[tex]\cfrac{1}{2}(4x-2)\leqslant 9+7x\implies 2x-1\leqslant 9+7x\implies -1\leqslant 9+5x \\\\\\ -10\leqslant 5x\implies \cfrac{-10}{5}\leqslant x\implies {\LARGE \begin{array}{llll} -2\leqslant x \end{array}}[/tex]
le's notice that, we divided by a positive number, thus the inequality sign didn't flip.
Two steamers leave a port on river at the same time traveling in opposite directions each is traveling 20mph how long will it take for them to be 140 miles apart
The correct answer is 3.5.
Let t be the amount of time each steamer takes.
Two steamers that are headed in opposite directions depart a port on a river at the same time, according to the information provided.
Given that both steamers move at the same speed, they would cover the same distance in t hours.
Given that both steamers covered 140 miles, we can write the following equation to reflect this data:
rate time distance
First stream 20 t 20t
Second stream 20 t 20t
140
setting the equation ,
20t + 20t = 140
40t = 140
t = 140/40
t = 3.5
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A person earns 16000 one year and gets a 5% raise in salary. What is the new salary?
Answer:
The new yearly salary is $16,800
Step-by-step explanation:
Amount of raise.
5% = 0.05
Multiply the original salary times the percentage of the raise.
$16000 * 0.05 = $800
New salary .
$16000 + $800 = $16,800
One-step Solution
$16000+($16000 * 0.05) =$16,800
Needed help asap please and thank you so much !
Step-by-step explanation:
based on the story told I expected completely different questions.
but for the actually asked question the whole thing about gaining our not gaining weight is competent irrelevant. ignore it.
so, all we need to do is looking at the row totals.
27.4% of the participants took 1 vitamin.
49.5% of the participants took more than 1 vitamin.
so, 49.5% + 27.4% = 76.9% of all participants are taking vitamins in some form.
therefore, the second answer option is correct.
if u arent beinggreat simply dont answer :)
Answer:
Step-by-step explanation:
The exponent is -3, making it 10 to the power of negative 3. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 3 times:
9.2 -> 0.0092
The answer is D.
Answer:
0.0092.
Step-by-step explanation:
I have an explanation on this same question. Apparently, you have a duplicate of this.
Shelby measured the volume of a cylinder and determined it to be 58.8 cm³. The teacher told her that she
was 4.98% too high in her determination of the volume. What is the actual volume of the cylinder?
The actual volume of the cylinder is 61.73 cm³
Percentage error is the error introduced in a measurement. The formula for the error is given as :
Error = Percentage error * measured volume
According to the question we have been given that
determined volume of cylinder = 58.8 cm³
Percentage error = 4.98%
thus, error = 4.98% * 58.8
= 0.0498 * 58.8
= ±2.93 cm³
The formula for the actual volume is given as
Actual volume = measured volume ± error
= 58.8 ± 2.93 cm³
As the error is high we will do addition we get
= 58.8 + 2.93 cm³
= 61.73 cm³
hence the actual volume is 61.73 cm³
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5:2:11=x:6:y
(that ratio btw)
Answer:
9=11
Step-by-step explanation:
Jamal has 34 toy soldiers. He wants to arrange the soldiers into one or more equal-sized lines. Which list shows all the possibilities for the number of toy soldiers Jamal could place in each line
The list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.
How to illustrate the information?From the information, Jamal has 34 toy soldiers. He wants to arrange the soldiers into one or more equal-sized lines.
It should be noted that the factors of 34 are 1, 2, 17, and 34.
Therefore, the list that shows all the possibilities for the number of toy soldiers Jamal could place in each line is 1, 2, 17 and 34.
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Do the 3 lengths form a triangle? 5, 17, 29 *
yes or no
Answer:
No they do not because it does not qualify for a triangle due to the extreme differences in messurments
Step-by-step explanation:
A model of the total cost C, in dollars, to produce n cell phones is given by
C = 240n + 800.
Find the C-intercept and the n intercept
Answer:
C intercept is 800, n intercept is -3.3333...
Step-by-step explanation:
C = 240n + 800 is a linear equation (the graph is a line)
C-intercept is the point with the coordinates ( 0, C-intercept ) where the line C = 240n + 800 is intersecting the vertical C-axis and
n-intercept is the point with the coordinates (n-intercept, 0) where the line C = 240n + 800 is intersecting the horizontal n-axis.
Find the C-intercept:
n has to be 0 for our line to intercept the C-axis, so substitute n = 0 in our given equation
C = 240n + 800
C = 240·0 + 800
C = 800
Find the n-intercept:
C has to be 0 for our line to intercept the n-axis, so substitute C = 0 in our given equation
C = 240·n + 800
0 = 240·n + 800, subtract 800 from both sides
-800 = 240 ·n, divide both sides by 240
-800/240 = n
-3.(3) = n
to lose 1 lb of body fat you need to burn 3.500 calories. If you burn 450 more calories than you take in each day, how long will it take to lose 1 lb? What about 10 lb?
Step-by-step explanation:
1 pound is equivalent to 3500 calories.
if you burn 450 more calories per day, it will take as many days as the times 450 fits into 3500 :
3500 / 450 = 7.77777777... days
for 10 pounds we need to burn 10×3500 = 35000 calories.
35000 / 450 = 77.77777777... days (10 times more logically than for 1 pound).
A small business office uses 307 pieces of paper every 3 days. Which is a reasonable estimate for the pieces of paper the business office uses in 7 days?
A.
600
B.
2,100
C.
900
D.
700
700 is a reasonable estimate for the pieces of paper the business office uses in 7 days
How to calculate the estimate ?The office uses 307 pieces of paper every 3 days
The first is to calculate the number of paper used per day
= 307/3
= 102.3
The number of paper used in 7 days can be calculated as follows
= 7 × 102.3
= 716
Hence 700 is a reasonable estimate for the pieces of paper the business office uses in 7 days
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Which expression is equal to (-3- i)+ (5 +6i)?
A.2 +5i
B. -7
C.-4+11i
D.77
Answer:
A
Step-by-step explanation:
[tex](-3-i)+(5+6i) \\ \\ =-3-i+5+6i \\ \\ =2+5i[/tex]
the equation of the line parallel to y=-X+11 through the point (-3,5)?
Step-by-step explanation:
I guess the result is needed again in slope-intercept form.
this is in general
y = ax + b
"a" being the slope, "b" being the y-intercept (y value when x = 0).
when a line is parallel to another line, this means they both have the same slope.
so, we can use the same "a" from the original line : -1
to get "b" we use the given point coordinates :
5 = -1×-3 + b = 3 + b
2 = b
so, the full equation is
y = -x + 2
Using inductive reasoning, what is the most reasonable conjecture for the number of triangles in the eighth figure in the pattern? Enter your answer as a number.
The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern
How to determine the most reasonable conjecture for the number of triangles in the eighth figure in the pattern?The given figure represents the given parameter
From the figure, we have the following parameters
Pattern 1 = 4 trianglesPattern 2 = 6 trianglesPattern 3 = 8 trianglesWhen represented as a sequence, we have the following terms
4, 6, 8.....
The above sequence represents an arithmetic sequence with the following properties
First term, a = 4
Common difference, d = 2 i.e. 6 - 4
The most reasonable conjecture for the number of triangles in the eighth figure in the pattern is calculated by the following arithmetic sequence formula
Tn = a + (n - 1) * d
So, we have
T8 = 4 + (8 - 1) * 2
Evaluate
T8 = 18
Hence, the most reasonable conjecture for the number of triangles in the eighth figure in the pattern is that there are 8 triangles in the eighth figure in the pattern
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Calculate the paychecks of the following people. They make time and a half for any hours beyond 40. Round all values to two decimal places.
Answer:
Sue Black: 40 hours, $270
Jerry Atrix: 30 hours, $154.50
Sam Ting: 38.75 hours, $339.06
Step-by-step explanation:
Firstly, 40 hours is a workweek of 8-hour shifts. It's good to remember. Otherwise, we can multiply 8 by 5 and get 40 anyway. That's the hours of Sue Black, and she earns:
40*$6.75 = $270
Jerry worked for (note you can easily add in memory if you do the fractions first):
7.25+3+6.75+8+5 = 7.25+6.75 + 3+8+5 = 14 + 16 = 30
Earnings:
30*$5.15 = $154.50
Sam worked a quarter of an hour less than Sue each day. That means that his total time was:
40 - 5 * 0.25 = 40 - 1.25 = 38.75
Earnings:
38.75*$8.75 = $339.0625 ≈$339.06
From the sample space S = {1, 2, 3, 4,.... 15) a single number is to be selected at random. Given the following events, find the indicated probability.
A: The selected number is even.
B: The selected number is a multiple of 4.
C: The selected number is a prime number.
P(CIA)
The probability that the selected number is even is 7/15.
The probability that the selected number is a multiple of 4 is 1/5.
The probability that the selected number is a prime number is 2/5.
How to illustrate the information?Based on the information illustrated, the following can be deduced:
Even numbers = 2, 4, 6, 8, 10, 12, 14.
Multiple of 4 = 4, 8 and 12.
Prime numbers = 2, 3, 5, 7, 11, and 13.
Therefore, the probability that the selected number is even will be:
= 7/15.
The probability that the selected number is a multiple of 4 is:
= 3/15 = 1/5.
The probability that the selected number is a prime number is:
= 6 / 15
= 2/5.
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A figure is transformed by T(x, y) = (x+3, y-1) and then transformed by S(x-3, y + 1). How does the preimage relate to the final image? please show work sorry
Answer: The preimage and final image are the same point
This applies to every point in the xy plane.
======================================================
Explanation:
Let's say we started with the example point of (5,7)
Put the coordinates of the point into the T(x,y) transformation
We'll replace every x with 5 and every y with 7
So,
T(x, y) = (x+3, y-1)
T(5, 7) = (5+3, 7-1)
T(5,7) = (8, 6)
What does this mean? It means that the original preimage point (5,7) moves to (8,6). This is a shift of 3 units right and 1 unit down.
------------------
Now we'll plug the coordinates of that result, the (8,6), into the transformation of S(x, y) = (x-3, y + 1)
Plug in x = 8 and y = 6 to get...
S(x, y) = (x-3, y + 1)
S(8, 6) = (8-3, 6 + 1)
S(8, 6) = (5, 7)
We have gone from (8,6) to (5,7). We're back where we started.
The second transformation of (x-3, y+1) shifts 3 units left and 1 unit up. Notice both of these undo the original "3 units right and 1 unit down" from earlier. So this is why we get back to the starting point. It's not a coincidence.
Therefore, transformation T and transformation S are inverse transformations of one another. They undo each other. It's like taking a step forward (transformation T) and then taking a step back (transformation S)
In terms of algebra, it's like how multiplication and division are inverses of each other.
As you can probably guess, there's nothing particularly special about (5,7). I chose two random numbers. Pick whatever two favorite numbers you want for x and y. Plug them into T(x,y) and then whatever that result is, plug it into S(x,y) to notice you should get back to your original choice of (x,y). I recommend GeoGebra as a useful tool to help with geometric transformations.
Evaluate x + y when x = -3/8 and y = 7/12.
Answer:
Solutions: x=1.
Step-by-step explanation:
The people go to a restaurant. Their bill comes to $78.00. They decide to split the cost. One person pays 4.50 the next person pays 3 time that amount. How much will the their person have to pay
Answer:
13
Step-by-step explanation:
u multiply 4.50 x 3 it makes it 13.5 so they basically need to pay more .
K
A bus traveled on a level road for 3 hours at an average speed 20 miles per hour faster than it traveled
on a winding road. The time spent on the winding road was 5 hours. Find the average speed on the
level road if the entire trip was 420 miles.
The bus's speed on the level road was
mph.
Answer: the bus's speed on the level road was 65 milles per hour
Step-by-step explanation:
Let the bus's speed on the level road is x mph
Hence, the bus's speed on the winding road is (x-20) mph
Thus,
3(x)+5(x-20)=420
3x+5x-100=420
8x-100=420
8x-100+100=420+100
8x=520
Divide both parts of the equation by 8:
x=65 mph
Odessa and Daxton are making a table that is 3 1/3m high and has an area of 32m2. What is the width?
Answer: 9.6 meters
Step-by-step explanation:
See attached image
Complete the table by dragging the correct sequence or formula to the correct container.
Sequence
Recursive Formula
0, 4.5, 9, 13.5, 18,
[Container 3]
[Container 5]
[Container 1]
anan-1-11; a₁ = 68
[Container 6]
12, 19, 33, 40...
Explicit Formula
[Container 2]
[Container 4]
an=5+7n
68, 57, 46, 35, 24,
an=-4.5+ 4.5n
Container 1 Container 2
Container 3
an = 79-11n
Container 4
anan-1+4.5; a₁ = 0 anan-1
Container 5 Container 6
-1+7; a₁ = 12
The following are the results:
[container 1] = aₙ = aₙ₋₁ ₊ 4.5 ; a₁ = 0
[container 2] = aₙ = ₋4.5 ₊ 4.5n
[container 3] = 68 , 57 , 46 , 35 , 24, ..
[container 4] = aₙ = 79 ₋ 11n
[container 5] = 12 , 19 , 33 , 40
[container 6] = aₙ = aₙ₋₁ ₊ 7; a₁ = 12
Given the sequence is : 0,4.5,9,13.5,18,..
recursive formula = aₙ=a₍ₙ₋₁₎+4.5 where a₁ = 0
Explicit formula = aₙ = a₁ ₊ (n ₋ 1)4.5
= 0 ₊ (n ₋ 1)4.5
aₙ = ₋4.5 ₊ 4.5n
b. given, we have recursive formula: aₙ = aₙ₋₁ ₋ 11 ; a₁ = 68
here we have the common difference as 11, and the initial term is 68.
hence the sequence will be 68 , 57 , 46 , 35 , 24, ..
Explicit formula = a₁ ₊ (n ₋ 1)11
aₙ = 68 ₊ 11n ₋ 11
aₙ = 79 ₋ 11n
c. the explicit formula is given, aₙ = 5 ₊ 7n
here we have the common difference as 7.
so the sequence is 12,19,33,40
and the recursive formula is aₙ = aₙ₋₁ ₊ 7; a₁ = 12
Hence we get the acquired results.
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Select all equations that are equivalent to -8x - 6 15. 2 - (Select all that apply.) 4x+3= 15 -4x-3=15 8x+6=30 (-4x - 3) = 15 — − ½ ( 8x + 6) = 15 -
Using the approximation 3.14 for I, what is the radius of a circle with circumference 44 m?
The radius is m. (Round to the nearest tenth as needed.)
Given the value of the circumference, the radius of the circle to the nearest tenth is 7.0m.
What is the radius of the given circle?A circle is simply a closed 2-dimensional curved shape with no corners or edges.
The circumference of a circle is expressed mathematically as;
C = 2πr
Where r is radius and π is constant pi ( π = 3.14 ).
Given the data in the question;
Circumference of the circle C = 44mConstant pi π = 3.14Radius r = ?Plug the given values into the circumference formula above and solve for r.
C = 2πr
44m = 2 × 3.14 × r
44m = 6.28 × r
Reorder the equation and divide both sides by 6.28
6.28 × r = 44m
( 6.28 × r )/6.28 = 44m/6.28
r = 44m/6.28
r = 7.0m
Given the value of the circumference, the radius of the circle to the nearest tenth is 7.0m.
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Leila got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 13 cents per yard. If after that purchase there was $8.63 left on the card, how many yards of ribbon did Leila buy?
_____yards
If 13 cents per yard is the price, and there was $8.63 left on the card, the yards of ribbon Leila bought is 49 yards of ribbon.
How to solve for the amountTo determine the number of yards of ribbon Leila bought, we need to calculate the difference between the initial balance on the prepaid debit card and the remaining balance after the purchase.
Initial balance: $15.00
Remaining balance: $8.63
The difference between these two amounts represents the amount spent on the ribbon:
$15.00 - $8.63 = $6.37
Now, we can calculate the number of yards of ribbon by dividing the amount spent by the price per yard:
$6.37 / $0.13 = 49
Therefore, Leila bought 49 yards of ribbon.
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Four friends went scuba diving today. Ali dove 70 feet, Tim went down 50 feet, Carl dove 65 feet, and Brenda reached 48 feet below sea level. Write the 4 friends’ names in order from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface.
The orders from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:
Brenda < Tim < Carlton < Ali
Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order. For example, a set of natural numbers are in ascending order, such as 1, 2, 3, 4, 5, 6, 7, 8… and so on.
If the information is sorted from highest to lowest, it is said to be in descending order. For example 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 are arranged in descending order. In other words, if the numbers are arranged from the largest to the smallest number, it is said to be in descending order.
We can write, four friends went scuba diving today,
Ali dove = 70 feet,
Tim went down = 50 feet,
Carl dove = 65 feet,
Brenda reach = 48 feet below sea level.
To determine the order from the person whose death was closest to the surface to the person whose death was the farthest from the surface.
Arrange in ascending order of distance from sea level.
Brenda < Tim < Carlton < Ali
48feet < 50 feet < 65 feet < 70 feet
Therefore,
The order from the person whose depth was closest to the surface to the person whose depth was the farthest from the surface as:
Brenda < Tim < Carlton < Ali.
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evaluate this please
Answer:
32⅘
(using indices)
32 = 2⁵
= 2⁵ × 1⅘
= 2²⁰
⁵
= 2⁴ = 16
Which expression could represent the product of 15 and the quantity 12 more than the number of wailles?
Use w-4 to solve once you have the correct expression! Does your expression make sense????
a. 15+12-w
bw(15+12)
45(w+12)
d. 15-12+w
15x+180 is the required expression. Let the number be 'x'. For more than we would use addition.
A mathematical expression is the collection of mathematical symbols that results from the valid combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.
2x + 3 is an illustration of a mathematical expression with a variable. Each and every variable needs to have a coefficient, or a value multiplied by the variable. The number 2 is the coefficient of x in the expression 2x + 3, which translates to 2x times plus 3.
Mathematical operators like addition, subtraction, multiplication, and division are used to create expressions in writing.
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In a particular class of 26 students , 13 are men. What fraction of the students in the class are women?
Answer:
1/2
Step-by-step explanation:
Since 13+13= 26 we know that 13 or 1/2 are girls
Solve the equation 3y + 17 = −2y + 25 for y
Answer:
y = 8/5
Terms:
3y, -2y, y
Leading term:
3y
Step-by-step explanation:
Subtract by 17 from all sides
[tex]3y+17-17=-2y+25-17[/tex]
Simplify
[tex]3y=-2y+8[/tex]
Add term 2y
[tex]3y+2y=-2y+8+2y[/tex]
Simplify further
[tex]3y + 2y = 5y\\= 5y\\5y = 8[/tex]
Divide all sides by 5
[tex]\frac{5y}{5}=\frac{8}{5}[/tex]
Cancel the current leading term, 5y, simplify one last time
[tex]y=\frac{8}{5}[/tex]
Answer:
y = [tex]\frac{8}{5}[/tex] or [tex]1\frac{3}{5}[/tex] or [tex]1.6[/tex] ✅
Step-by-step explanation:
[tex]3y+17=-2y+25[/tex]
⬆️
Move the variable to the left-hand side and change its sign
⬇️
[tex]3y+17+2y=25[/tex]
⬆️
Move the constant to the right-hand side and change its sign
⬇️
[tex]3y+2y=25-17[/tex]
⬆️
Collect like terms
⬇️
[tex]5y=25-17[/tex]
⬆️
Subtract the numbers
⬇️
[tex]5y=8[/tex]
⬆️
Divide both sides of the equation by 5
⬇️
[tex]\frac{5y}{5} =\frac{8}{5}[/tex]
⬇️
Solution
[tex]y=\frac{8}{5}[/tex] ✅
Alternative form
[tex]y=1\frac{3}{5} , y=1.6[/tex] ✅
I hope this was helpful!
Have a blessed day! (✿◠‿◠)