a) Issac get £10.75 as change after buying all masks
b) The price of the e-scooter in the sale is £277.50
a)
Isaac buys 17 anti-pollution masks for £5.25 each, so the total cost is
17 * 5.25 = £89.25
He pays with five £20 notes, which is a total of 5 * 20 = £100
So, the change he should get is £100 - £89.25 = £10.75
Therefore, Isaac should get £10.75 as change.
b)
In the sale, there is 1/4 off the cost price of the e-scooter, which means that the scooter is discounted by 1/4 * £370 = £92.50.
To work out the price of the e-scooter in the sale, you need to subtract the discount from the normal price, so
£370 - £92.50 = £277.50
Therefore, the price of the e-scooter in the sale is £277.50
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In which of the following intervals does the trigonometric inequality sec(x)
The Trigonometric inequality Sec (x)< cot(x) will hold true in π/2 < x < π.
How can a trigonometric inequality be expressed?
The intervals where the trigonometric inequality sec (x) cot (x) always holds true are what we are looking for.
This can also be expressed as: 1/cos (x) < 1/tan (x)
Now, this is only possible in the fourth quadrant, where cos x is positive and tan (x) is negative, where: π/2 < x < π.
The values for sin, cos, and tan are all positive in the first quadrant.
Only positive values for sin are present in the second quadrant.
The tan values in the third quadrant are all positive.
Only positive values for cos are present in the fourth quadrant.
Therefore the inequality Sec(x) < cot(x) will hold true in π/2 < x < π.
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You have $5$ red shirts, $5$ green shirts, $6$ pairs of pants, $8$ green hats and $8$ red hats, all of which are distinct. How many outfits can you make consisting of one shirt, one pair of pants, and one hat without having the same color of shirts and hats
Total = 240+240 = 480 potential combinations with a red shirt, green pants, and a green hat, or a green shirt, red pants, and a red hat, respectively.
How many outfit combinations can be put together from 6 shirts?The total number of possible outcomes for all four of these scenarios is 208, which is equivalent to 64 + 64 plus 16 plus 64. Consequently, we have a total of 120 different costumes to choose from (8 + 5 + 3). 8 × 5 × 3 = 120 . Given that you have 4 options for shirts, 3 options for shorts, and 2 options for shoes, the formula should be formatted as 4 × 3 ×2. You now have 24 wardrobe choices.
A "set" is made up of one top and one bottom. Since every bottom can be worn with every top, multiplying the tops by the bottoms gives us the total number of possible outfit combinations. Since dresses often aren't worn with tops or bottoms, they are introduced after the multiplication has occurred.
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What is the difference between polynomials and not polynomials equation explain your answer?
By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.
Expressions are polynomials, but expressions that equal zero are polynomial equations.
A polynomial may be written as the sum of a finite number of terms, where each term is the product of one or more variables raised to a positive integer exponent and a constant coefficient (or power).
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
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In ΔWXY, w = 470 inches, mm∠W=55° and mm∠X=42°. Find the length of y, to the nearest 10th of an inch.
The length of y using sine rule is 6664.2 inches
What is sine rule?The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.
in this case w/sinW = y/sinY
Y = 180-(55+42)
Y = 180-(97)
Y = 83°
Therefore 470/sin55 = y/sin83
470× sin83 = y sin55
= 466.50 = 0.707y
divide both sides by 0.707
y = 466.50/0.707
y = 6664.2 inches
therefore the length of y is 6664.2 inches
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In 6-7, explain whether each graph represents a linear function.
Answer:
In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line.
Step-by-step explanation:
In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line. A linear function is defined as a function of the form y = mx + b, where m and b are constants. The graph of a linear function is a straight line with a constant slope, and so any graph that is not a straight line is not a linear function.
Without the actual graph it's hard to say for sure, but based on the provided information, "The graph does not contain the point (20, –8)" indicates that the graph does not pass through this point (20, -8), and it could be indicating that it's not a straight line, So, The graph does not represent a linear function.
Hi!
ik -2x+9 is x=4.5 so are the number 4.5 apart and if so what do i do after that
The function y = -2x + 9 have ordered pairs (-4, 17), (-2, 13), (0, 9), (2, 5) and (4, 1)
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Given that:
y = -2x + 9
When x = -2; y = -2(-2) + 9 = 13
When x = 0; y = -2(0) + 9 = 9
When x = 2; y = -2(2) + 9 = 5
When x = 4; y = -2(4) + 9 = 1
The function y = -2x + 9 is a linear equation
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-1 23/40 = 9/10p
.................................................
Answer:
p = -7/4 or -1 3/4
Step-by-step explanation:
-1 23/40 = 9/10p
-1 23/40 = -63/40
So, our equation is
-63/40 = 9/10p
Divided both sides by 9/10
p = -7/4
So, the answer is
p = -7/4
or
-1 3/4
pls solve the question (i will mark u the brainliest)
Step-by-step explanation:
May be (p³)³ would be the answer!!!
BRAINLY ME PLEASE IF HELPFUL!!!
What word describes the genotype TT?
Answer: It's a homozygous dominant genotype.
Step-by-step explanation: Two capital letters or two lowercase letters are homozygous.
Using Euler's Method with a step size of h = 0. 2, estimate the value for y(1. 4) for the differential equation y plus 2 times dy dx equals the product of the natural logarithm of y and the sine of x, with y(1) = 2
Describe what moves you could use to create the transformation of the original image shown below.
original
The required transformations of the original image are the first translation of 7 units to the right side, then a reflection across the x-axis.
What is a transformation?A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.
The triangle is given in the represented graph, which vertices are as follows :
(-5, -1)
(-2, -1)
(-5, -3)
The image after a translation of 7 units to the right side will be given a triangle the vertices are as follows :
(-5 + 7, -1) → (2, -1)
(-2 + 7, -1) → (5, -1)
(-5 + 7, -3) →(2, -3)
Then the image after a reflection across the x-axis will be a triangle the vertices are as follows :
(2, -1) → (2, 1)
(5, -1) → (5, 1)
(2, -3) → (2, 3)
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Find the measurements of the exterior angles of the polygon
Explain (not optional)
On solving the question, sum of exterior angle is 360 degree. Hence, the value of x is 120°.
How do you calculate a triangle's total exterior angles?The exterior angle of a triangle is equal to the sum of its two opposite interior angles, according to the external angle theorem. Remember that the total external angle, measured from each vertex, is always 360°. Alternatively stated, d + e + f = 360°.The angle that is created between a triangle's extended side and one of its sides is known as the external angle. A triangle has a total of 360 degrees in its outside angles.
x + ( x+6) +114 = 360
2x = 240
x = 120
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A meteorologist set up rain gauges at various locations around a city and recorded the rainfall amounts in the table below. Use data in the table to create a line plot using 1/8 inches.
The data of the rainfall amount in inches to the locations are used to plot the attached line plot created with MS Excel.
What is a line plot?A line plot is a graph is the graphical display of data as check marks or points above a number line.
A line plot shows the frequency of the values in the data on the number line, using dots or check marks. The frequency of the data is shown above the specified locations on the graph of a line plot.
The line plot is therefore, indicative of how frequent particular values in the dataset are.
The possible data in the question are presented as follows;
Rainfall Amount; 1/8,[tex]{}[/tex] 3/8, 3/4, 3/4, 1/4, 1 1/4, 1/8, 1/4, 1, 1/8
Location; [tex]{}[/tex] 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
The frequency of the data in a tabular form are;
Rainfall [tex]{}[/tex] Frequency
1/8 [tex]{}[/tex] 3 locations
3/8 [tex]{}[/tex] 1 location
3/4 [tex]{}[/tex] 2 locations
1/4 [tex]{}[/tex] 2 locations
1 1/4 [tex]{}[/tex] 1 location
1 [tex]{}[/tex] 1 location
The above frequency values can be used to create the attached line plot created with MS Excel
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Two cars start from the same intersection with one traveling southbound while the other travels eastbound going 10 mph faster. If after 2 hours they are 10sqrt(34) apart, how fast was each car traveling?
The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.
What is meant by intersection ?They are referred to be intersecting lines when two or more lines in a plane cross each other. The point of intersection, which can be found on all intersecting lines, is the common point shared by the intersecting lines.
Let speed of Car 1 = x mph
Speed of car 2 = (x + 10) mph
Hence,
OA = Distance travelled by car2 in 2 hours
⇒ OA = (x + 10) × 2 = 2x + 20
And, OB = Distance travelled by Car 1 in 2 hours
⇒ OB = x × 2 = 2 x
Now, In ΔOAB, OA² + OB² = AB²
substitute the values in the above equation
⇒ (2 x+20)² + (2 x)² = [tex](10 \sqrt{34})^2 \\[/tex]
⇒ 4x² + 400 + 80x + 4x² = 3400
simplifying the equation
⇒ 8x² + 20x - 3000 = 0
⇒ x² + 10x - 375 = 0
⇒ x² + 25x - 15x - 375 = 0
simplifying the above equation, we get
⇒ x(x + 25) - 15(x + 25) = 0
⇒ (x + 25)(x - 15) = 0
⇒ x + 25 = 0, x - 15 = 0
⇒ x = -25, x = 15
Since speed can not be negative.
Hence, x = 15 mph
⇒ x + 10 = 15 + 10 = 25 mph.
Hence, speed of car moving towards south =15 mph.
And, speed of (as moving towards East = 25 mph.
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The speed of car moving towards south exists 15 mph and, speed of (as moving towards East = 25 mph.
What is meant by intersection ?When two or more lines in a plane cross one another, they are referred to as intersecting lines. The common point shared by all intersecting lines is the point of intersection, which can be found on all of them.
What do you mean by Speed?The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.
Let speed of Car 1 = x mph
Speed of car 2 = (x + 10) mph
Hence,
OA = Distance travelled by car2 in 2 hours
⇒ OA = (x + 10) × 2 = 2x + 20
And, OB = Distance travelled by Car 1 in 2 hours
⇒ OB = x × 2 = 2 x
Now, In ΔOAB, OA² + OB² = AB²
substitute the values in the above equation
⇒ (2 x+20)² + (2 x)² =
⇒ 4x² + 400 + 80x + 4x² = 3400
simplifying the equation
⇒ 8x² + 20x - 3000 = 0
⇒ x² + 10x - 375 = 0
⇒ x² + 25x - 15x - 375 = 0
simplifying the above equation, we get
⇒ x(x + 25) - 15(x + 25) = 0
⇒ (x + 25)(x - 15) = 0
⇒ x + 25 = 0, x - 15 = 0
⇒ x = -25, x = 15
Since speed can not be negative.
Hence, x = 15 mph
⇒ x + 10 = 15 + 10 = 25 mph.
Hence, speed of car moving towards south =15 mph.
And, speed of (as moving towards East = 25 mph.
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This year’s favorite to win the frog jumping event is Newton. The objective is to take the longest jumps and stop as close as possible to 120 steps. Pythagoras and Fermat are Newton’s toughest competition. ● Newton takes 4 jumps and falls short of the mark by 4 steps. ● Pythagoras takes 5 jumps and overshoots the mark by 5 steps. ● Fermat hits the mark exactly after 6 jumps. How long, in steps, is each frog’s jump?
The length of jump by Pythagoras = 25 units
The length of jump by Newton = 29 units
The length of jump by Fermat = 20 units
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the length of the jump by Pythagoras be P
Let the length of the jump by Newton be N
Let the length of the jump by Fermat be F
Now , the equation will be
The total number of steps = 120 steps
The number of jumps by Pythagoras = 5 jumps
The number of steps overshoot by Pythagoras = 5 steps
So , P ( 5 ) - 5 = 120 be equation (1)
On simplifying the equation , we get
Adding 5 on both sides of the equation , we get
5P = 125
Divide by 5 on both sides of the equation , we get
P = 25 units
The number of jumps by Newton = 4 jumps
The number of steps fell short by Newton = 4 steps
So , N ( 4 ) + 4 = 120 be equation (2)
On simplifying the equation , we get
Subtracting 4 on both sides of the equation , we get
4N = 116
Divide by 4 on both sides of the equation , we get
N = 29 units
The number of jumps by Fermat = 6 jumps
So , F ( 6 ) = 120 be equation (2)
On simplifying the equation , we get
Divide by 6 on both sides of the equation , we get
F = 20 units
Therefore , the value of P , N and F are 25 , 29 and 20 units respectively
Hence , the length of each jump is 25 , 29 and 20 units
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Describe the distribution of the ages of the Best Actor Oscar winners [LINK]:
A) What is the BEST description of the SHAPE?
- The distribution is not skewed
- The distribution is skewed left.
- The distribution is skewed right.
The correct option is option (c)-"The distribution is skewed right."
The distribution of the ages of the Best Actor Oscar winners is slightly skewed to the right.
A histogram of the ages of the Best Actor Oscar winners shows that the majority of the ages are centered around the mean age, with a few ages on the higher end that extend the right tail of the distribution. This creates a small skewness to the right.
The distribution seems to be centered at around 42-43.
The age distribution ranges from about 30 to about 75, without taking into account an outlier.
It's worth noting that the distribution is not extremely skewed, and the majority of the ages are still grouped around the center of the distribution.
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Describe a sequence of transformation that maps DOG onto CAT
Sequence of transformation is first moving 5 unit in y axis than mirror image with y axis.
What would you say about the order of the transformations?A particular order of transformational events is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.
What kind of figure can a series of transformations map onto itself?The line of reflection must pass through the centre point for the figure to map onto itself. The sides of the figure are cut by two lines of reflection. The vertices of the figure are intersected by two lines of reflection. As a result, there are four potential lines of reflection that pass through the center.
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Use the table to convert the following unit length as indicated. Choose the right answer.
1,000 yards to kilometers
1000 yards in kilometers will be 0.9 km.
The yard is a United States customary measurement. In this form of measurement, we have yards, feet, and inches.
1 Yard = 3 feet.
1 foot = 12 inches.
Here we are given 1000 yards,
1000 yards = 3 X 1000 feet
= 3000 feet
= 36000 inches.
Now, converting this to the metric measures we know that
1 inch = 2.5 cm
Hence, 36000 inches = 90000 cm.
1 cm = 1/100 m
Hence, 90000 cm = 90000/100 m
= 900 m
1 m = 1/1000 km
Hence, 900 m = 900/1000 km
= 0.9 km
Hence, 1000 yeard = 0.9 km.
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How many solutions does 5x 2y =- 7?
There is no single answer to this question. It depends on what values are chosen for x and y , equation has an infinite
The equation 5x + 2y = -7 is an indeterminate equation with two unknowns, x and y. This means that the equation has an infinite number of solutions, depending on the values of x and y. For example, if x = 3 and y = -2, then the equation would be satisfied. If x = 2 and y = -3, then the equation would also be satisfied. Therefore, the number of solutions for this equation is infinite.There is no single answer to this question. It depends on what values are chosen for x and y.
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To determine the mean number of children per
household in a community, Tabitha surveyed
20 families at a playground. For the 20 families
surveyed, the mean number of children per
household was 2.4 .4 Which of the following
statements must be true?
A) The mean number of children per household in
the community is 2.4 .
B) A determination about the mean number of
children per household in the community should
not be made because the sample size is too small.
C) The sampling method is flawed and may
produce a biased estimate of the mean number
of children per household in the community.
D) The sampling method is not flawed and is likely
to produce an unbiased is not flawed and is likely
number of children per household in the
community.
True statement is number C.
What is biased and unbiased sample in statistics?
The method of sampling where a portion of population are given priority over the rest of the population is called biased sample.
In the unbiased sampling method almost, each population is valued, and they are given chance to be selected in the data list.
flawed sampling means the method of sampling is inappropriate such as survey works that taken in non-random way. As example, researchers start to ask people walking in the street.
Which statement is true as given in question?The survey was taken at a playground on 20 families.
the survey estimated that mean number of children per household in the community was 2.4.
The main purpose of the survey was to determine the mean number of children per household in the community.
but the survey study was held at the playground and the sample size is too small.
The above data could not give the true estimation.
So, the sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.
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Solve for x in this triangle. Round your answer to the nearest tenth. 13 35⁰ X
Answer:
x ≈ 10.6
Step-by-step explanation:
using the cosine ratio in the right triangle
cos35°= [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{13}[/tex] ( multiply both sides by 13 )
13 × cos35° = x , then
x ≈ 10.6 ( to the nearest tenth )
Which value of b makes the equation b/4 =12 true? a. 48 b. 16 c. 9 d. 3
help please i have 4 mins to finish ;((
The correct option is (a) 48.
In algebra, an equation is a statement of equality between two expressions. These expressions can be numbers, variables, or a combination of both.
In the equation:
b/4 = 12, the variable b is on one side of the equation and the value 12 is on the other side.
To find the value of b that makes the equation true, we need to isolate the variable b on one side of the equation.
In this case, we can do this by multiplying both sides of the equation by 4.
This cancels out the denominator of the fraction on the left side, and we get,
b = 12*4= 48.
This means that when b is equal to 48, the equation b/4 = 12 is true.
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-7x+y=-19 In standard form
Answer: x= 1/7y + 19/7 (Standard form will be:7x−y=19)
Step-by-step explanation:
Step 1: Add -y to both sides.
−7x+y+−y=−19+−y
−7x=−y−19
Step 2: Divide both sides by -7.
−7x/−7
= −y−19/−7
x= 1/7y + 19/7
What type of triangle is 35 55 90?
35-55-90 is a right-angle triangle because one of the angles is 90 degrees.
The explanation for a right triangle says that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or simply, a right triangle.
The right triangle formula can be presented in the following way: The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
In a right triangle we have: (Hypotenuse)² = (Base)² + (Altitude)²
Properties of Right Triangle:
The largest angle is always 90º.The longest side is called the hypotenuse which is always the side opposite to the right angle.The measurements of the sides obey the Pythagoras rule.It cannot have any obtuse angle.Read more about the right-angle triangle:
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Need help ASAP Geometry Assignment
The figure also has a line symmetry for the vertical line x is 5, and a line symmetry for the horizontal line y is 5 .Therefore the figure has both symmetry
What is meant by line symmetry ?A form or item is divided into two equal and symmetrical portions by a line of symmetry. Because it creates a symmetrical split in the figure and the separated pieces look like mirror reflections of one another, we also refer to this line as the axis of symmetry or the mirror line.
An imaginary line that splits a line or shape into two identical parts is called the axis or line of symmetry. The symmetry axis of a parabola will be required of you at higher level mathematics. This u-shaped line on the graph is a parabola.
B) The transformation that maps the figure unto itself are therefore;
1) Rotating the figure 180° about the point (5, 5) which is the center of the figure
2) The figure reflected across the line x = 5 and the figure reflected across the line y = 5
The complete question is : Determine if the figure below has rotational symmetry, line symmetry or both and
describe the transformation that mas the figure onto itself. BE SPECIFIC. You must
name the center of rotation and degree of rotation if it has rotational symmetry or lines of reflection if it has line symmetry
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Together, Hermione and Luna bought 2016 Chocolate Frogs for Harry. If Hermione paid 98 coins and Luna paid 28 coins, for how many Chocolate Frogs did Hermione pay?
If Hermione paid 98 coins and Luna paid 28 coins, Hermione paid for 672 Chocolate Frogs.
We can start the problem by using algebra. Let x be the number of Chocolate Frogs that Hermione paid for. Then we know that:
x + (2016 - x) = 2016 (the total number of Chocolate Frogs)
Also, we know that the cost of the Chocolate Frogs Hermione paid is 98 coins, and the cost of the Chocolate Frogs Luna paid is 28 coins. Let's assume the cost of each Chocolate Frog is y. Then we can write:
x * y = 98 and (2016 - x) * y = 28
Now we have a system of two equations with two variables (x and y). To find the value of x, we can use any method to solve the system of equations, such as substitution or elimination.
Using substitution, we can solve for y in the second equation and substitute it into the first equation:
(2016 - x) * y = 28
y = 28 / (2016 - x)
x * (28 / (2016 - x)) = 98
x * (28 / (2016 - x)) = 98
x = 98 * (2016 - x) / 28
Solving for x, we get:
x = 2016/3
So Hermione paid for 2016/3 = 672 Chocolate Frogs.
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Answer:
Hermione paid for 1,568 frogs.
Step-by-step explanation:
First, do 98 + 28. That will give you 126. Then do 2,016 / 126. That gives you 16. 16 x 98 = 1568 frogs.
Let's do Luna's to check our work.
28 x 16 = 448 frogs. 448 + 1568 = 2,016. So, Hermione paid for 1,568 frogs.
help help help help help
Answer:
the answer is (3,4) and (2,3)
Step-by-step explanation:
that's my answer
hi how do you solve x/5 + 6 < 2
Answer:
x < -20
Step-by-step explanation:
To solve x/5 + 6 < 2,
First subtract 6 from both sides of the equation.
This makes x/5 < -4.
Then multiply both sides of the equation by 5.
This makes x < -20.
Therefore, the solution to the equation is x < -20.
Use the table to write the ratio of the total number of houses to the number of houses that painted green.
Color of Houses
Red
Green
Yellow
Blue
Number of houses
34
17
48
4
Answers:
103:34
103:17
17:103
34:17
34
Please show me step by step!
The ratio of the green houses to the the total number of houses is 17:103
What is a ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here, The number of green houses as 17 and total number of houses altogether 103
Therefore the required ratio is 17:103
Hence, The ratio of the green houses to the the total number of houses is 17:103
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Can you please help me?
Answer:
[tex]t = \dfrac{I}{Pr}[/tex]
Step-by-step explanation:
Given the equation [tex]I = Prt[/tex]:
To solve for [tex]t[/tex], all we have to do is divide both sides by [tex]Pr[/tex].
[tex]\textrm{} \ \, I = Prt\\\overline{Pr} \ \ \ \overline{\: Pr \: }[/tex]
[tex]t = \dfrac{I}{Pr}[/tex]
Text form:
t = I / Pr
Answer:
[tex]t= \frac{I}{Pt}[/tex]
Step-by-step explanation:
Given the equation,[tex]I=Prt[/tex], solve for the value, t.
[tex]I=Prt[/tex], divide both sides of the equation by [tex]Pr[/tex]. We get,
[tex]t= \frac{I}{Pr}[/tex], final answer.