
sin 2x - cos x = cos x (2 sin x - 1)
So, the expression sin 2x - cos x can be rewritten as cos x (2 sin x - 1).
Mr. Nordman gets a commission of $2.30 on each pair of women's shoes he sells, and a commission of $3 on each pair of men's shoes he sells. To meet his sales targets, he must sell at least 10 pairs of women's shoes and at least 5 pairs of men's shoes. He also wants to make at least a $60 a week in commissions. Define the variables, write a system of inequalities to represent this situation, and name one possible solution.
Answer:
x ≥ 5
y ≥ 10
3x + 2.3y ≥ 60
Step-by-step explanation:
Lets the number of men's shoes he sells be x and women's shoes be y.
For each men's shoes , he gets a commission of $3 and for each women's shoe, he gets a commission of $2.30 .
He needs to sell atleast 10 women's shoes and 5 men's shoes.
Also he needs to make atleast $60 per week.
x ≥ 5
y ≥ 10
3x + 2.3y ≥ 60
These are are the 3 required inequalities.
Now we will see an example.
If he sells 20 womens shoes and 10 mens shoes , he will meet the requirements.
He will make a total profit = [tex]2.3\times 20 + 3\times 10[/tex] =$76
A boy thinks he has discovered a way to drink extra orange juice without alerting his parents. For every cup of orange juice he takes from a container of orange juice, he pours one cup of water back into the container. If he completes this process three times on the same container of juice, the resulting mixture will be exactly 50% water and 50% juice. How many cups of orange juice were originally in the container. (P.S ITS NOT 6)
Answer:
4.847 cups
Step-by-step explanation:
Let's say x is number of cups of orange juice originally in the container.
The boy takes 1 cup of orange juice out, so there is x−1 cups left out of a total volume of x cups. So the new concentration in the container is:
(x − 1) / x
Next, he takes another cup out, but this time, it isn't 100% orange juice any more. So the number of cups of orange juice left in the container is x − 1 − (x − 1) / x. The total volume is still x cups, so the new concentration is:
[x − 1 − (x − 1) / x] / x
Repeating this logic, after he replaces the third cup with water, the final concentration is:
{x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
This final concentration is equal to 1/2.
1/2 = {x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x} / x
1/2 x = x − 1 − (x − 1) / x − [x − 1 − (x − 1) / x] / x
1/2 x² = x (x − 1) − (x − 1) − [x − 1 − (x − 1) / x]
1/2 x² = x (x − 1) − (x − 1) − (x − 1) + (x − 1) / x
1/2 x² = x (x − 1) − 2 (x − 1) + (x − 1) / x
1/2 x³ = x² (x − 1) − 2x (x − 1) + (x − 1)
1/2 x³ = x³ − x² − 2x² + 2x + x − 1
0 = 1/2 x³ − 3x² + 3x − 1
0 = x³ − 6x² + 6x − 2
Using a calculator to solve this:
x = 4.847
There are originally 4.847 cups in the container.