To celebrate Diwali raina lights a diya a samall clay lamp filled with oil and a cotton wick the diya hold 35 milliliters of oil The oil burns at a rate of 14.8 milliliters per hour. if y represents the number of milliiters of oil and x represents the time in hours which equation models this relationship

A. y = 35 + 14.8x
B. y = -35x + 14.8
C. y = -14.8 + 35x
D. y = -14.8x + 35

Answer: 20 hrs

Step-by-step explanation:

6 hours

Explanation:

30 divide by 4 = 7.5

7.5 multiplied by 48 = 360 minutes / 6 hours

Answer:

6.4 miles

Step-by-step explanation:

Set up a ratio.

4 miles is to 30 minutes as x miles is to 48 minutes.

4/30 = x/48

X=4(48)/30

x 96/15 or x = 6.4 miles.

The distance between the tops of the buildings is 28.5 meters.

To find the distance between the top of the buildings, we can use the concept of similar triangles.

Let's denote the height of the shorter building as "a" (12 m) and the height of the taller building as "b" (19 m). The distance between the buildings can be denoted as "c" (18 m), and the distance between the top of the buildings as "x" (which we need to find).

We can set up a proportion based on the similar triangles formed by the buildings:

a/c = b/x

Substituting the known values:

12/18 = 19/x

To find "x," we can cross-multiply and solve for "x":

12x = 18 * 19

12x = 342

x = 342/12

x = 28.5 m

Therefore, the distance between the tops of the buildings is 28.5 meters.

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Answer:

-18 if youre asking about simple subtraction

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

its like saying (-45)+27.

you have to add the 27 to 45 to get to 0 and them see how much you have left

Answer:

$ 7770.81

Step-by-step explanation:

2.5 % each year means the car retains  97.5 % ( or .975 in decimal)  of its value per year

    8599 ( .975) ^4  = $ 7770.81

The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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The cost of each ticket bought by each of the group is $15.

The linear equation that represents the total cost spent by group 1 on the tickets is:

Amount spent = total amount spent on the tickets - discount

9x - 120

The linear equation that represents the total cost spent by group 2 on the tickets is:

3x - 30

Where:

x = is the cost of the tickets

If both groups spend the same amount, the above two linear equations would be equal to each other

3x - 30 = 9x - 120

In order to determine the value of x, take the following steps:

Combine similar terms together: 120 - 30 = 9x - 3x

Add similar terms: 90 = 6x

Divide both sides by 6

x = 90 / 6

x = 15

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Answer:

Step-by-step explanation:

First, move the -11/4 to the other side, so the expression can equal 0.

\(x^2+6x+11/4=0\)

To make the equation easier to work with, multiply both sides by 4, cancelling out the fraction.

\(4x^2+24x+11=0\)

There are many ways to solve a quadratic equation (factoring, quadratic formula, completing the square).

Solving this equation by factoring is the easiest. Factoring with a leading coefficient greater than one can be difficult and there are many ways to accomplish it. The way I'm going to do it is to first find the factors of \(4x^2\) and then the factors of 11. And then multiply across, add the middle terms (derived from multiplying) and try to make it equal 24x.

\(4x^2\):      24x         11:

2x         22x          11

2x           2x            1

           24x (works)

I'll then take the factors diagonal. (2x+1)(2x+11)=0

So \(x=-\frac{1}{2}, -\frac{11}{2}\)

9514 1404 393

Answer:

  x ≈ 9.3

Step-by-step explanation:

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  cos(50°) = 6/x

Solving for x gives ...

  x = 6/cos(50°) ≈ 9.3343

  x ≈ 9.3

__

There is no 'c' to find the value of.

Answer:

x ≈ 9.3

Step-by-step explanation:

Since , this is right triangle, we can use trigonometry functions;

cos θ = Adjacent side / Hypotenuse

Where, θ = 50°

Solve for x

cos 50° = 6 / x

Multiply both side by x

cos 50° × x = 6 / x × x

cos 50° × x = 6

divide cos50° by both sides

cos 50° / cos 50° × x = 6 / cos 50°

x = 6 / cos 50°

x ≈ 9.33434296

Nearest tenth :- x ≈ 9.3

Answer:

u have to work out the letters by adding and timesing and then u change the letters for numbers

The distance between the points P and Q is 10 units using the Pythagorean theorem.

The right-angled triangle's three sides are related in accordance with the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of the other two sides. According to the Pythagoras theorem, if a triangle has a right angle, the hypotenuse's square is equal to the sum of the squares of the other two sides.

The coordinates of the point P and Q are (3, 2) and (9, 10).

Using the Pythagoras theorem:

c² = (x2 - x1)² + (y2 - y1)²

Substitute the values:

c² = (9 - 3)² + (10 - 2)²

c² = 36 + 64

c² = 100

c = 10 units.

Hence, the distance between the points P and Q is 10 units using the Pythagorean theorem.

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The vertices of triangle image are L'(1, -4), M'(6, 4) and N'(7, -2).

Given that, triangle LMIN with vertices L(2, -8), M(12, 8) and N(14,-4).

Here, scale factor k=1/2

Now, by applying scale factor to the vertices, we get

L(2, -8)→1/2 (2, -8)→L'(1, -4)

M(12, 8)→1/2 (12, 8)→M'(6, 4)

N(14,-4)→1/2 (14, -4)→N'(7, -2)

Therefore, the vertices of triangle image are L'(1, -4), M'(6, 4) and N'(7, -2).

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"Your question is incomplete, probably the complete question/missing part is:"

Triangle LMIN with vertices L(2, -8), M(12, 8), and N(14,-4): k = ½.

Answer:

The cost of 1 ruler and 1 pencil are $0.35 and $0.25 respectively,

Step-by-step explanation:

Let the cost of 1 ruler be x

Let the cost of 1 pencil be y

Cost of 4 rulers = 4x

Cost of 3 rulers = 3x

Cost of 3 pencils = 3y

Cost of 4 pencils = 4y

We are given that Four rulers and three pencils cost £2.15

4x+3y=2.15 ---- Black line

We are also given that Three rulers and four pencils cost £2.05

3x+4y=2.05 --- Red line

Plot the lines on the graph

Point of Intersection of lines is (0.35,0.25)

Cost of a ruler = $0.35

Cost of a pencil = $0.25

Hence The cost of 1 ruler and 1 pencil are $0.35 and $0.25 respectively,

Answer:

38

Step-by-step explanation:

Notice that the first triangle is an isosceles triangle, meaning that the base angles are equivalent. Since one angle is 62, we know that the other is 62 as well, which makes 124. This means that angle 2 is 56 degrees. Since 2 and 3 are on the same 'line', they both add up to 180. If 2 is 56, then angle 3 is 124. So the three angles inside the triangle are 124, 18, and x. So, 124+18=142. 180-142= 38

Answer:

She swims 8 kilometers a week 8KM

Step-by-step explanation:

Answer:0.8p+1 and 1+0.8p

Step-by-step explanation:

0.5p+0.3p=0.8p

7-6=+1

0.8p+1

and

Swap both numbers

(0.5p+7)+(0.3p-6)=1+0.8p

Answer:

40.32

Step-by-step explanation:

112 ÷ 100 = 1.12

1.12 × 36 = 4.032

Answer:

a) 3 to 4

b) 3 : 4

\(\sf \dfrac{girls }{boys} = \dfrac{3}{4}\)

Notice that girls = 3, boys = 4

So, Ratio of girls to boys can be rewritten as 3 : 4 and 3 to 4

Fractions are usually represented in ratio like

So

here

Answer:

3 1/2

Step-by-step explanation:

.5 equals one half or 1/2

3.5 equals 3 1/2

Answer:

3 ½

Step-by-step explanation:

when you convert your decimal to a mixed number it is the easiest to find a common value of it. if you take ½ and turn it into a decimal it would be .5 or 50/100. its all about finding the lowest common denominator

Answer:

--------------------

The range of the given function has one restriction, its denominator can't be zero, hence:

Therefore the function can get any value but zero:

The matching answer choice is D.

Linear function is f(x) = mx + b.

Reciprocal of a function f(x)  is 1/f(x).

So the reciprocal of linear function has a form of f(x) = 1 / (mx + b).

The only answer choice in same form is D.

Substitute x = - 5/3 into function to get:

This is undefined value, therefore it represents the vertical asymptote.

The function gets close to - ∞ when x → - 5/3 from left and gets close to +∞ when x → - 5/3 from right (see attached graph).

Therefore the correct choice is B.

Answer:

b

Step-by-step explanation:

sinA = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{s\sqrt{3} }{2s}\) ( cancel s on numerator/ denominator ), then

sinA = \(\frac{\sqrt{3} }{2}\) → b

Answer:

the greatest common factor is 1.

Step-by-step explanation:

The factors of 3 are: 1, 3

The factors of 3 are: 1, 3

The factors of 4 are: 1, 2, 4

The factors of 5 are: 1, 5

The factors of 5 are: 1, 5

The factors of 17 are: 1, 17

Then the greatest common factor is 1.

The Mann-Whitney U test is not appropriate for a comparison of two means in a causal comparative study.

To determine if two samples are likely to come from the same population, researchers employ the Mann Whitney U test, also known as the Mann Whitney Wilcoxon Test or the Wilcoxon Rank Sum Test (i.e., that the two populations have the same shape). When a continuous level variable is measured across all observations in two groups and we wish to test if the distribution of this variable differs between the two groups but we are unable to assume normality in both groups, we use the Mann-Whitney test.

Here,

Mann-Whitney test In a causal comparative investigation, comparing two means is not acceptable using the U test.

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A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

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Answer:     James is incorrect in his statement i do not agree.

Step-by-step explanation: the fraction 3/4 is equivalent to 0.75 while 4 divided by 3 is 1.33333333.

Answer:

James is  

incorrect√

. A fraction can be interpreted as the division of the

numerator is 1√

 by the

denominator is 2√

Step-by-step explanation:

Answer:

11.6

Step-by-step explanation:

Add all numbers together and divide by 7.

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

The surface area of the triangular prism is B. 1,008 \(cm^{2}\)

Triangular Prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.

How to determine this

The surface area of the triangular prism =  Area of the front Triangle + Area of the triangle + Each sides of the triangle by the length of the triangular prism.

Area of the front and back triangle will be the the same given the same base and height

To find the area of the triangle = 1/2 * Base * Height

Where base = 12 cm

Height = 9 cm

Area = 1/2 * 12 cm * 9 cm

Area = 6 * 9 \(cm^{2}\)

Area of the one triangle = 54 \(cm^{2}\)

So, by multiplying each sides of the triangle by the length

= Base * Length

= 12 cm * 25 cm

= 300\(cm^{2}\)

Height * Length

= 9 cm * 25 cm

= 225 \(cm^{2}\)

Then, Hypotenuse * Length

= 15 cm * 25 cm

= 375 \(cm^{2}\)

Surface area = 54\(cm^{2}\) + 54\(cm^{2}\) * 300\(cm^{2}\) + 225\(cm^{2}\) + 375\(cm^{2}\)

Surface Area = 1,008\(cm^{2}\)

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