On a team 3 girls and 2 boys scored a total of 29 points. The difference between the number of points scored by the 3 girls and the number of points scored by the 2 boys is 13. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy


HELP ONLY RIGHT ANSWERS GET THE POINTS

The equation of line in point-slope form of the line, is y = 5x - 1.

What is point - slope form of the line?

The general form of a linear equation is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

The line passes through the points (1, 4) and (2, 9).

We have to find the equation of line in point - slope form.

First to find the slope from the given points.

Since,

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]

So, [tex]m = \frac{9-4}{2-1} = 5[/tex]

Now consider, the point slope form of the line

[tex]y-y_1=m(x-x_1)[/tex]

Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]

⇒

[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]

Hence, the equation of line in point-slope form of the line, is y = 5x - 1.

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The solution of the given expression is equal to 2.17.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,

[tex]2^{x+1}=9[/tex]

Take logs on both sides,

(x+1) ln(2) = ln(9)

(x+1) = ln(9) / ln(2)

x + 1 = 3.17

x = 2.17

Hence, the expression will be solved by taking log on both sides.

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The original selling price of the ski is $385.

From the information, the sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns as 15% making the one-day sale price of the ski set $327.

Let the original selling price of the ski be x.

This will be:

x - (15% × x) = 327

0.85x = 327

Divide

x = 327 / 0.85

x = 385

The original price is $385.

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Complete question

A sporting goods manager was selling a ski set for a certain price. The manager offered the markdowns as 15% making the one-day sale price of the ski set $327. Find the original selling price of the ski set.

Answer:

[tex]\sf m=-\frac{5}{6}[/tex]

Step-by-step explanation:

The formula to find the slope is :

[tex]\sf m=\frac{y_1-y_2}{x_1-x_2}[/tex]

For that, let us use the given two coordinates.

( 9 , 4 ) ⇒ ( x₁ , y₁ )

( 3 , 9 ) ⇒ ( x₂ , y₂ )

Let us solve it now.

[tex]\sf m=\frac{y_1-y_2}{x_1-x_2}\\\\\sf m=\frac{4-9}{9-3}\\\\\sf m=-\frac{5}{6}[/tex]

Answer:1020.2

Step-by-step explanation:

The inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

        ≤ : less than or equal to

        ≥ : greater than or equal to

        < : less than

        > : greater than

        ≠ : not equal to

Given is the maximum load for a certain elevator is 2000 pounds. The total weight of the passengers on the elevator is 1400 pounds. A delivery man who weighs 243 pounds enters the elevator with a crate of weight [w].

        1400 + 243 + w ≤ 2000

        w + 1643 ≤ 2000

        w + 1643 ≤ 2000

        w ≤ 2000 - 1643

        w ≤ 357

Therefore, the inequality to show the values of [w] that will not exceed the weight limit of the elevator is w + 1643 ≤ 2000. On solving the inequality, we get w ≤ 357. The graph of the inequality is attached.

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The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.

Area of rectangle = length × breadth

Area of rectangular plot = 500× 200 = 1,00,000 sq m

Cost of tilling 1 sq m of land = Rs. 8

Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000

Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.

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Answer:

29, 61

Step-by-step explanation:

x = smaller

y = larger

y = 3x - 26

x + y = 90

x + 3x - 26 = 90

4x - 26 = 90

4x = 116

x = 29

x + y = 90

29 + y = 90

y = 90 - 29

y = 61

Answer:

smaller angle = 29°

larger angle = 61°

Step-by-step explanation:

Let x be the larger angle and y be the smaller angle

Larger angle is 26° less than 3 times the smaller angle

i. e x = 3y-26°

Since x and y are complementary angles, we can write,

x + y = 90°

or, (3y - 26°) + y = 90°

or, 4y = 90° + 26°

or, y = 116°/4

or, y = 29°

So,

x = 3 * 29° - 26° = 61°

The value of the expression 24 + x ÷ 12 when x = −180 is (b) 9

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

From the question, we have the following parameters that can be used in our computation:

24 + x ÷ 12

Also, we have the value of the variable to be

x = −180

Substitute the known values in the above equation, so, we have the following representation

24 - 180 ÷ 12

Evaluate the quotient in the above equation

So, we have the following representation

24 - 180 ÷ 12 = 24 - 15

Evaluate the difference in the above equation

So, we have the following representation

24 - 180 ÷ 12 = 9

Hence, the value of the expression is (b) 9

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a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.

To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.

Applying this rule to the expression 1/58^8, we get:

1/58^8 = 1/(58^8) = 58^-8

Therefore, the correct answer is 58^-8.

It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:

1/58^8 = (1/58)^8 = 58^-8

This simplification shows that the correct answer is still 58^-8.

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Answer:

  12 units

Step-by-step explanation:

You want to know the perimeter of rectangle ABCD after it has been dilated by a factor of 1.

The original rectangle ABCD has a perimeter of ...

  P = 2(L +W) = 2(4 +2) = 12

The perimeter of the dilated rectangle is the original perimeter multiplied by the dilation factor:

  P' = 12·1 = 12

The dilated rectangle has a perimeter of 12 units.

__

Additional comment

Dilation by a factor of 1 changes nothing at all. The center of dilation is irrelevant.

Lisa's change in speed is 4 miles per hour.Lisa's acceleration is 2 miles per hour.

According to the question,

The speed of Lisa is = 3 miles per hour

A dog starts to chase her, and she  speeds up to seven miles per hour.

The change in speed after dog chase her is,

= 7 miles per hour - 3 miles per hour

= 4 miles per hour

Lisa's change in speed is 4 miles per hour.

When Lisa increased her speed in letter c,  the increase took two seconds.

Then,

The Lisa acceleration is,

Acceleration = Change in speed/Change in time

Acceleration = 4/2

Acceleration = 2 per mail.

Hence, Lisa's acceleration is 2 miles per hour.

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The volume of the tunnel is 225.476cm³

We should know that the volume of an object entails the quantity of things it can hold at a particular time.

The volume of the tunnel = Volume of semi circle + volume of the rectangle

This is given by

V=3/4[tex]\frac{4}{3} \pi r^{3}[/tex] + lbh

volume of the tunnel = 4/3*3.142*(5/2)³ + 4*5*8

Simplifying the expression

(65.476 + 160)cm³

Volume = 225.476cm³

Given that the car exhaust  at 10m³

226cm = 2.26m

Note that 60 seconds = 1 Minute

Therefore 10*2.26=22.6m

=22.6/60 = 3 hours,  46 mins and 2 seconds.

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A vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a two factor chi Square test.

The Pearson chi-square (χ²) test, often simply called the chi-square test, is one of the most common non-parametric tests. Nonparametric tests are used for data that do not follow the assumptions of parametric tests, especially the assumption of normal distribution.

To test hypotheses about the distribution of a categorical variable, you should use the chi-square test or another non-parametric test. Categorical variables can be nominal or ordinal and represent groups such as species or nationality. They can only have a small number of specific values, so they cannot have a normal distribution.

Bidirectional chi-square is one of several tests of goodness of fit between the actual values ​​of two nominal or ordinal variables and the values ​​expected if the variables were unrelated or independent. Chi-square is also known as Pearson Chi-square and Chi-square test of independence. The symbol for the chi-square test is the lowercase Greek letter chi (χ) with a superscript 2, such as χ2. χ2 is a test of significance and should be accompanied by an appropriate test of strength. The strength test should be chosen based on the number of rows and columns in the table of observations. In particular, one of the most commonly used strength tests is the π coefficient.

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Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.

Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.

Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.

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A point estimate (mean) for the average height of all people at the place where you work is 62.26

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

Given,

Number of observations =  20

Mean = sum of all observation / number of observations

Mean =  66 +65 +66+ 67+ 62+ 70+ 69+ 68+ 71+ 78+ 61+ 62.5+ 64+ 64.2+ 64.3+ 58+ 60+ 63+ 65+ 66.2 / 20

Mean = 1245.2 / 20 = 62.26

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Answer:

three billion eight hundred million

Step-by-step explanation:

Answer: x < 5

What does this mean?

This simply means that any point that is five or below is going to be outlined.

How do I do it?

It's as simple as drawing a point at value 5, and everything below is going to contain a line.

Representation

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The value of x for the given function at the value of y = 4 will be 2.536.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the function is y = x² - x. On drawing the graph of the function y = x² - x we get the parabola at the vertex of ( 0.5,-0.25).

When we plot the coordinate y = 4, the value of the coordinate x on the graph will be x = 2.536. The graph of the function is attached with the answer below.

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Answer:2(8x-5)

Hope this helps!

2 points of inflection will f(x) = 3x5+2x4 - 5x - 12 have.

What is Inflection points definition?

An inflection point is a point on the graph at which the second derivative is equal to zero or undefined and changes sign.

The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

If [tex]$f^{\prime \prime}(x) > 0$[/tex]then f(x) concave upwards.

If [tex]$f^{\prime \prime}(x) < 0$[/tex]then f(x) concave downwards.

[tex]$$f^{\prime \prime}(x)=126 x^5+40 x^3$$[/tex]

Show Steps

Find intervals: Concave Downward: [tex]-\infty < x < 0$, Concave Upward: $0 < x < \infty$[/tex]

Plug x=0 into [tex]$3 x^7+2 x^5-5 x-12: \quad-12$[/tex]

(0,-12)

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Total coats should the store plan to sell this winter is 952.

Last winter, a store sold 408 coats in 3 months. This winter, the store plans to sell coats for 4 months.

What is sell?

Determine the total cost of all the purchased units. To find the cost price, divide the total cost by the quantity of units purchased. To get the final price, use the formula for selling price (SP), which is: SP = CP + Profit Margin. The cost of the commodity will then be increased by the margin to determine the proper pricing. Retail math describes the mathematical techniques or formulae utilised in the sales industry. It is earning money or receiving change in the most basic sense. Business owners, retailers, managers, and sales representatives all utilise retail math in their daily work.

3month = 408 coats

1 month = 408/3 =136 coats

Then, 4 months = 136*4 = 544 coats

Total coats should the store plan to sell this winter = 544+408 = 952.

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Answer:

Tabatha drives 1/6 mile more per minute than Horatio drives

Step-by-step explanation:

The translation rule that maps the preimage to the image is (x, y) ⇒ (x + 5, y + 1)

From the question, we have the following parameters that can be used in our computation:

Pre-image: L(-4,0), M(-2,0) and N(-3,-3)

Image: L'(1,1), M'(3,1) and N'(2,-2)

The translation rule is calculated as

(x, y) = L' - L

Substitute the known values in the above equation, so, we have the following representation

(x, y) ⇒ (x + 1 + 4, y + 1 - 0)

Evaluate

(x, y) ⇒ (x + 5, y + 1)

Hence, the translation is (x, y) ⇒ (x + 5, y + 1)

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Answer:

Below

Step-by-step explanation:

Circumference of a circle = pi * diameter

                             circumference of ferris wheel = 3.14159 * 520=1633.6 ft

Answer: 12

Step-by-step explanation:

The y-intercept in the equation that is in slope-intercept form is the constant.

Answer:

-x + 8y = 56

Step-by-step explanation:

.................

Answer:

I think it's 100.8

Step-by-step explanation:

I'm pretty sure

Answer: 100.8666666666667 (rounded to the nearest hundredth: 100.87)

Answer:

C = 0.30m + 1.00

Answer:

C= $1,00 +(M×$0,30)=$1.00+$.30M

Step-by-step explanation: