The variable term can be added to both sides to solve an inequality with a positive coefficient when it is solved with a negative coefficient.
What is inequality?In mathematics, inequalities specify the connection between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equivalent. But various inequalities are used to compare the values, whether it is less than or larger than.
What is a coefficient?A coefficient in mathematics is a multiplicative component in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. When the coefficients are themselves variables, they may also be termed parameters.
Recognize that the variable term can be added to both sides to solve an inequality with a positive coefficient when it is solved with a negative coefficient; in this instance, the relationship between the variable and the inequality symbol has flipped.
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Plss hurry!!! Each row of the table shows two of the interior angle measures of two triangles.
Which triangles are similar?
Choose Similar or Not Similar for each pair of triangles.
Triangles Similar Not Similar
Triangle 1: 80°, 62° Triangle 2: 62°, 38°
Triangle 1: 29°, 47° Triangle 2: 91°, 76°
Triangle 1: 100°, 45° Triangle 2: 25°, 45°
Triangle 1: 80°, 62° Triangle 2: 62°, 38° - Similar
Triangle 1: 29°, 47° Triangle 2: 91°, 76° - Nοt Similar
Triangle 1: 100°, 45° Triangle 2: 25°, 45° - Nοt Similar
What is Similarity οf Triangles?Twο triangles are similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal, meaning that they have the same shape but nοt necessarily the same size.
Triangles Similar οr Nοt Similar
Triangle 1: 80°, 62° Triangle 2: 62°, 38° - Similar
Triangle 1: 29°, 47° Triangle 2: 91°, 76° - Nοt Similar
Triangle 1: 100°, 45° Triangle 2: 25°, 45° - Nοt Similar
Tο determine if twο triangles are similar, we need tο check if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal.
In the first pair οf triangles, the measures οf the twο angles in Triangle 2 are cοrrespοnding angles tο the twο angles in Triangle 1, sο if we subtract the angle measures frοm 180 degrees, we can see that the third angles in bοth triangles are cοngruent:
Angle 1 in Triangle 1 = 80 degrees, Angle 2 in Triangle 1 = 62 degrees, Angle 3 in Triangle 1 = 180 - 80 - 62 = 38 degrees
Angle 1 in Triangle 2 = 62 degrees, Angle 2 in Triangle 2 = 38 degrees, Angle 3 in Triangle 2 = 180 - 62 - 38 = 80 degrees
Since the cοrrespοnding angles are cοngruent, the triangles are similar.
In the secοnd pair οf triangles, nοne οf the angles are cοngruent and the side lengths are nοt prοpοrtiοnal, sο the triangles are nοt similar.
In the third pair οf triangles, the measures οf twο angles in Triangle 1 are 100 degrees and 45 degrees, while the measures οf twο angles in Triangle 2 are 25 degrees and 45 degrees. The angles are nοt cοngruent, sο the triangles are nοt similar.
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I need to know the z score of 2,-2 and also the mean and standard deviation
Answer: two standard deviations below the average value.
Step-by-step explanation: The z score tells you how far below the average value that person or group is, on a scale from -2 to 2. The higher the z score, the more abnormal or anomalous the data being compared is. A z score of 1 indicates that the data is exactly average, while a z score of -2 indicates that the data is two standard deviations below the average value.
A rectangular sheet of paper 72 cm x 48 cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.
Answer:
5
Step-by-step explanation:
this is wrong
A rectangular prism is 4 inches long, 3 inches wide, and 8 inches tall. Eli packs the prism with unit cubes to find the volume. Abby uses a formula to find the volume.
Part A]
Answer:
The volume of this rectangular prism is
4 × 3 × 8 = 96 square inches. So Eli would need 96 unit cubes.
114509772 rounded to the nearest ten thousand
Answer: 114,510,000
Delete the commas if needed.
============================================
Explanation:
The given number is 114,509,772
The 0 is in the ten thousandths place value. Just to the right of it is 9, which fits the criteria of "5 or larger". So we'll bump the "509" up to "510". Everything to the right of 9 will be replaced with zeros.
That's how we go from 114,509,772 to 114,510,000
-------------
Put another way:
Temporarily ignore the 114 up front and focus on the remaining portion 509,772
This number can be verbalized as "509 thousand" in an approximate sense. The 772 at the end means it's much closer to 510 thousand than it is to 509 thousand. That's why the 509 bumps up to 510.
Therefore, we have 509,772 round to 510,000
Overall, we have 114,509,772 round to 114,510,000
can y’all show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11х - 4.
Answer:
To show that a x - 4 is a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4, we need to show that f(a x - 4) = 0 for all values of x.
We can use polynomial long division or synthetic division to divide f(x) by (a x - 4) and check if the remainder is zero. Here, we will use synthetic division:
4/a | 2 -5 -11 -4
| 8a 12a 4a-16
+------------------
2 8a-5 a-11 4a-20
The last term in the bottom row of the table is the remainder, which is 4a - 20. We can see that this remainder is equal to zero if a = 5.
Therefore, if we substitute x = (5/ax - 4) into the function f(x), we get:
f(a x - 4) = 2(5/ax - 4)^3 - 5(5/ax - 4)^2 - 11(5/ax - 4) - 4
Simplifying this expression, we get:
f(a x - 4) = 0
This means that a x - 4 is indeed a factor of the function f(x) = 2x^3 - 5x^2 - 11x - 4 when a = 5.
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who received medication A, 84 said this pain reliever was effective. Of the 108 people in the other group, 66 reported that pain reliever B was effective.
(a)Find a 95% confidence interval for the difference in the proportions of people who may find these medications effective. Interpret your interval.
(b) Does this interval contain zero? What does that mean for the hypothesis test of the difference in proportions?
(a) The 95% confidence interval for the difference in proportions of people who may find these medications effective is 0.029 to 0.231, which suggests that medication A is more effective than medication B in relieving joint pain.
(b) No, the interval does not contain zero, which means that the difference in proportions is statistically significant and supports the hypothesis that medication A is more effective than medication B.
A spinner is divided into many sections of equal size. Some sections are red, some are blue, and the remaining are green. The probability of the arrow landing on a section colored red is 9/20 . The probability of the arrow landing on a section colored blue is 6/20 . What is the probability of the arrow landing on a green-colored section? (1 point)
A. 11/20
B. 5/20
C. 15/20
D. 6/20
Answer: B. 5/20
Step-by-step explanation: We have 3 sections. Red, blue, and green. Red is 9/20, blue is 6/20. If we do 9+6, it equals 15. Since it's out of 20, you have to do 20-15 which equals 5. Your answer is 5/20.
if the minimum commission that an agent can earn per tank is R713,76 determine the lowEST amount that agent C could have earned in 2014
Answer:
To determine the lowest amount that agent C could have earned in 2014, we need to know the number of tanks that agent C sold in 2014 and the commission rate per tank.
Let's assume that the commission rate per tank for agent C is R x. We need to find the lowest value of R that would result in the agent earning a minimum commission of R713.76 per tank.
We know that the commission earned per tank is the product of the commission rate and the selling price of the tank. Let's assume that the selling price of each tank is SP.
So, the commission earned per tank is R x SP.
We also know that the minimum commission per tank is R713.76. Therefore,
R x SP >= R713.76
Solving for R, we get:
R >= R713.76 / SP
This means that the commission rate per tank must be at least R713.76 / SP in order for the agent to earn a minimum commission of R713.76 per tank.
Now, let's assume that agent C sold a total of T tanks in 2014. The total commission earned by agent C in 2014 would be:
Total Commission = R x SP x T
From the above equation, we can see that the total commission earned by agent C depends on the commission rate per tank, the selling price per tank, and the number of tanks sold.
To find the lowest amount that agent C could have earned in 2014, we need to minimize the total commission earned by agent C subject to the constraint that the commission rate per tank is at least R713.76 / SP.
Assuming that the selling price per tank is fixed, the lowest amount that agent C could have earned in 2014 would be when the commission rate per tank is equal to R713.76 / SP. In this case, the total commission earned by agent C would be:
Total Commission = R713.76 x T
Therefore, the lowest amount that agent C could have earned in 2014 is R713.76 x T, where T is the number of tanks sold by agent C in 2014.
4. Given that cos theta= 3/10 and 3pi/2 < theta < 2pi, find the exact value of each of the following:
a) sin 2theta
b) The quadrant in which the angle theta/2 is located.
B) cos theta/2
(a) The value of sin 2θ is -3√(91)/50.
(b) θ/2 is located in the third quadrant.
(c) The value of cos θ/2 is -√65/10.
What is the value of the sine and cosine functions?We know that cos θ = 3/10, so we can find sin θ using the Pythagorean identity:
sin² θ + cos² θ = 1
sin²θ + (3/10)² = 1
sin²θ = 1 - (3/10)² = 91/100
sin θ = ±√(91)/10
Since 3π/2 < θ < 2π,
we know that sin θ < 0, so sin θ = -√(91)/10.
a) To find sin 2θ, we can use the double angle formula:
sin 2θ = 2 sin θ cos θ
sin 2θ = 2 (-√(91)/10) (3/10)
sin 2θ = -3√(91)/50
b) To find the quadrant in which θ/2 is located, we first need to find θ/2:
θ/2 = (3π/2 + 2π)/2 = 5π/4
5π/4 is in the third quadrant, so θ/2 is located in the third quadrant.
c) To find cos θ/2, we can use the half angle formula:
cos θ/2 = ±√((1 + cos θ)/2)
Since 3π/2 < θ < 2π, we know that cos θ < 0, so we take the negative square root:
cos θ/2 = -√((1 + 3/10)/2)
cos θ/2 = -√(13/20)
Simplifying the radical by dividing both numerator and denominator by 4:
cos θ/2 = -√(13)/2√5
Multiplying numerator and denominator by √5 to rationalize the denominator:
cos θ/2 = -√65/10
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(URGENT)!!!!!!!
Write one sentence that addresses the issue of globalization from the text and one sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers
Answer:
Step-by-step explanation:
One sentence on globalization from the text: The process of globalization has brought significant changes to the world economy, including the emergence of new trade patterns and the increasing interconnectedness of markets.
One sentence on how the absence of plantation owners perpetuated cruel treatment of slaves by overseers: In the absence of plantation owners, overseers were left with unchecked power over the enslaved population, often resulting in brutal treatment and violence
79 Points!!! Algebra question. A biologist plotted the data from his latest experiment and connected the points to form the graph shown. He recognizes that the graph is a translation of y=x^2. Write a function f(x) to represent the graph of his data. Photo attached. Thank you!
11). Evaluate the definite integral.
The value of the definite integral is determined as -1/28.
What is a definite integral?A definite integral is a mathematical concept that represents the area under a curve between two specific points, called the limits of integration. The definite integral is denoted by the symbol ∫, and the limits of integration are written as a and b, where a is the lower limit and b is the upper limit.
To evaluate the definite integral, we will use the following method:
[tex]\int\limits^2_0 {- \frac{6x}{(3x + 2)^2} } \, dx ; u = 3x^2 + 2[/tex]
We can start by substituting [tex]$u=3x^2+2$[/tex], which gives us [tex]$du/dx=6x$[/tex], or [tex]$x,dx=du/6$[/tex].
Using this substitution, we can rewrite the integral as:
[tex]\int\limits^2_0 - \frac{6x}{(3x^2 + 2)^2} , dx &\\\\\\\=\ \int\limits^{u(2)}{u(0)} -\frac{1}{u^2},du/6\\\\\\&= \left[ \frac{1}{6u} \right]^{u(2)}{u(0)} \\\\\\&= \frac{1}{6}\left(\frac{1}{u(2)} - \frac{1}{u(0)}\right)\\\\\\\&= \frac{1}{6}\left(\frac{1}{3(2)^2 + 2} - \frac{1}{3(0)^2 + 2}\right) \\\\\\\&= \frac{1}{6}\left(\frac{1}{14} - \frac{1}{2}\right)\\\\\\\ &= \frac{1}{6}\left(-\frac{6}{28}\right) \\\\\\\\&= \boxed{-\frac{1}{28}}\end{align*}[/tex]
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Question 29 Which expression represents the distance between points J and K on the number line?
On the number line, there are five spaces between the points J and K.
What does a number line exactly mean?A number line is a horizontal line with consistently spaced numerical increments. How you respond to the number on the line will depend on the numbers on the line. Depending on the question that goes with it, a number can be used in a variety of ways, such as when graphing a point.
The absolute value of the difference in the coordinates between points J and K on the number line can be used to calculate the distance between them.
Points J and K in this instance have coordinates of -4 and 1, respectively. As a result, the following formula may be used to indicate the distance between locations J and K:
|1 - (-4)|
If we condense this expression, we get:
|1 + 4|
= |5|
= 5
Hence, the distance on the number line between points J and K is 5.
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A block of metal with volume 15 m³ 3 and density 8,800 kg/m³ is combined with another metal of 3 mass 850 kg and volume 6.2 m³ to form an alloy. What is the density of the alloy to the nearest integer?
Answer:
Step-by-step explanation:
The total mass of the alloy is the sum of the masses of the two metals:
mass = density x volume = (8800 kg/m³ x 15 m³) + 850 kg = 132,000 kg + 850 kg = 132,850 kg
The total volume of the alloy is the sum of the volumes of the two metals:
volume = 15 m³ + 6.2 m³ = 21.2 m³
Therefore, the density of the alloy is:
density = mass / volume = 132,850 kg / 21.2 m³ ≈ 6266 kg/m³
Rounding to the nearest integer, the density of the alloy is 6266 kg/m³.
If you need $25,000 eight years from now, what is the minimum amount of money you need to deposit into a bank account that pays an annual percentage rate (APR) of 5% that is compounded--
i need an answer ASAP because i need to bring up my grade thanks also its due today
The minimum amount of money to be deposited in the bank account is $16,921. The solution has been obtained by using compound interest.
What is compound interest?
Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period. In mathematics, compound interest is frequently referred to as C.I.
We are given that we need $25,000 eight years from now and the account pays an annual percentage rate (APR) of 5% which is compounded annually.
So, using the compound interest formula, we get the principal as
⇒ P = [tex]\frac{A}{(1 + \frac{r}{n} )^{nt} }[/tex]
⇒ P = [tex]\frac{25000}{(1 + \frac{0.05}{1} )^{8} }[/tex]
⇒ P = $16,920.98
Hence, the minimum amount of money to be deposited in the bank account is $16,921.
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A cone has a radius of 6 centimeters and a height of 10 centimeters. What is the volume of the cone in cubic centimeters?
centimeters?
A 480π cm³
B 120π cm³
C 360π cm³
D 60π cm³
The volume of the cone in cubic centimeters in terms of π = 120π cm³. That is option B.
How to calculate the volume of a cone?To calculate the volume of a cone, the formula that is to be used;
Volume = 1/3 πr²h
Where;
Height = 10 centimetres
Radius = 6 centimetres
Volume = 1/3 × π × 6²× 10
= 360π/3
= 120π cm³
Therefore the volume of the cone whose dimensions are given = 120π cm³.
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A truck is traveling due north at 60km/hr approaching a crossroad. On a perpendicular road a police car is traveling west toward the intersection at 75km/hr. Both vehicles will reach the crossroad exactly one hour. Find the vector currently representing the displacement of the truck with respect to the police car.
Displacement d=
In the given problem, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
How to Solve the Problem?To solve this problem, we can use vector addition. Let's assume that the police car is at the origin, and let the positive x-axis point west and the positive y-axis point north. Then, the initial position of the truck can be represented by the vector (-d, 0), where d is the distance between the police car and the crossroad.
Since the truck is traveling due north, its velocity vector is (0, 60). Similarly, the velocity vector of the police car is (-75, 0). We know that both vehicles will reach the crossroad at the same time, which means that their displacement vectors will have the same magnitude and direction.
Let's call the displacement vector we're looking for "D". Using the formula for displacement, we can write:
D = vt
where v is the average velocity of both vehicles, and t is the time it takes for them to reach the crossroad (which is one hour). The average velocity is given by the vector sum of the velocities of the truck and the police car:
v = (0, 60) + (-75, 0) = (-75, 60)
Substituting in the values for v and t, we get:
D = (-75, 60) * 1 = (-75, 60)
Therefore, the displacement vector of the truck with respect to the police car is (-75, 60). This means that the truck is 75 km to the west and 60 km to the north of the police car.
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Help me pleaseeeeee!
Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn
In algebra, what is a rectangle?A rectangle is a type οf quadrilateral that has its parallel sides equal tο each οther and all the fοur vertices are equal tο 90 degrees. Hence, it is alsο called an equiangular quadrilateral. Since, the οppοsite sides are equal and parallel, in rectangle, therefοre, it can alsο be termed as a parallelοgram.
Using the pοlygοn tοοl a rectangle with length 5 unit and width 3 units has been drawn
check the attachment given belοw tο understand.
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A golfer is standing at the tee, looking up to the green on a hill. If the tee is 38 yards lower than the green and the angle of elevation is 15 degrees, find the distance from the tee to the hole.
Answer:
146.82 yards is the distance from tee to hole.
Step-by-step explanation:
Let A is the position of tee and where the golfer is standing.
C is the position of hole.
CB is the vertical distance between greens and tee.
Angle of elevation,
To find: side AC.
Using trigonometric functions, we know that value of sine is:
[tex]sin\theta=\dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]
Here [tex]\theta=\angle BAC=15^\circ[/tex]
Perpendicular is side CB.
Hypotenuse is side AC.
[tex]\text{sin}12^\circ=\dfrac{\text{CB}}{\text{AC}}[/tex]
[tex]\implies\text{CB}=\dfrac{38}{\text{sin}15^\circ}[/tex]
[tex]\implies\text{CB}=146.82[/tex]
Hence, 146.82 yards is the distance from tee to hole.
How would I do this and what would the answer be.
Answer:
28x + 40
Step-by-step explanation:
Since all four sides of a square are equal, we can make an equation:
[tex]4(7x + 10) = 28x + 40[/tex]
Joe made
4
identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all
4
necklaces was
$
25.60
. If the beads cost
$
2.70
for each necklace, how much did each pendant cost?
Answer:
Each pendant costs $3.70.
Step-by-step explanation:
Let's assume that the cost of each pendant is x dollars.
The total cost of the beads for all 4 necklaces is 4 * $2.70 = $10.80.
The total cost of the beads and pendants for all 4 necklaces is $25.60.
So, the total cost of the pendants for all 4 necklaces is
$25.60 - $10.80 = $14.80.
Since there are 4 necklaces and each necklace has a pendant, the total cost of all the pendants is 4x dollars.
So we can write
4x = $14.80
Dividing both sides by 4, we get
x = $3.70
Therefore, each pendant costs $3.70.
Suppose 50 rabbits are on Groff Farm… DOUBLING every SIX MONTHS…
How many rabbits after 5 years?
How many rabbits after 10 years?
Using geometric progression Rabbits after 5 years will be 5120. Rabbits after 10 years will be 52,428,800.
What is geometric progression?When each term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the series. It should be mentioned that the common ratio is obtained by dividing any succeeding term by its preceding term.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate organizations or groups.
In this question,
The number of rabbits initially=50=a
rabbits after 6 months=100
common ratio=r= 100/50=2
Since it is a geometric progression, the 11th term will give us the number of rabbits after 5 years.
a₁₁=a₁(r)¹¹⁻¹
=50(2)¹⁰=5120
the 21th term will give us the number of rabbits after 10 years.
a₂₁=a₁(r)²¹⁻¹
=50(2)²⁰=52,428,800
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The gasoline gauge on a van initially read
1/4 full. When 12 gallons were added to the tank, the gauge read 3/4 full. How many more gallons are needed to fill the tank?
Initially, 1/4 of the tank was filled.
After adding 12 gallons, it was 3/4 full.
Increase in fuel filled portion =
[tex]\dfrac{3}{4} -\dfrac{1}{4} =\dfrac{3-1}{4} =\dfrac{2}{4}[/tex]
So 2/4 of the tank = 12 gallons
1/4 of tank [tex]= 12 \div 2 = 6[/tex] gallons
4/4 of tank [tex]= 6\times4 = 24[/tex] gallons
____________________
Portion remaining to be filled =
[tex]1-\dfrac{3}{4} =\dfrac{4-3}{4} =\dfrac{1}{4}[/tex]
Fuel needed [tex]= \dfrac{1}{4} \times 24 = 6[/tex] gallons
So you need 6 more gallons to fill the tank
I need help anyone wants to help me with this to write it out :) thank you<3!!!
Answer:
Dip your finger in both whichever one is salty don't give to your plant
Step-by-step explanation:
Here are the first five terms of a geometric sequence.
√√5
10 20 √5
(a) Work out the next term of the sequence.
5√2
The 4th term of a different geometric sequence is
4
The 6th term of this sequence is
5√2
8
Given that the terms of this sequence are all positive,
(b) work out the first term of this sequence.
You must show all your working.
200
400 √5
Answer:
1/2
Step-by-step explanation:
20/√5 = 4√5
4√5 * (5√2 / 4√5) = 5√2
8 / 4 = 2
4 / (2^3) = 1/2
|1/2| = 1/2
The first term of this sequence is equal to 1/2
What is a geometric sequence and how to find its nth terms?Suppose the initial term of a geometric sequence is a and the term by which we multiply the previous term to get the next term is r
Then the sequence would look like
[tex]a, ar, ar^2, ar^3, \cdots[/tex]
Thus, the nth term of such sequence would be; [tex]T_n = ar^{n-1}[/tex](you can easily predict this formula, as for nth term, the multiple r would've multiplied with initial terms n-1 times).
We are given that The 4th term of a different geometric sequence is
4, The 6th term of this sequence is 5√2
20/√5 = 4√5
4√5 (5√2 / 4√5) = 5√2
8 / 4 = 2
Therefore,
4 / (2^3) = 1/2
|1/2| = 1/2
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HELPPP PLEASE
X^2+8x+5=0
Answer:
hope its right
Step-by-step explanation:
1/2 + 3/9 = The first time a team is
Answer:
Step-by-step explanation:
To get the LCM in the denominator:
1/2 x 9/9 = 9/18
3/9 x 2/2 = 6/18
9/9 and 2/2 both equal 1, so multiplying these fractions by ny number will result in the same number since any number times 1 is the same number.
9/18 - 6/18 = 3/18
Simplifying this answer:
3/18 = 1/6 because both the numerator and denominator are both multiples of three and are divisible by three.
The answer is 1/6.
Answer: 7/9 or 0.83333333333
Step-by-step explanation:
:D Hope it helped!!! :)
Alen has read 60% of a book. He has 32 more pages to finish. How many pages are there in the book?
Alen has read 60% of a book in which there are 80 pages in the book.
What is total number?The term "total number" typically refers to the complete quantity or count of something. It can refer to the number of items in a set, the number of people in a population, the total sales of a company, or any other numerical quantity that represents a whole.
According to question:Let's say the total number of pages in the book is "x".
According to the problem, Alen has read 60% of the book, which means he has completed 0.6x pages.
He still has 32 more pages to finish, so the number of pages he has left to read is (x - 0.6x) = 0.4x.
We can set up an equation:
0.4x = 32
Solving for x:
x = 80
Therefore, there are 80 pages in the book.
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during a sale, all shirts cost $35 and all pants cost $50. jonathan is buying new clothes for school and planes to spend at least $350
The minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
Assuming Jonathan only wants to buy shirts and pants, let's represent the number of shirts he buys as "s" and the number of pants as "p". Then we have two equations:
1. The total cost of Jonathan's purchase:
35s + 50p >= 350
2. Jonathan wants to spend at least $350:
s, p >= 0
To solve this problem, we can start by finding the minimum number of pants Jonathan needs to buy to meet his spending requirement.
When s = 0, 50p >= 350, so p >= 7.
Therefore, Jonathan needs to buy at least 7 pants.
If Jonathan buys 7 pants, the total cost of his purchase is 35s + 50(7) = 35s + 350. To spend at least $350, he needs to buy enough shirts to make the total cost of his purchase at least $350.
35s + 350 >= 350
35s >= 0
s >= 0
Since s must be a non-negative integer (you can't buy a fractional part of a shirt), Jonathan needs to buy at least 0 shirts.
So the minimum purchase Jonathan can make to meet his spending requirement is 7 pants and 0 shirts, which will cost him $350.
Of course, Jonathan can buy more than 7 pants and/or some shirts to meet his spending requirement. For example, he could buy 5 pants and 4 shirts, which would cost him $375.
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