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The actual length of the swimming pool be 15m if the scale used by Luke is 7cm : 3m.

Let the actual length of the pool be x m.

According to the given question.

Luke measured a swimming pool and made a scale drawing. The scale he used was 7 centimeters : 3 meters.

⇒ The scale is 7cm : 3m.

Also, the length of the pool in the drawing is 105cm.

Therefore, the actual length of the swimming pool is given by

7cm : 3m  = 105cm : x          (by proportion fromula)

⇒ 7x = 105

⇒ x = 15m

Hence, the actual length of the swimming pool be 15m if the scale used by Luke is 7cm : 3m.

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The speed of the plane and wind in km/hr is 187.5 and 37.5 respectively.

A linear equation has highest degree of 1.

According to the given question a small plane flies for 3 hours to an airport 450 kilo meters away against a strong headwind. the plane then returns to its starting location flying with the wind, taking 2 hours.

Form these we can form two linear equations in two variables.

Assuming speed of the plane to be x km/hr and speed of wind to be y km/hr.

We know Distance = speed × time.

3( x - y) = 450. and 2( x + y) = 450.

3x - 3y = 450...(i) and 2x + 2y = 450...(ii)

multiplying eqn (i) by 2 and eqn (ii) by 3 and solving we get

x = 187.5 km/hr and y = 37.5 km/hr.

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Answer:

(2, - 1 )

Step-by-step explanation:

to determine which point belongs on the line, substitute the x- coordinate into the right side and if the value obtained is equal to the y- coordinate then it lies on the line.

(1, 3 ) : y = 2(1) - 5 = 2 - 5 = - 3 ≠ 3 ← not on line

(0, 7 ) : y = 2(0) - 5 = 0 - 5 = - 5 ≠ 7 ← not on line

(2, - 1 ) : y = 2(2) - 5 = 4 - 5 = - 1 ← lies on line

(3, - 11 ) : y = 2(3) - 5 = 6 - 5 = 1  ≠ - 11 ← not on line

Answer:

3/64

Step-by-step explanation:

12/156

DIvide both numbers by two

6/78

Divide both numbers by two

3/64

Answer: 1/13

Step-by-step explanation:

[tex]\displaystyle\\\frac{12}{156}=\\\\ \frac{3*4}{3*52}=\\\\ \frac{4}{52}=\\\\ \frac{4}{4*13}=\\\\ \frac{1}{13}[/tex]

In the polynomials;

The value of variable = q

The value of exponent = 5

The value of constant = -6

The value of coefficient = -14

Here,

The given polynomial is;

-14q⁵ - 6

We have to find the variable, exponent, constant, and coefficient in the polynomial.

What is an Exponent?

An exponent is refer to number of times a number is multiplied by itself.

Now,

In the given polynomial;

-14q⁵ - 6

The variable is = q

Since, the power of q is 5.

Hence, The value of exponent = 5

And, The value of constant term = -6

And, The value of coefficient = -14

Therefore, In the polynomials;

The value of variable = q

The value of exponent = 5

The value of constant = -6

The value of coefficient = -14

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Answer: Pretty sure the answer is -10

Step-by-step explanation: If you replace f(x) with 6, you can figure out the answer more quicker.

6 = -x-4

10 = -x

x=-10

Answer:

2

Step-by-step explanation:

Since f(x) is 6, we can plug that into the equation:

6-4,

which gives us 2

Using the normal approximation to the binomial, there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

This problem is incomplete, but researching it on a search engine, it asks the probability that the sum of these Bernoulli variables is of less than 60.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The binomial distribution is a series of n Bernoulli trials with p probability of a success on each trial, hence the parameters for the binomial distribution are given as follows:

n = 100, p = 0.5.

The mean and the standard deviation are given by:

Using continuity correction, the probability that the sum is less than 60 is P(X < 59.5), which is the p-value of Z when X = 59.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (59.5 - 50)/5

Z = 1.9

Z = 1.9 has a p-value of 0.9713.

Hence there is a 0.9713 = 97.13% probability that the sum of these variables is less than 60.

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Answer: 440

Step-by-step explanation: You add 12 to -452

I believe how you find the difference between two numbers is by adding their absolute value. The absolute value ignores the negative and positive values and is really just the distance of the number from 0.

So, with -452 and 12, the distance between them is 464 units

answer: 464

Im sorry if that was confusing!

Angle vqt is congruent to Angle squ by the vertical angles theorem. because angles squ and wrs are corresponding angles, they are congruent according to the Corresponding angles theorem.

Option b is true.

Here,

Segment uv is parallel to segment wz,

Angles squ and vqt are vertical angles.

Angle vqt is congruent to Angle squ by the Vertical angles theorem.

What is corresponding angles?

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

Now,

Angle vqt is congruent to Angle squ by the vertical angles theorem.

When, two angles are corresponding angle then, Angle vqt is congruent to Angle squ by the Vertical angles theorem.

And, they are congruent according to the Corresponding angles theorem.

Hence, Segment uv is parallel to Segment wz, while Angles squ and vqt are Vertical angles. Angle vqt is congruent to Angle squ by the vertical angles theorem. Because angles squ and wrs are corresponding angles, they are congruent according to the corresponding angle theorem. finally, Angle vqt is congruent to Angle wrs by the transitive property of equality.

So, Option b is true.

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Answer:

x + y

Step-by-step explanation:

x + y = - [tex]\frac{11}{8}[/tex] + (- [tex]\frac{11}{4}[/tex]) = - [tex]\frac{11}{8}[/tex] - [tex]\frac{11}{4}[/tex] = - [tex]\frac{11}{8}[/tex] - [tex]\frac{22}{8}[/tex] = - [tex]\frac{33}{8}[/tex]

x - y = - [tex]\frac{11}{8}[/tex] - (- [tex]\frac{11}{4}[/tex] ) = - [tex]\frac{11}{8}[/tex] + [tex]\frac{11}{4}[/tex] = - [tex]\frac{11}{8}[/tex] + [tex]\frac{22}{8}[/tex] = [tex]\frac{11}{8}[/tex]

then

x + y < 0 , that is x + y is negative

Answer:

i dont get what the question is

It should be noted that the hypotenuse is the longest side in the triangle. The opposite is the side facing the angle and the adjacent is the last side.

The hypotenuse is the longest side of a right triangle. An "opposite" side is one that is across from a given angle, while a "adjacent" side is one that is close to a given angle.

According on the angle requested, adjacent and opposing sides can differ. The side that is opposite to the requested angle is the opposite side, and the side that is immediately adjacent to the requested angle is the adjacent side.

In conclusion, the opposite is the side facing the angle and the adjacent is the last side.

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The transformation in reflection is that triangle may have identical aspect lengths and perspective measure.

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Answer:

b

Step-by-step explanation:

Using a proportional relationship, the numbers that could be used as the missing values in the table are:

35 kg, 1.4 ml.

The table is given by:

It asks for the missing value in the table, and the options are given as follows:

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Considering point (50,2), the relationship is given by:

y = 0.04x.

As k = 2/50 = 0.04.

When x = 35, we have that:

y = 0.04 x 35 = 1.4.

Which means that the point is:

35 kg, 1.4 ml.

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Answer:

c and d

Step-by-step explanation:

The pair of angles from the given options that are a pair of alternate exterior angles is:

C. ∠2 and ∠8

What are Alternate Exterior Angles?

Alternate exterior angles are pairs of exterior angles that lie alternate to each other along a transversal that cuts across two parallel lines.

Thus, in the image given, we have the following alternate exterior angles:

∠2 and ∠8

∠1 and ∠7

Therefore, the pair of angles from the given options that are a pair of alternate exterior angles is:

C. ∠2 and ∠8

the complete question is

Which angle are a pair of alternate exterior angles

A. Angle 4 and angle 6

B. Angle 3 and angle 6

C. Angle 2 and angle 8

D. Angle 1 and angle 5

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Answer: x=-2

Step-by-step explanation:

-3(x+5)= 3(x-1)

-3x-15=3x-3

-3x-15=3x-3

-15=6x-3

6x=-12

x=-2

Answer:

x = -26

Step-by-step explanation:

ab - cd = ?

2(-3) - 4(5) = x

-6 - 20 = x

-26 = x

Answer:

a) 1800000663.4

b) 0.0000000000587

Step-by-step explanation:

Answer:

(a) (1.8×10^9)=1800000000

(6.2×107)=663.4

So therfore,

(1.8×10^9)+(6.2×107)=1800000663

Note: "^" means exponential (power)

Step-by-step explanation:

(b) (6.4×10^-11)=0.000000000064

(5.3×10^-12)=0.0000000000053

Therefore ,

Answer= 0.0000000000587

This tire will save $0.008 per mile

First of all the given information is

110 gallons per 55,000 miles

We need to find

Money saved per mile

55000 = 110

1 = 110/55000

1 miles = 0.002 gallons

Price of 1 gallon = $4.00

Price for 1 mile = 0.002 x 4.00

Price for 1 mile = $0.008

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The question is missing vital information. Therefore, complete question is

The manufacturer of Brand A automobile tires claims that its tire can save 110 gallons of fuel over 55,000 miles of driving, as compared to a popular competitor (brand B). If gasoline costs $4.00 per gallon, how much per mile driven does this tire save the customer (Brand A versus Brand B)?

The probability that the three balls have different colours is [tex]\frac{2}{7}[/tex]

Given that An bag contains nine balls, three of which are red, four of which are blue, and two of which are green. Three balls are drawn at random from the bag without replacement and asked to find the probability that the three balls have different colours is [tex]\frac{2}{7}[/tex]

Selecting of 3 balls=9c3

selection of 3 different colour balls=3c1×4c1×2c1

probability:

probability is the ability to happen. The subject of this area of mathematics is the occurrence of random events. From 0 to 1 is used to express the value. To determine how likely an event is to occur, mathematics has created the concept of probability.

probability=[tex]\frac{3c1.4c1.2c1}{9c3}[/tex]

probability= [tex]\frac{2}{7}[/tex]

Therefore,The probability that the three balls have different colours is [tex]\frac{2}{7}[/tex]

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To find the equation of a line, you need to use the formula [tex]m=\frac{y-y_0}{x-x_0}=\frac{rise}{run}[/tex] to find the slope first.

To find the respective points that we need to plug into this formula, we need to use the axes and their values.

We can see that the first point (point on the left) has a position of (-1, -1). For the second point, we see that it has a position of (5, 1).

** remember, whenever you find the position of a point, it's always (x, y). Now that we have our values, we can plug and chug!

[tex]m=\frac{y-y_0}{x-x_0}\\m= \frac{1-(-1)}{5-(-1)} \\m=\frac{1+1}{5+1} \\m=\frac{2}{6} \\m=\frac{1}{3}[/tex]

So your answer should be 1/3 for your slope.

Now you need to find your y intercept, or what y will equal if x = 0. We can find this by using the information we now have. Remember, the equation for a linear line is [tex]y=mx+b[/tex]. So now, we plug in any of the two points (it doesn't matter which pair!) and solve for b!

[tex]y=mx+b\\-1=\frac{1}{3}(-1)+b\\ -1=-\frac{1}{3}+b\\-1+\frac{1}{3}=b\\b=-\frac{2}{3}[/tex]

Now we have b!

So now, we can fully finish the equation of this line. Your final answer should be: y = (1/3)x - 2/3 or [tex]y=\frac{1}{3}x-\frac{2}{3}[/tex].

Hope this helps!

The linear function that models the relationship between the two variables is y = 1200x+ 45000

The given parameters are

Rate = $1200 per year

Initial price in 1960 = $45000

In a linear function, we have

Slope, m = Rate

Y-intercept, c = Initial price

A linear equation is represented s

y = mx + c

So, we have

y = 1200x+ 45000

Hence, the linear function that models the relationship between the two variables is y = 1200x+ 45000

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The student got 87% in the quiz.

Given,

Marks obtained by student = 13/15

percentage received = 13/15 × 100

= 86.6%

= 87%(nearest whole percent)

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

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Answer:

[tex](f \cdot g)(x)=18x^3+15x^2[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=6x^2+5x \\ g(x)=3x\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

The composite function (f · g)(x) means to multiply function f(x) by function g(x):

[tex]\begin{aligned}\implies(f \cdot g)(x) & = f(x) \cdot g(x)\\& = (6x^2+5x)(3x)\\& = 6x^2 \cdot 3x+5x\cdot 3x\\& = 18x^3+15x^2\end{aligned}[/tex]

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The ratio in the form of n:1 is 2.25:1.

When comparing two amounts of the same sort, ratio is utilised. For two numbers, a and b, the ratio formula is written as a: b or a/b. Two or more ratios are said to be in proportion if they are all equal.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same sort and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

ratio 9:4

Now we have to write the ratio in the form of n:1

So, divide the ratio by 4

=9 /4 : 4/4

=9/4: 1

=2.25 :1

Hence, the ratio in the form of n:1 is 2.25:1.

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The baseballs produced in a day would fill 88 boxes and there would be 8 baseballs leftover.

An equation is an expression that shows the relationship between two or more numbers and variables.

A variable can either be dependent or independent. A dependent variable depend on other variable while an independent variable does not depend on other variables.

The assembly line produces 122 baseballs in a batch, If 8 batches are made in one day hence:

Total baseballs produced = 8 batches * 122 balls per batch = 976 balls

Each box contain 11 baseballs each, hence:

number of boxes = 88 boxes and 8 baseballs remaining

The baseballs produced in a day would fill 88 boxes and there would be 8 baseballs leftover.

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Answer:

y=-5/6x-8

Step-by-step explanation:

Slope intercept form: y=mx+b

5x+6y=-48

6y=-5x-48  

y=-5/6x-8

Answer:

Skip counting

Step-by-step explanation:

Skip counting is when you count at intervals of any number you like. If I were to skip count by seven, I would count 7, 14, 21, and so on. You can easily accomplish single-digit multiplication with this method. For example, suppose your teacher asks you to multiply 4 x 7 =. Simply count sevens four times, 7, 14, 21, and 28. 4 x 7 = 28 is the answer.

Go over the skip-counting list until you get to the halfway mark (3, 6, 9, 12, 15, and 18). Allow yourself to speak it out loud while pointing to the answers one by one with a finger or a pen.  This engages many senses at the same time.

Repeat the list from memory after they have gone over it a few times.

The mind is similar to muscles in that it requires exercise to grow stronger.

Memorize this list in both ascending and descending order.

Go through the remaining items on the list: 21, 24, 27, 30, 33, 36.

Finally, go over the entire list of answers. Repeat the list UP AND DOWN until it seems natural and effortless.

Step-by-step explanation:

First write it down by looking at a picture.

Then try writing it down without looking at a picture

Keep doing this.

Also study for 10 mins and then ask someone else to test you

The expression that is NOT equal to the others is ab + c

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expressions are given as

ab + ac

(b + c)a

a(b + c)

ab + c

Next, we evaluate the expressions as follows

So, we have

ab + ac = ab + ac

(b + c)a = ab + ac

a(b + c) = ab + ac

ab + c = ab + c

See that all but the  last expression have a value of ab + ac

Hence, the expression that is NOT equal to the others is ab + c

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