Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Given equation: [tex]\frac{3}{4}y + \frac{1}{2} = 3 \frac{1}{4}[/tex]
In the given equation, [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable.
coefficient is a constant number or quantity multiplied to a variable in an algebric expression. Like in the above equation [tex]\frac{3}{4}[/tex] is a coefficient and y is the variable. We use term variable for y as its value may vary or change. If variable does not have any coefficient in any expression then in that case, we consider 1 as coefficient, for example: [tex]x+4[/tex], here variable have 1 as coefficient.
Hence, the fractional coefficient is [tex]\frac{3}{4}[/tex].
Final answer:
The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.
In the given equation, the fractional coefficient is 3/4, which is the fraction that multiplies the variable y.
Explanation:
The fractional coefficient in the equation 3/4y+1/2=3 1/4 is 3/4.
In the equation 3/4y + 1/2 = 3 1/4, the fractional coefficient refers to the fraction that is multiplied by the variable y.
In this case, the coefficient is 3/4.
When working with algebraic expressions and equations, understanding how to identify and manipulate coefficients is essential for problem-solving.
The student's query seems to be aimed at identifying the coefficient of the variable in the equation. In algebra, fractions like 3/4 can be seen as coefficients when they are directly next to a variable.
No unit cancellations are needed here as the question pertains to pure algebra and not to unit conversions or applied mathematics.
Write each decimal as a fraction or a mixed number in simplest form.
Answer:
what decimals?
Step-by-step explanation:
the average cost of jeans in the us is around $50. if the cost of jeans increases by 2% per year, what will be the cost of jeans in 25 years? what did jeans cost 20 years ago?
$ 82.03 in 25 yrs
$ 74.30 in 20 yrs
Step-by-step explanation:
Every year, the cost of the jeans increases by 2% which is equivalent to 0.02 in decimal points. The get the cost of the jean for every year we are multiplying the principle cost by;
100 % + 2% = 102% OR 1.02 in decimal
This increase occurs 25 time for 25 years. Therefore;
1.02 ^ 25 * 50
= 1.641 * 50
= $ 82.03
To get the price in 20 years;
1.02 ^ 20 * 50
= 1.486 * 50
= $ 74.30
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Solve the equation.
9x + 33 = -30
Answer:
x=-7
Step-by-step explanation:
Subtract 33 from -30 (because subtraction is the opposite of addition.
that's leaves 9x=-63
you want to isolate the variable so divide -63 by 9 (since division is the opposite of multiplication)
x=-7
Simplify negative 2 and 1 over 9 – negative 4 and 1 over 3.
Answer:The answer can be calculated by doing the following steps;
Step-by-step explanation:
Answer:
the Answer should be 2 2/9
Step-by-step explanation:
I can assure you i i worked this problem out and i'm 100% sure :) Hope i helped some of ya'll! :>
in th fig , d is the mid point of ab and cd is perpendicular to ab. prove abc is congurence to bcd.
Statement Reason
-------------------------------------------------------------------------------------
1. CD=DC Reflexive Property
2. D-midpoint of AB Given
3. AD=BD Definition of Midpoint
4. CD⊥AB Given
5. m<CDA=m<CDB Definition of Perpendicular Lines
6. ΔACD≅ΔBCD SAS
At a meeting with 25 businessmen, twelve businessmen drank coffee, and ten businessmen drank tea. Five businessmen drank both coffee and tea. How many businessmen drank neither coffee nor tea?
Answer:
Step-by-step explanation:
25 total people
5 drank coffee and tea
tea drinkers only : 10 - 5 = 5
coffee drinkers only : 12 - 5 = 7
total people who drank anything : 7 + 5 + 5 = 17
number of people who drank neither : 25 - 17 = 8 <=====
What is the verbal description for y=3x-2
Answer:
Y equals three x minus two
Final answer:
The equation y = 3x - 2 represents a line with a slope of 3 and a y-intercept of -2.
Explanation:
The equation y = 3x - 2 represents a line in the Cartesian coordinate system. This equation follows the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope (m) is 3, meaning that for every one unit increase in x, y increases by 3 units.
The y-intercept (b) is -2, indicating that the line crosses the y-axis at the point (0, -2). To find an equation for a line given a point and a slope, you can use the point-slope form, y - y1 = m(x - x1). With the point (-7, 1) and slope 3, the equation is y - 1 = 3(x + 7).
How can you express 5 1/3 + (-7 2/3) as the sum of its integer and fractional parts
Answer:
-7/3
Step-by-step explanation:
-7 2/3=-23/3
5 1/3=16/3
-----------------
16/3+(-23/3)
16/3-23/3
-7/3
Final answer:
To express 5 1/3 plus (-7 2/3), separate and add the integers to get -2, then add the fractions to find -1/3, resulting in the final expression -2 1/3.
Explanation:
To express the sum of 5 1/3 and (-7 2/3) as the sum of its integer and fractional parts, we need to perform the following steps:
First, separate the integers from the fractions: 5 + 1/3 and -7 + (-2/3).Now, add the integers: 5 + -7 = -2.Next, add the fractions: 1/3 + (-2/3). Recall that subtracting a negative is the same as adding a positive, so this becomes 1/3 - 2/3 = -1/3.Combine the integer and fractional results to get the final expression: -2 1/3.Our intuition about addition and subtraction of fractions can be helpful in visualizing the mixing of different pie pieces to form a whole, and understanding how changing the sign affects the direction of the operation.
For a large batch of cupcakes, the robots use 1/5 of a gallon of milk. They pour it into two separate cups , each the same size. How much milk goes into each measuring cup?
Answer:
12.8oz.
Step-by-step explanation: 128 oz in a gallon/5/2
Michelle receives 32K per year as an assistant fast food manager. Her benefits include health insurance, paid holidays, retirement contributions, and a 2-week paid vacation each year. Because she wears a uniform, Michelle calculates that she saves $2,500 on clothing costs per year. She constructed this table to show the value of each benefit. What is her annual salary, including benefits?
Michelle's annual salary, including benefits, is $43,330.
Explanation:To calculate Michelle's annual salary, we need to add up her base salary and the value of her benefits. Based on the information given, her base salary is $32,000 per year. In addition, her benefits include health insurance, paid holidays, retirement contributions, and a 2-week paid vacation, as well as saving $2,500 on clothing costs. Let's calculate the value of these benefits:
Health insurance: This benefit is not given a specific value, so we will assume a typical cost of $5,000 per year. (Note: This is an assumption and may vary depending on the specific circumstances).Paid holidays: Assuming 10 paid holidays per year, at an average daily rate of $100, the value of this benefit is $1,000.Retirement contributions: Assuming a 5% contribution from Michelle's salary, the value of this benefit is $1,600.2-week paid vacation: Assuming Michelle's base salary is $32,000 per year, the value of a 2-week paid vacation is $1,230 (($32,000/52)*2).Savings on clothing costs: As given, Michelle saves $2,500 on clothing costs per year.Now let's add up the base salary and the value of the benefits:
Base salary: $32,000
Health insurance: $5,000
Paid holidays: $1,000
Retirement contributions: $1,600
2-week paid vacation: $1,230
Savings on clothing costs: $2,500
Total annual salary, including benefits: $43,330
If a reflection takes triangle CAT to C'A'T', what is A'C'?
triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of 3 units, side TC has a measure of 4 units, and side AC has a measure of 5 units
3
4
5
Cannot be determined
Answer:
The length of A'C' will also be 5 units.
Step-by-step explanation:
If a reflection takes triangle CAT to C'A'T', what is A'C'?
Starting with ΔCAT triangle as shown in figure (a).
Reflections are said to be Isometries as it does preserve the distances.
If the shape or triangle ΔCAT reflected it will remain the same size. As a result, the reflected image would be 'congruent' to the original object.
Lets suppose, ΔCAT is reflected across y axis.
The rule for reflection of the point (x,y) across the y-axis is actually the point (-x,y).
Reflect a point across the y-axis, the y-coordinate will remain the same, but the x-coordinate will be transformed into its opposite (the sign of x-coordinate will be changed).
C(0, 0) → C'(0, 0)
A(-2, 1) → A'(2, 1)
T(-1, 4) → T(1, 4)
length of Side AT = 3 units
length of Side TC = 4 units
length of Side AC = 5 units
As reflections are said to be Isometries as it does preserve the distances.
So, if ΔCAT reflected is reflected across y axis. ΔC'A'T' preserves the distances. The length of each segment of the preimage would be equal to its corresponding side in the image as shown in figure (a).
So, the length of A'C' will also be 5 units.
Keywords: reflection, transformation, triangle
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Answer:
The length of A'C' will also be 5 units.
Step-by-step explanation:
Hey can anyone help me figure out these values? Thank you.
Answer:
1680
Step-by-step explanation:
12+7+6=25
12+20*12=252
20+20+7=47
7*20*12=1680
Can someone please help!
Answer:
(x, y ) → (- y, - x )
Step-by-step explanation:
Consider the coordinates of corresponding vertices of the 2 triangles, that is
A(1, 7 ) → D(- 7, - 1 )
Note the coordinates of D are the negative reversals of A
Thus (x, y ) → (- y, - x )
What is the probability that a registered voter voted in the election?
Answer:
0.4714
Step-by-step explanation:
The diagram shows:
3,371,556 registered voters which did not vote;3,006,202 registered voters which voted in the election.Then the total number of registered voters is
[tex]3,371,556+3,006,202=6,377,758[/tex]
Thus, the probability that a registered voter voted in the election is
[tex]\dfrac{3,006,202}{6,377,758}\approx 0.4714[/tex]
The probability that a registered voter participated in the election can vary significantly. In the U.S. 2020 Presidential Election, 77 percent of registered voters voted. However, it's vital to consider the full context, including the total and voting-age populations, and understand that turnout rates can vary by factors like age.
Explanation:The probability that a registered voter voted in the election depends on various factors such as the year, voters' ages and other socioeconomic factors. In the U.S., for instance, in the 2020 Presidential Election, 77 percent of registered voters cast their vote. However, it's vital to keep in mind that while this data is significant, it doesn't give full context without considering factors such as the eligible voting-age population or the total population.
Furthermore, it's useful to understand the concept of a 90 percent confidence level when interpreting statistics related to voter turnout. In this context, the statement 'We estimate with 90 percent confidence that between 56.4 percent and 63.6 percent of all students are registered voters.' suggests that there's a 90 percent probability that the actual percentage of registered voters among all students falls between the specified range.
On a related note, the age group also influences voter turnout. For instance, in 2016, 51 percent of eligible voters between the ages of eighteen and twenty-four registered, but only 39 percent of them voted. Conversely, 75 percent of eligible voters aged from sixty-five to seventy-four registered, and of these, 68 percent voted. Hence, the probability of a registered voter voting in the election can vary quite a bit based on age, among other factors.
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the area of a rectangle is w^2+4w=60 where w is the width. find the width.
The width of rectangle is 6.
Step-by-step explanation:
Given,
Area of rectangle; w²+4w=60
As w is the width, we will solve the equation to find w.
[tex]w^2+4w=60[/tex]
Subtracting 60 from both sides
[tex]w^2+4w-60=0[/tex]
Factorizing the equation;
[tex]w^2+10w-6w-60=0\\w(w+10)-6(w+10)=0\\(w+10)(w-6)=0[/tex]
Either,
w+10=0 => w=-10
Or,
w-6=0 =>w=6
As width cannot be negative, therefore
Width = 6
The width of rectangle is 6.
Keywords: area, rectangle
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Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
Write the formula to calculate the height, h.
The formula to calculate the height (h) of a cone, given its volume (V) and radius (r), is [tex]\(h = \frac{3V}{\pi r^2}\)[/tex]. This formula isolates the height by multiplying both sides of the volume formula by [tex]\(3/\pi r^2\).[/tex]
To isolate the height (h) in the volume formula of a cone ([tex]\(V = \frac{1}{3}\pi r^2 h\)[/tex]), we can rearrange the formula to solve for h.
Starting with the given formula:
[tex]\[ V = \frac{1}{3}\pi r^2 h \][/tex]
To find h, we can multiply both sides of the equation by [tex]\(3/\pi r^2\)[/tex] to isolate h:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
Therefore, the formula to calculate the height (h) of a cone, given its volume (V), radius (r), is:
[tex]\[ h = \frac{3V}{\pi r^2} \][/tex]
This formula allows you to determine the height of a cone when you know its volume and radius.
Simplify x + 4 – 5x – 2.
Answer: -4x+2
Step-by-step explanation: Simplify the expression.
Hope this helps you out! ☺
There are 20 cars in my building's parking lot. All of the cars are red or white. Also, all the cars are either 2-door or 4-door. 12 of them are red, 15 of them are 4-door, and 4 of them are 2-door and white. How many of the cars are 4-door and red?
Answer:
11 cars
Step-by-step explanation:
There are 20 cars in my building's parking lot, 15 cars are 4-door, then
[tex]20-15=5[/tex] cars are 2-door.
5 cars are 2-door, 4 of them are 2-door and white, then
[tex]5-4=1[/tex] car is 2-door and red.
12 cars are red, 1 car is 2-door and red, then
[tex]12-1=11[/tex] cars are 4-door and red.
(1/3) are red = 30 *1/3 = 10 are red
So...20 are white
50% are 4 door = 15 are 4 door
So....15 are 2 door
8 are 2 door and white.....so 12 are 4 door and white since we have 20 white total
And since 15 are 4 door and 12 of these are white...then 3 must be 4 door and red
ORRRRMake a two-way table as follows:
RED WHITE
2-DOOR 7 8
4-DOOR 3 12
TOTALS 10 20
So, it looks like you have 3 cars that are red and have 4 doors.
Karen has $1.70 in coins. Karen has 8 coins, all of which are quarters or dimes.
So can someone help me with these 3 parts?
Answer:
Karen has 6 quarters and 2 dimes
Step-by-step explanation:
Let
x ----> the number of quarter coins Karen has
y ----> the number of dimes coins Karen has
Remember that
[tex]1\ quarter=\$0.25\\1\ dime=\$0.10[/tex]
we know that
Equation that represent the amount of coins Karen has
[tex]x+y=8[/tex]
isolate the variable y
[tex]y=8-x[/tex] ----> equation A
Equation that represent the value of coins Karen has
[tex]0.25x+0.10y=1.70[/tex] ----> equation B
Solve the system of equations by substitution
substitute equation A in equation B
[tex]0.25x+0.10(8-x)=1.70[/tex]
solve for x
[tex]0.25x+0.80-0.10x=1.70[/tex]
[tex]0.25x-0.10x=1.70-0.80[/tex]
[tex]0.15x=0.90[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=8-x[/tex] ----> [tex]y=8-6=2[/tex]
therefore
Karen has 6 quarters and 2 dimes
Lo is leaving from work today at 6:15 p.m. She has errands to run before she meets her friends for dinner at 8 p.m. If it takes Lo of an hour to run each errand, how many errands does she have time to run between work and dinner?
Lo has time to run 7 errands between work and dinner.
Lo has 1 hour and 45 minutes between leaving work at 6:15 p.m. and meeting her friends at 8:00 p.m.
She needs around 1/4 of an hour for each errand.
To find out how many errands she can run, we divide the total time available by the time required for each errand:
Convert 1 hour 45 minutes to minutes: 1 hour = 60 minutes, so 1 hour 45 minutes = 60 + 45 = 105 minutes.
Calculate how many errands she can run: 105/15 = 7.
Therefore, Lo has time to run 7 errands between work and dinner.
The force F needed to stop a car varies directly as its weight W and the square root of velocity V are inversely as the distance d travelled. When F=36 Newtons, W=120kg,V=100km/h and d=50km. Calculate the force required for V=256km/h,W=200kg and d =800km. This is the question pls answer it dont by pass it pls
Final answer:
To calculate the force required, we use the formula F = k * (W / sqrt(V)) * (1 / d), where F is the force, W is the weight, V is the velocity, and d is the distance. We can find the constant of variation k by substituting the given values of F, W, V, and d into the formula. After finding k, we can plug in the new values of W, V, and d to calculate the force required.
Explanation:
To solve this problem, we can use the formula F = k * (W / sqrt(V)) * (1 / d), where F is the force, W is the weight, V is the velocity, and d is the distance.
First, we can calculate the constant of variation k by substituting the given values of F, W, V, and d into the formula. This gives us: 36 = k * (120 / sqrt(100)) * (1 / 50).
Solving for k, we get k = 36 * 100 * 50 / 120 = 1500.
Next, we can plug in the new values of W, V, and d into the formula and solve for F. Substituting W = 200, V = 256, and d = 800, we have: F = 1500 * (200 / sqrt(256)) * (1 / 800).
Simplifying further, we get F = 1500 * 200 / (16 * 800) = 18.75 Newtons.
Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a scale factor of 14.
The coordinates of the vertices of triangle ABC are given. You can use the scale factor to find the coordinates of the dilated image.
Enter the coordinates of the vertices of triangle A'B'C' below.
(Decimal values may be used)
pls answer ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]A'(-0.25,0.75)\\\\B'(1.75,-0.25)\\\\C'(-1,-0.25)[/tex]
Step-by-step explanation:
A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.
When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".
When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".
In this case you know that the triangle ABC was dilated by this scale factor:
[tex]scale\ factor=\frac{1}{4}[/tex]
With the origin as the center of dilation.
Since:
[tex]0<\frac{1}{4}<1[/tex]
It is a Reduction.
You can identify that the vertices of the triangle ABC are:
[tex]A(-1,3)\\\\B(7,-1)\\\\C(-4,-1)[/tex]
So you need to multiply the coordinates of each vertex of the triangle ABC by [tex]\frac{1}{4}[/tex], in order to get the coordinates of the triangle A'B'C. Then, you get:
[tex]A'=(\frac{1}{4}(-1),\frac{1}{4}(3))=(-0.25,0.75)\\\\B'(\frac{1}{4}(7),\frac{1}{4}(-1))=(1.75,-0.25)\\\\C'(\frac{1}{4}(-4),\frac{1}{4}(-1))=(-1,-0.25)[/tex]
The coordinates of the vertices of triangle A'B'C' include the following;
A' (-1/4, 3/4).
B' (7/4, -1/4).
C' (-1, -1/4).
What is dilation?In Mathematics and Euclidean Geometry, dilation is a type of transformation that is used for altering the dimensions of a geometric figure, but not its shape.
In this scenario and exercise, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:
Ordered pair A (-1, 3) → (-1 × 1/4, 3 × 1/4) = Ordered pair A' (-1/4, 3/4).
Ordered pair B (7, -1) → (7 × 1/4, -1 × 1/4) = Ordered pair B' (7/4, -1/4).
Ordered pair C (-4, -1) → (-4 × 1/4, -1 × 1/4) = Ordered pair C' (-1, -1/4).
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Missing information;
Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a scale factor of 1/4.
The coordinates of the vertices of triangle ABC are given. You can use the scale factor to find the coordinates of the dilated image.
Enter the coordinates of the vertices of triangle A'B'C' below.
(Decimal values may be used)
h(y)=-3y^2+5
p(y)=y^3-7y
Find (h-p)(y)
[tex](h-p))(y) = -y^3-3y^2+7y+5[/tex]
Step-by-step explanation:
Given
[tex]h(y) = -3y^2+5\\p(y) = y^3-7y[/tex]
We have to find the difference of two functions given
So,
[tex](h-p)(y) = h(y) - p(y)\\= (-3y^2+5)-(y^3-7y)\\=-3y^2+5-y^3+7y\\=-y^3-3y^2+7y+5[/tex]
Hence,
[tex](h-p))(y) = -y^3-3y^2+7y+5[/tex]
Keywords: Functions, variables
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Malachy and Paul win some money and share it in the ratio 4:5. Malachy gets £44. How much did Paul get?
Answer:
I believe the answer is 55.
Step-by-step explanation:
Because if Malachy gets 44 and the ratio is 4:5 it would only make sense if Paul got 55.
How many 5-member chess teams can be chosen from 15 interested players? Consider only the members selected, not their board positions. 3,003 120 360,360
Answer:
3003 number of 5-member chess teams can be chosen from 15 interested players.
Step-by-step explanation:
Given:
Number of the interested players = 15
To Find:
Number of 5-member chess teams that can be chosen = ?
Solution:
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula[tex]nCr = \frac{n!}{r!(n - r)!}[/tex]
where
n represents the total number of items,
r represents the number of items being chosen at a time.
Now we have n = 15 and r = 5
Substituting the values,
[tex]15C_5 = \frac{15!}{5!(15- 5)!}[/tex]
[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]
[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]
[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}[/tex]
[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11}{(5 \times 4 \times 3 \times 2 \times 1)}[/tex]
[tex]15C_5 = \frac{360360}{120}[/tex]
[tex]15C_5 = 3003 [/tex]
The length of a rectangle is 6 yards longer than its width and
If the perimeter of the rectangle is 72 yards, find its length and width.
Let...
length=x+6
width=x
x+x+x+6+x+6=72
4x+12=72
4x=60
x=15
x+6=21
answer: length=21 and width=15
To solve for the length and width of the rectangle, we first need to understand the formulas and relationships involved:
- The perimeter (P) of a rectangle is the total distance around its boundary, which is calculated by adding together twice the length (L) and twice the width (W): `P = 2L + 2W`.
- We have two pieces of information to work with:
1. The length is 6 yards longer than the width, which we can express as `L = W + 6`.
2. The perimeter is 72 yards, so `P = 72`.
With these equations, we can set up our system to solve for the length and width:
1. Substitute the expression for L from the first piece of information into the perimeter formula:
`P = 2(W + 6) + 2W`
2. Plug in the value for the perimeter:
`72 = 2(W + 6) + 2W`
3. Distribute the 2 through the parentheses:
`72 = 2W + 12 + 2W`
4. Combine the W terms:
`72 = 4W + 12`
5. Isolate the W term by subtracting 12 from each side:
`72 - 12 = 4W`
`60 = 4W`
6. Divide by 4 to solve for W:
`W = 60 / 4`
`W = 15`
Now that we have the width, we can use the first equation to solve for the length:
`L = W + 6`
`L = 15 + 6`
`L = 21`
So, the width (W) is 15 yards and the length (L) is 21 yards.
Dani spend her summers at her grandparents cabin in canada. The cabin is 42 kilometers upriver from the nearest town. The river has a downstream current of 4 kilometers per hour. If Dani can canoe from the cabin to town and back in 14 hours, what is her average canoeing speed in still water?
Answer:
8 kilometer per hour
Step-by-step explanation:
Given: Dani spend her summers at her grandparents cabin in canada. The cabin is [tex]42[/tex] kilometers upriver from the nearest town. The river has a downstream current of [tex]4[/tex] kilometers per hour.
To Find: If Dani can canoe from the cabin to town and back in [tex]14[/tex] hours, what is her average canoeing speed in still water.
Solution:
Let the speed of Dani in still water is [tex]=\text{s}[/tex]
speed of downstream current is [tex]=4\text{kmph}[/tex]
speed of Dani in downstream current [tex]=\text{s}+4[/tex]
speed of Dani in upstream current [tex]=\text{s}-4[/tex]
Now,
Total time taken by Dani to canoe from the cabin to town and back [tex]=14\text{hours}[/tex]
[tex]\frac{42}{\text{s}-4}+\frac{42}{\text{s}+4}=14[/tex]
[tex]{\text{s}}^2-6\text{s}-16=0[/tex]
[tex](\text{s}-8)(\text{s}+2)[/tex]
[tex]\text{s}=8,-2[/tex]
as speed can't be negative the average speed of dani in still water is [tex]8\text{kmph}[/tex]
you want to limit the amount of television you watch to an average of at most two hours per week do an eight week. How many hours acts of television must you watch in the eighth week to meet your goal.
PLEASE SHOW YOUR WORK
Answer:
16 hours acts of television we must watch in eighth weeks to meet your goal.
Step-by-step explanation:
This problem requires us to determine the total hours we spend on watching television in eight week if we spend two hours watching television each week. This problem can easily be solved by multiplying 2 hours with number of week that is 8 week.
= 8 * 2 = 16
Is -x+4y=-2 a direct variation?
Answer:
No
Step-by-step explanation:
Direct variation: two variables, one variable is a constant multiple of another variable
y = k x .... k constant
-x+4y=-2
4y = x - 2
y = 1/4 x -1/2 ..... y = k x + b y is not a simple multiple of x
Miss Isaac took her family out to eat at Jay’s deli. their mail came to 25. 40. missed Isaac wants to tip the waitress 18% and sales tax is 5.5% final total price of our meal after tax and tip
Answer:
The total price of the meal after tax and tip is $31.62.
Step-by-step explanation:
Given:
Their bill is = $25.40.
Sales tax = 5.5%.
Tip to waitress = 18%.
Now, to find the total price of the meal after tax and tip.
So, to get the price of the meal after sales tax :
$25.40 + 5.5% of $25.40.
[tex]=25.40+\frac{5.5}{100} \times 25.40.[/tex]
[tex]=25.40+\frac{139.70}{100}[/tex]
[tex]=25.40+1.397=\$26.797[/tex]
Now, to get the total price after tax and tip:
$26.797 + 18% of $26.797.
[tex]=26.797+\frac{18}{100} \times 26.797[/tex]
[tex]=26.797+0.18\times 26.797[/tex]
[tex]=26.797+4.823[/tex]
[tex]=\$31.62.[/tex]
Therefore, the total price of the meal after tax and tip is $31.62.