Answer:
c) 4
Step-by-step explanation:
The sum of two numbers is 14. The larger number minus three times the lesser number is -2
To solve this question, we need to write the statement mathematically;
Let the two numbers be x and y
"The sum of two numbers is 14" can be mathematically written as x+y = 14
and
"The larger number minus three times the lesser number is -2" can be mathematically written as x - 3y = -2
x + y = 14 ------------------(1)
x - 3y= -2 -------------------(2)
Subtract equation (2) from equation (1)
[x - x = 0 y - (-3y)=4y 14-(-2)=16]
4y = 16
To get the value of y divide both-side of the equation by 4
4y/4 = 16/4
y = 4
Substitute y=4 into equation (1)
x + y =14
x +4 =14
Subtract 4 from both-side of the equation
x + 4 -4 = 10]-4
x = 10
x=10 and y =4
Therefore the lesser number is 4
Please help
Linda and Ralph have signed a contract to purchase a home. The closing date is April 27, and the buyer owns the property on the day of closing The selling price of the
home is $782,500. Linda and Ralph obtained a fixed-rate mortgage from a bank for $685,000 at 7 35% interest. The seller has already paid $14,578.15 in property taxes
for the coming year. How much will Linda and Ralph owe in prorated expenses? (3 points)
Final answer:
Linda and Ralph will owe approximately $9,905.52 in prorated property taxes for the year, after calculating the daily property tax rate and multiplying it by the number of days they will own the home in the current tax year.
Explanation:
Linda and Ralph need to determine their prorated expenses for the property taxes that have already been paid by the seller. To calculate this, we first need to determine the daily property tax rate, and then calculate how much they owe from the closing date, April 27, until the end of the year, December 31.
Calculating the Daily Property Tax Rate
The seller paid $14,578.15 for the full year. There are 365 days in a year, so the daily property tax rate is:
Daily rate = Total annual taxes / Number of days in the year
Daily rate = $14,578.15 / 365
Daily rate ≈ $39.94
Calculating Prorated Property Tax from Closing Date
Linda and Ralph will own the property starting on April 27, and there are 248 days remaining in the year from April 27 to December 31 (inclusive). Therefore, the prorated amount they owe for property taxes is:
Prorated taxes = Daily rate * Number of days from closing to end of year
Prorated taxes = $39.94 * 248
Prorated taxes ≈ $9,905.52
Linda and Ralph will owe approximately $9,905.52 in prorated property taxes for the year.
6. Find the sum of 2x and 8x.
Answer:
16x
Step-by-step explanation:
its basically saying (2x)x(8x) which would equal 16x
Answer: 10x
Step-by-step explanation:
Sum of 2x and 8x means the addition of 2x and 8x
Written as 2x + 8x= 10x
Which of the following events are dependent?
Beth and Corrie take turns picking a card at random and recording each outcome. They replace the selected card at the bottom of the pile after each turn.
Archie and Harris take turns picking yellow- or purple-colored chips from a dish.
Jared pulls out a sock from the laundry basket containing white and black socks, puts it back, and then draws another sock at random.
Lily draws a marble from a bag filled with red and blue marbles, places her selection in a separate bag, and draws from the original bag of marbles again.
Answer:
A. Archie and Harris take turns picking yellow- or purple-colored chips from a dish.
C. Lily draws a marble from a bag filled with red and blue marbles, places her selection in a separate bag, and draws from the original bag of marbles again.
Step-by-step explanation:
Two events will be dependent if the first event influences the probability of the second event. If the first event takes something and doesn't put it back, that means the second event can't pull the same roll and the total pool of items changed.
A. Beth and Corrie take turns picking a card at random and recording each outcome. They replace the selected card at the bottom of the pile after each turn.
This option put replace the card, so it is independent
B. Archie and Harris take turns picking yellow- or purple-colored chips from a dish.
No replacement, the event should be dependent.
C. Jared pulls out a sock from the laundry basket containing white and black socks, puts it back, and then draws another sock at random.
This option put back the pulls, so it is independent
D. Lily draws a marble from a bag filled with red and blue marbles, places her selection in a separate bag, and draws from the original bag of marbles again.
No replacement for the marble taken, each draws probability should depend on the earlier draw result.
A type of bacteria has a very high exponential growth rate of 80% every hour. If there are 10 bacteria, determine how many will be in 5 hours,1 day, and 1 week
Solution:
Given that,
A type of bacteria has a very high exponential growth rate of 80% every hour
There are 10 bacteria
The increasing function is given as:
[tex]y = a(1+r)^t[/tex]
Where,
y is future value
a is initial value
r is growth rate
t is time period
From given,
a = 10
[tex]r = 80 \5 = \frac{80}{100} = 0.8[/tex]
Determine how many will be in 5 hours
Substitute t = 5
[tex]y = 10(1 + 0.8)^5\\\\y = 10(1.8)^5\\\\y = 10 \times 18.89568\\\\y \approx 188.96[/tex]
y = 189
Thus, there are 189 bacteria in 5 hours
Determine how many will be in 1 day ?
1 day = 24 hours
Substitute t = 24
[tex]y = 10(1 + 0.8)^{24}\\\\y = 10(1.8)^{24}\\\\y = 10 \times 1338258.84\\\\y = 13382588.45\\\\y \approx 13382588[/tex]
Thus, there are 13382588 bacteria in 1 day
Determine how many will be in 1 week
1 week = 168
Substitute t = 168
[tex]y = 10(1 + 0.8)^{168}\\\\y = 10(1.8)^{168}[/tex]
Thus there are [tex]10(1.8)^{168}[/tex] bacteria in 1 week
A 30° 60° 90° triangle is shown below. Find the length of the side labeled y.
Answer:
Part 1) [tex]y=3\ units[/tex]
Part 2) The length of the hypotenuse is 6 units
Step-by-step explanation:
Part 1) we know that
In the right triangle of the figure
[tex]sin(60^o)=\frac{y}{2\sqrt{3}}[/tex] ----> by SOH (opposite side divided by the hypotenuse)
solve for y
[tex]y=sin(60^o)2\sqrt{3}[/tex]
Remember that
[tex]sin(60^o)=\frac{\sqrt{3}}{2}[/tex]
substitute
[tex]y=(\frac{\sqrt{3}}{2})2\sqrt{3}[/tex]
[tex]y=3\ units[/tex]
Part 2)
Let
h ----> the length of the hypotenuse
we know that
In the right triangle of the figure
[tex]sin(45^o)=\frac{3\sqrt{2}}{h}[/tex] ----> by SOH (opposite side divided by the hypotenuse)
[tex]h=\frac{3\sqrt{2}}{sin(45^o)}[/tex]
Remember that
[tex]sin(45^o)=\frac{\sqrt{2}}{2}[/tex]
substitute
[tex]h=3\sqrt{2}:\frac{\sqrt{2}}{2}[/tex]
[tex]h=6\ units[/tex]
There are 7 special subjects at Ichiro's school: art, music, gym, library,
enrichment, typing, and research. Students only take 1 special subject
each school day. A special subject is not taken more than once a week.
Assume that special subjects are assigned randomly.
Ichiro has library on Monday. If the remaining subjects during the school week
are assigned randomly from the other 6 subjects, what is the probability that he
has art on Friday?
Final answer:
The probability that Ichiro has Art on Friday, given that he has already had Library on Monday and the subjects are assigned randomly, is 1/6 or approximately 16.67%.
Explanation:
The subject of this question is Probability. Ichiro has Library on Monday, and since he cannot have the same special subject more than once in a week, there are six subjects left to schedule from Tuesday to Friday. The special subjects are considered to be assigned randomly.
To determine the probability that Ichiro has Art on Friday, we need to consider there are four days left in the school week (Tuesday to Friday) after Monday. Since the subjects are assigned randomly, each of the remaining subjects has an equal chance of being assigned to any day. By the time we get to Friday, there will be only one subject left unassigned, which has a 1 out of 6 chance of being Art, as the remaining subjects are randomly assigned to the days preceding.
The probability that Ichiro has Art on Friday is therefore 1/6, or approximately 16.67%
V
Harlon recorded this set of data, which contains an outlier.
163, 97, 184, 199, 169, 175
What is the range of this set of data?
12
97
102
172
Answer:5
Step-by-step explanation:
Answer:
102
Step-by-step explanation:
To find the range of a set of data, you have to put all of the values in order from smallest to largest. Then you subtract the smallest and largest value to find your answer.
199 - 97 = 102
which expression is equivalent to 3/4(-12x+4) + 1/2(6x
Answer:
y = -6x + 3
Step-by-step explanation:
y = 3/4(-12x+4) + 1/2(6x)
y = -9x + 3 + 3x
y = -6x + 3
If this answer is correct, please make me Brainliest!
I walked for 2 1/2 hours at 4km/h and for 4 hours at 2 1/2 km/h. What was the average speed for the entire journey?
Average speed of the entire journey is 3.08 km/hr
Step-by-step explanation:
Step 1: In the first half, given that the speed = 4 km/h and time = 2 1/2 = 2.5 hrs. Calculate the distance covered.Distance = Speed × Time = 4 × 2.5 = 10 km
Step 2: In the second half, given that speed = 2 1/2 = 2.5 km/hr and time = 4 hrs. Calculate the distance covered.Distance = 2.5 × 4 = 10 km
Step 3: Calculate average speed.Average Speed = Total distance/Total time
= 10 + 10/2.5 + 4 = 20/6.5
= 3.08 km/hr
log base 2(6x+5)=3
Please help! thanks
Answer:
i think the answer is x = -7/12 or in decimal form x = -0.583, the 3 is repeating.
Step-by-step explanation:
1. 3x + 18 х = (0)
Completing the square
On the coordinate plane, Kyle graphs a line that represents a proportional relationship between x and y. Which point MUST be on the line?
A) (0, 1)
B) (1, 0)
C) (1, 1)
D) (0, 0)
Answer:
its d (0,0)
Step-by-step explanation:
just figured it out.
There are 50 runners in a race. How many ways can the runners finish first, second, and third?
Number of ways can the runners finish first, second, and third is 1,17,600 .
Step-by-step explanation:
Permutation is the act of arranging the members of a set into a sequence or order, or, if the set is already ordered, rearranging (reordering) its elements—a process called permuting. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). Formula of Permutation is : [tex]P(n,r) = \frac{n!}{(n-r)!}[/tex] where n is the number of things to choose from, and we choose r of them, no repetitions, order matters. Here , n = 50 , r= 3
⇒ [tex]P(n,r) = \frac{n!}{(n-r)!}[/tex]
⇒ [tex]P(50,3) = \frac{50!}{(50-3)!} = \frac{50(49)(48)47!}{47!}[/tex]
⇒ [tex]P(50,3) = 50(49)(48)[/tex]
⇒ [tex]P(50,3) = 1,17,600[/tex]
∴ Number of ways can the runners finish first, second, and third is 1,17,600 .
someone who's good at math plz!!!!
There is 1 gram of fat in a serving of refried beans. Each serving is 110
calories. How many calories are from fat?
Final answer:
To calculate the number of calories from fat in a serving of refried beans, multiply the grams of fat by the calories per gram of fat. In this case, there are 9 calories from fat in a serving of refried beans.
Explanation:
In order to determine the number of calories from fat in a serving of refried beans, we need to know the total amount of fat per serving. The question states that there is 1 gram of fat in a serving. It also mentions that each serving is 110 calories. To calculate the number of calories from fat, we can use the formula:
Calories from fat = Fat (in grams) × Calories per gram of fat
Plugging in the values: Calories from fat = 1 gram × 9 Calories/gram of fat = 9 Calories
Therefore, there are 9 calories from fat in a serving of refried beans.
Final answer:
In a serving of refried beans that contains 1 gram of fat, there are 9 calories from fat.
Explanation:
The question asks how many calories are from fat in a serving of refried beans. To answer this, we need to know the amount of fat and the calories in the serving. The question provides that there is 1 gram of fat in the serving and that the serving is 110 calories. Therefore, 1 gram of fat in the serving would contribute 9 calories (since fat contains 9 calories per gram). So, the number of calories from fat in the serving of refried beans is 9 calories.
To calculate the number of calories from fat in a serving of refried beans, we need to use the fact that fat provides 9 calories per gram. With 1 gram of fat in a serving of refried beans, we do the following calculation:
Multiply the amount of fat in grams by the number of calories that fat provides per gram: 1g × 9 calories/g = 9 calories.
Therefore, 9 calories of the total 110 calories in a serving of refried beans come from fat.
30 out of 40 is equal to what percent
Answer:
%75
Step-by-step explanation:
30/40 is equal to 0.75
0.75 is also %75
Answer: %75
The population of deer in a forest was measured to be 1938 in the year 2010. If the population increased by a steady 4% a year which of the following calculations would predict its population in 2013
Answer:
6046.56
Step-by-step explanation:
1938+4%=2015.52*3=6046.56
Suppose f(x) is a function such that if p
Answer:
I think in a function of f(x) P is also another variable like P is the price then Q is the quantity.
Step-by-step explanation:
Solve using a fraction multiplication sentence .005 x .3
Answer:
15/10,000
Step-by-step explanation:
0.005 = 5/1000
0.3 = 3/10
5/1000 * 3/10 = 15/10,000
Answer: 15/10,000
102 chairs at 6 tables find the unit rateat 6 tables . Find the unit rate
The unit rate is 17 chairs per table.
Step-by-step explanation:
Given,
Total number of chairs at 6 tables = 102 chairs
Number of tables = 6
Unit rate in terms of tables = [tex]\frac{Total\ chairs}{Number\ of\ tables}[/tex]
Unit rate in terms of tables= [tex]\frac{102}{6}[/tex]
Unit rate in terms of tables = 17
The unit rate is 17 chairs per table.
"The correct unit rate is 17 chairs per table.
To find the unit rate, we need to divide the total number of chairs by the number of tables. The question states there are 102 chairs and 6 tables. The unit rate is the number of chairs per table, which can be calculated as follows:
Unit rate = Total number of chairs / Number of tables
Unit rate = 102 chairs / 6 tables
Now, we divide 102 by 6 to find the unit rate:
Unit rate = 102 / 6
Unit rate = 17
Therefore, the unit rate is 17 chairs per table. This means that at each table, there are 17 chairs."
what is the value of x
Answer:
4
Step-by-step explanation:
Sin(30) = LJ/8sqrt(3)
Sin 30 = ½
LJ = 4sqrt(2)
LM = JM = x
x² + x² = (4sqrt(2))²
2x² = 32
x² = 16
x = 4
Can someone please explain how to do this?
Answer:
e = 30
Step-by-step explanation:
Since 114 and the adjacent angle are supplementary, that means they add up to 180.
114 + x - 114 = 180 - 114
x = 66
Now, solve inside the triangle which adds up to 180.
54 + 66 + 2e = 180
120 + 2e - 120 = 180 - 120
2e / 2 = 60 / 2
e = 30
Answer: e = 30
(a)The area of a rectangular field is 7392 .
If the length of the field is 96 , what is its width?
(b)The perimeter of a rectangular painting is 372 .
If the width of the painting is 88 , what is its length?
Answer:
W = 77
L = 98
Step-by-step explanation:
Question a:
Area of a rectangular field = 7392
Length L = 96
Width w = ?
Area of a rectangle = L x W
7392 = 96 x W
Divide both sides by 96
7392/96 = 96/96 x w
77 = w
W = 77
Question b:
Perimeter of a rectangular painting = 372
Width = 88
Length = ?
Perimeter of a rectangle =
2(L + w)
372 = 2(L + 88)
Distribute 2 into (L + 88)
We have
372 = 2 x L + 2 x 88
372 = 2L + 176
Subtract 176 from both sides
372 - 176 = 2L + 176 - 176
196 = 2L
Divide both sides by 2
196/2 = 2L/2
98 = L
L = 98
a movie is 2 hours and 23 minutes long. if the moive ends at 4:25 what time did the movie start?
Acos²theta + Bsin²theta = C
Show that
tan²theta =C- A/B-C
[tex]Tan^2x= \frac{C -A}{(B-C)}[/tex]
Step-by-step explanation:
Here we have , Acos²theta + Bsin²theta = C or , [tex]Acos^2theta + Bsin^2theta = C[/tex]
Let theta = x , So [tex]Acos^2x + Bsin^2x = C[/tex] . Let's solve it further
⇒ [tex]Acos^2x + Bsin^2x = C[/tex]
⇒ [tex]\frac{Acos^2x}{cos^2x} + \frac{Bsin^2x}{cos^2x} = \frac{C}{cos^2x}[/tex]
⇒ [tex]A + B(\frac{sin^2x}{cos^2x}) = C\frac{1}{cos^2x}[/tex] { [tex]\frac{sin^2x}{cos^2x} = Tan^2x , \frac{1}{cos^2x} = sec^2x[/tex] }
⇒ [tex]A + B(Tan^2x) = C(sec^2x)[/tex] { [tex]sec^2x=1+Tan^2x[/tex] }
⇒ [tex]A + B(Tan^2x) = C( 1+Tan^2x )[/tex]
⇒ [tex]A + B(Tan^2x) = C+C(Tan^2x )[/tex]
⇒ [tex]B(Tan^2x)-C(Tan^2x ) = C -A[/tex]
⇒ [tex](B-C)(Tan^2x)= C -A[/tex]
⇒ [tex]Tan^2x= \frac{C -A}{(B-C)}[/tex]
Therefore , [tex]Tan^2x= \frac{C -A}{(B-C)}[/tex] .
Factor:
x2 + 9x - 36
Answer:
11x-36
for your answers
Answer:
x= -12
or
x=3
Step-by-step explanation:
in order to factorise the equation x² + 9x - 36
it will be expressed like this to make it a complete equation by subtracting 36 from both sides
x² + 9x - 36=0
the next step is to look for two numbers that when multiplied will give us -36 and when added together it will give us 9.
the numbers would be -3 and 12
so we have
x²-3x + 12x -36 =0
x(x-3) + 12(x-3) = 0
(x+12)(x-3)=0
we have,
x + 12 =0
x = -12
or
x-3 =0
x= 3
Therefore, the factors for x are -12 or 3.
Which describes how to calculate the range of this data set?
4, 5, 6, 8, 11, 12
Subtract 11-5
Subtract 12-4
Add 11+5.
Add 12+4.
Answer:
12 - 4
Step-by-step explanation:
Which figures are polygons ? Select each correct answer.
Figure A Figure B Figure C Figure D
Polygons are closed, two-dimensional shapes with straight, fully connected sides. Figure A, Figure B, Figure C are polygons.
To determine which figures are polygons, we must understand that a polygon is a closed, two-dimensional shape with straight sides that are fully connected at each endpoint.
There should be at least two or more straight sides in a polygon.
Figure A: It is a polygon as it has more than two sides and is closed.
Figure B: It is also a polygon as it has 6 sides and angles and is also closed in shape.
Figure C: It is not a polygon as it does not have straight line more than two, it is closed but it contains curved line.
Figure D: It is polygon as it contains straight lines and is closed.
help!!!!!!!!!!!!!!!!!!!!!!
Answer:
4
Step-by-step explanation:
Rate of change = Slope (if Sidelength = x, and perimeter= y)
(1,4) and (2,8) are point (if it was a line)
Use the slope formula...
(8-4)/(2-1)=
4/1=
4
The polygon's are similar. Find the values of x and y.
Answer:
x = 9 y = 27
Step-by-step explanation:
Since the two polygons are similar, we know that they are proportionate to each other. If we divide the values of corresponding sides:
16 ÷ 12 = 1 ¹/₃
32 ÷ 24 = 1 ¹/₃
We now know that the figure on the left is 1 ¹/₃ times the figure on the right. With this information, we can figure out the measurements of the two sides and then find the values of x and y.
6 · 1 ¹/₃ = 8
21 · 1 ¹/₃ = 28
Now that we know the values of each side, we can plug our equations in to find the values of x and y.
x - 1 = 8
x = 9
y + 1 = 28
y = 27
~Hope this helps!~
What is the slope of the following graph?
Slope is 20/3 or 6.67
Step-by-step explanation:
Step 1: Slope, m is given by the equation (y2 - y1)/(x2 - x1). Here, x1 = 6, x2 = 12, y1 = 40 and y2 = 80⇒ m = (80 - 40)/(12 - 6)
= 40/6 = 20/3 or 6.67