On a 3 section math test a student correctly answered 17/20 11/15 20/25 what percentage of questions on the entire test did the student answer correctly

Answer:

x = 4

Step-by-step explanation:

The sum of the interior angles of a triangle equal 180.

2x + 15 + 67 + 90 = 180  Combine like terms

2x + 172 = 180  Subtract 172 from both sides

2x + 1752 - 172 = 180 - 172

2x = 8  Divide both sides by 2

[tex]\frac{2x}{2}[/tex] = [tex]\frac{8}{2}[/tex]

x = 4

Answer:

x= 4

Step-by-step explanation:

67+2x+15+90=180 (Sum of measures of a Triangle)

2x + 172 = 180

2x=180-172

2x=8

x=[tex]\frac{8}{2}[/tex]

x= 4

Answer:

  (c)  -42

Step-by-step explanation:

You want the product ab given that ...

The function (f+g)(x) is the sum of the other two functions. For the purpose here, we only need to look at terms that involve 'a' and 'b'.

Comparing coefficients of x², we have ...

  ax² +3x² = 9x²

  a = 9 -3 = 6

Comparing coefficients of x, we have ...

  -5x +bx = -12x

  b = -12 +5 = -7

The product is ...

  ab = (6)(-7) = -42

The arrangement of the given numbers in ascending order is -19, -15, -13, -11, -8, 13

What is Ascending Order?

Ascending order refers to the arrangement of numbers in ascending order, from least to greatest. We must first compare numbers before we may arrange them in any order. Compare first, then order. Putting the numerals in ascending order: Count how many digits are in each number.

Solution:

Given the order is -19, 13, -15, -8, -11, -13

Arranging them in the Ascending Order

-19, -15, -13, -11, -8, 13

In the above arrangement the given numbers are arranged into ascending order

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Answer:

The answer is 256

Step-by-step explanation:

Answer:

256

Step-by-step explanation:

4 · 4 · 8 · 2 = 256

the triangle could represent in a relation as x = 60 - 2(y + z)  and x = 2z + 20.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

The following linear equation accurately describes the circumstance where "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles":

x = 60 - 2(y + z) —- (1)

The following linear equation sums up the statement, "The largest angle is twice the smallest angle plus 20 degrees," as it applies to angles:

x = 2z + 20 —- (2)

Hence the triangle could represent in relation as x = 60 - 2(y + z)  and x = 2z + 20.

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The dimensions of the rectangle with area 35 m² is

length = 7.6 m and width = 4.6 m

The dimension of the rectangle is calculated using the formula for area of rectangle

= length x width

where

area of rectangle

35 = (w + 3) * w

35 = w² + 3w

w² + 3w - 35 = 0

solving for w gives

w = 4.6 OR -7.6

using the positive value, the w = 4.6 m, l = 4.6 + 3 = 7.6 m

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l

The value of the function at day 5 is 822000 and it means that the laser rangefinder locked on the comet is at a distance of 822000 km

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

g(x) = 300,000csc(π/42x)

Also from the question, we have

Number of days = 5

This means that

x = 5

Substitute x = 5 in the equation g(x) = 300,000csc(π/42x)

So, we have the following representation

g(5) = 300,000csc(π/42 x 5)

Evaluate the products

So, we have the following representation

g(5) = 300,000csc(5π/42)

Evaluate the cosec expression

g(5) = 300,000 * 2.74

So, we have

g(5) = 822000

Hence, the value of the function is 822000

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Complete question

A laser rangefinder is locked on a comet approaching Earth. The distance g(x) , in kilometers, of the comet after x days, for x in the interval 0 to 42 days, is given by g(x) = 300,000csc(π/42x)

Evaluate g(5) and interpret the information

Solving a system of equations, we will see that there are 37 elves helping Santa, and 21 reindeer.

Let's define the variables:

We know that there are 58 of them, then we can write:

x + y = 58

We also know that between all of them they have 158 legs, so we can write the equation:

x*2 + y*4 = 158

Then the system of equations is:

x + y = 58

x*2 + y*4 = 158

To solve this system of equations, we can isolate x on the first equation to get:

x = 58 - y

Replacing that in the other equation we will get:

(58 - y)*2 + y*4 = 158

Now we can solve this equation for y.

(58 - y)*2 + y*4 = 158

116 - 2y + 4y = 158

116 + 2y = 158

2y = 158 - 116

2y = 42

y = 42/2

y = 21

Then the value of x is:

x = 58 - y

x = 58 - 21

x = 37

there are 37 elves.

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The equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

An intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is the slope and c is the y-intercept.

There are basically two intercepts, x-intercept and y-intercept. The point where the line crosses the x-axis is the x-intercept and the point where the line crosses the y-axis is the y-intercept.

The equation of the line, which intersects the y-axis at a point is given by:

                           y = mx + c

Suppose the line passes through (t,0) and (3,5), where t>3. Then the y-intercept is at (0, 5t/t-3).

So the area of the triangle is:

[tex]\frac{1}{2}[/tex]×[tex]t[/tex]×[tex]\frac{5t}{t-3}[/tex] [tex]=[/tex][tex]\frac{5(t^{2} )}{3(t-3)}[/tex]

Then:

d(5t²/2(t-3))/dt = (5t/t-3) - 5t²/2(t-3)²

=  5t²(2(t-3)-t)/2(t-3)²

=5t(t-6)/2(t-3)²

Since we require t >3, the zero of the derivative that we see is when t=6.

We can write the equation of this line as: 5x +3y -30 = 0

Thus, the equation of the line through the point (3,5) that cuts off the least area from the first quadrant is 5x +3y -30 = 0.

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The system of inequalities represents this solution is:

6c + 7.5d ≥ 75

d + c ≤ 15.

A statement of an order relationship, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

Now it is given that,

Money from walking neighbor's dog = $6 per hour

Money from car wash = $7.5 per hour

Total Number of hours of work not more than 15 hours

Now, if d represents the number of hours walking his neighbor's dog and c represents the number of hours washing car

So, money from walking neighbor's dog = 6c

and money from car wash = 7.5d

Therefore total money saved = 6c + 7.5d

∵ Total Number of hours of work is not more than 15 hours

⇒ d + c ≤ 15

∵ Tom needs to make at least $75 to cover prom expenses

⇒ 6c + 7.5d ≥ 75

The system of inequalities represents this solution is:

6c + 7.5d ≥ 75 ;

d + c ≤ 15.

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The complete question is as follows:

To save money for prom this weekend, Tom is going to walk his neighbor's dog for $6 per hour and wash cars for $7.50 per hour. His mother said he can work no more than 15 hours to ensure he keeps up with his homework. Tom needs to make at least $75 to cover prom expenses. If d represents the number of hours walking his neighbor's dog and c represents the number of hours washing cars, which system of inequalities represents this solution?

Total four triangles of B fit into triangle A as length of the equilateral triangle A is twice the length of triangle B.

As given in the question,

Types of triangles : Equilateral triangle

Number of triangle = 2

Triangle A and Triangle B

Let 'x' be the length of the triangle A

And 'y' be the length of the triangle B

As per given condition:

x = 2y

Area of equilateral triangle A = (√3/4)x²

Area of equilateral triangle B = (√3/4)y²

Now x = 2y

⇒Area of equilateral triangle A = (√3/4)(2y)²

⇒Area of equilateral triangle A = (√3/4)4y²

⇒Area of equilateral triangle A = 4 [(√3/4)y²]

⇒Area of equilateral triangle A = 4 ( area of equilateral triangle B)

Therefore, total number of four equilateral triangle of B fit into equilateral triangle A.

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Step-by-step explanation:

Press ''CTRL + /'' to access the list of features.

Find the “Text Formatting” section.

Choose “Superscript” from the list of options.

On the right-hand side, you'll see the ''CTRL +. '' shortcut. Use it to make the number or letter in your text appear in exponent form.

Step-by-step explanation:

1. Place your cursor where you want an exponent. For example, if you want to place an exponent after the number 10 in a document, place your cursor directly after the 10 with no space.

2. Type Alt+0185 for the exponent 1. For example, you can type the number 10¹ holding the Alt key and typing 0185.

3. Type Alt+0178 for the exponent 2. For example, you can type the number 10² holding the Alt key and typing 0178.

4. Type Alt+0179 for the exponent 3. For example, you can type the number 10³ by holding the Alt key and typing 0179.

For statement 'A chi-square test of independence is used when both variables are ___.'

b. ordinal

d. nominal

In this question we have been given a statement 'A chi-square test of independence is used when both variables are ___.'

We need to select the correct choices for the given statement.

We know that the Chi-Square Test of Independence is used to test if two categorical variables are associated.

It is a nonparametric test.

It can only compare categorical variables.

The categorical variables are classified as nominal and ordinal variables.

Chi-Square Test is used to test for a statistically significant relationship between nominal and ordinal variables.

Therefore, for a chi-square test of independence is used when both variables ordinal  and nominal.

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The following steps would apply conditional formatting to the range:

The given parameters in the question are:

The Conditional Formatting is located on the home tab

So, the first step to select the range and locate the Conditional Formatting option

Then set the necessary conditions and formats

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Answer:

1280 cm³

I presume you are looking for the solution steps and these are below

Step-by-step explanation:

If the each side of the square pyramid is 16 and the slant height is 17, then the height of the pyramid, half the side and the slant edge form a right triangle.

The height of the pyramid can be computed using the Pythagorean theorem

Let a be each side, h the height and s the slant height

[tex]s^2 = h^2 + (a/2)^2\\\\\\s^2 = h^2 + \dfrac{a^2}{4}\\\\\textrm{Plugging in known values,}\\17^2 = h^2 + \dfrac{16^2}{4}\\\\289= h^2 + 64\\\\h^2 = 289 - 64\\\\h^2 = 225\\\\h = \sqrt{225} = 15\\\\[/tex]

The volume, V of a square pyramid of side a and height h is given by the formula:

[tex]V = \dfrac{1}{3}a^2h\\\\\\\textrm{Plugging in values,}\\\\V = \dfrac{1}{3}\cdot 16^2 \cdot 15\\\\[/tex]

[tex]V = \dfrac{1}{3} \cdot 256 \cdot 15\\\\V = 256 \cdot 5\\\\V = 1280[/tex]

The volume of the pyramid is 1280 cubic cm.

Given the slant height of the pyramid is 17 cm and the length of square base of the pyramid is 16 cm.

Now we know the volume of the pyramid with a square base = [tex]\frac{1}{3}[/tex]×area of the base×height.

So we need the values for area of the base and height of the pyramid.

Area of the square base=16×16 sq. cm.= 256 sq. cm.

Again we can apply the relation to find the value of height,

(Slant height)² = (Height)² + ([tex]\frac{1}{2}[/tex]×Length of the base)²

So, putting the values we get,

[tex](17)^2 = (height)^2 +(\frac{16}{2})^2[/tex]

⇒ [tex]289 = (height)^2+64[/tex]

⇒ [tex](height)^2= 225[/tex]

⇒ [tex]height = 15cm[/tex]

Now by appyling the volume of the pyramid we get,

Volume = [tex]\frac{1}{3} \times 256 \times 15[/tex] cubic cm. = 1280 cubic cm.

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By using algebraic expression, the proof of

(a + b)(a - b) = a² - b² has been shown below-

What is algebraic expression?

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Algebraic expressions are of different types based on number of terms.

They are monomial, binomial, trinomial and so on

Algebraic expression with one term is called monomial

Algebraic expression with two terms is called binomial

Algebraic expression with three terms is called trinomial

The given algebraic expression is

(a + b)(a - b)

a² - ab + ba - b²

a² - ab + ab - b² [Commutative law of addition]

a² - b²

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Graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]

What is the inverse of a function?

The visual representation of a function's inverse, given by the symbol f-1(x), is the original function mirrored across the line y=x. Only when f is a one-one and onto function does it exist.

The inverse of [tex]\sqrt{x+1} -2[/tex] is [tex]x^{2} +4x+3[/tex].

Plotting the inverse, we get the graph to be option 1.

Therefore, graph 1 represents the inverse of the function [tex]f(x)=\sqrt{x+1} -2[/tex]

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The inverse function of the function given as f(x) = [tex]\sqrt{x+1}[/tex] - 2 is f⁻¹(x) = x² + 4x +3. So, option 1 is since the point on f(x), (-1, -2) is mapped to (-2, -1) in its inverse function.

The steps for finding the inverse function, the steps to be followed are:

The given function is f(x) = [tex]\sqrt{x+1}[/tex] - 2  

Consider the given function as f(x) = y ⇒ y =  [tex]\sqrt{x+1}[/tex] - 2

Then, on rewriting the function for x, we get

y + 2 =  [tex]\sqrt{x+1}[/tex]

⇒ (y + 2)² = (x + 1)

⇒ x = y² + 4y + 4 - 1

⇒ x = y² + 4y + 3

Interchanging the variables y to x and x to y we get

y = x² + 4x + 3

Thus, the inverse of the given function is obtained. I.e,

f⁻¹(x) = x² + 4x +3

To identify the graph, the point that satisfies the given function is

f(x) = [tex]\sqrt{x+1}[/tex] - 2; for x = -1,

f(-1) = -2

So, the point is (-1, -2).

Then, its inverse is mapped from y to x. So, they are interchanged and it is (-2, -1).

From the given graphs, graph 1 shows this point on it. So, that is the required option.

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The characteristic polynomial of the given matrix is -λ³ + 16λ² - 67λ +60.

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

A polynomial matrix or matrix of polynomials is a matrix whose elements are univariate or multivariate polynomials.

OR a linear combination of the powers of a square matrix.

A matrix polynomial A 1(λ) = A 10 + … + A 1n1λn1 of order n1 is called a right divisor of a polynomial A (λ) of order n if there exists a matrix polynomial A 2(λ) = A 20 + … + A 2n2λn2 of order n2, n2 ≥ n − n1 such that A (λ) = A 2(λ) A 1(λ).

Let A =  4  -4 0

            -4  7  0

             4  6  5

The characteristics polynomial of A is |A -λɪ|

 |A -λɪ| = (4 -λ)    -4      0

                -4      (7-λ)    0

                 4         6     (5-λ)

 = (4-λ) [(7-λ)(5-λ) - 0] + 4[-4(5-λ) - 0] + 0[-4 -4(7-λ)]

 = (4-λ) [35 - 7λ - 5λ + λ²] +4[-20 + 4λ] + 0

 = (4-λ) [35 - 12λ + λ²] -80 + 16λ

 = 140 -48λ + 4λ² - 35λ + 12λ² - λ³ -80 +16λ

 = -λ³ + 16λ² - 67λ +60

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Answer:

The answer is 3x12 + 3x6

Step-by-step explanation:

You have to multiply each number inside the brackets by the number outside the brackets

3(12+6)

= 3x12 + 3x6

= 36 + 18

= 54

Answer:

The park has 20 climbing activities.

Step-by-step explanation:

Given, 

Total activities = 50

Percent of climbing activities = 40%

Number of climbing activities = 40% of total activities

Number of climbing activities =  40/100 * 50

Number of climbing activities = 0.40 * 50 = 20

Hope this helps!!

The quadratic inequality (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y contains all the ordered pairs outside the parabola.

What is  parabola?

A parabola could be a U-shaped plane curve wherever any purpose is at an equal distance from a hard and fast purpose (known because the focus) and from a fixed line that is understood because the directrix.

Main body:

In this problem we must determine a quadratic inequality of the form:

a · x² + b · x + c < y

Where a, b, c are the real coefficients of the inequality.

First, determine the coefficients of the quadratic inequality (parabola) by solving the system of linear equations:

25 · a - 5 · b + c = 0

4 · a + 2 · b + c = 0

a + b + c = - 18

(a, b, c) = (18 / 7, 54 / 7, - 180 / 7)

Second, write the quadratic in equation:

(18 / 7) · x² + (54 / 7) · x - 180 / 7 < y

hence , the equation is (18 / 7) · x² + (54 / 7) · x - 180 / 7 < y

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The vertex B' is at (1, 1)

Let's update the guidelines for translating a point.

Let's apply the guidelines to resolve our issue.

Vertex A equals (-5, 2)

Vertex A' equals (2, -2)

The two points' coordinates changed, indicating that the

horizontal and vertical translations of a quadrilateral

A's x-coordinate is equal to -5.

A' has an x-coordinate of 2

Which indicates it goes to the right, therefore adhere to the first guideline presented above.

The translation formula is T (x, y) (x + h, y).

∴ x → x + h

x = -5, and x + h = 2.

∴ -5 + h = 2

Increase both sides by 5.

∴ -5 + 5 + h = 2 + 5

∴ h = 7

∴ The quadrilateral is moved seven units to the right.

A has a y-coordinate of 2

A"s y-coordinate is equal to -2.

Which means it descends, therefore apply the fourth rule listed above.

T (x, y) is the translational rule (x, y - k)

∴ y → y - k

Because y = 2 and y - k = -2,

∴ 2 - k = -2

Increase K on both sides.

∴ 2 - k + k = -2 + k

∴ 2 = -2 + k

Increase both sides by 2.

∴ 2 + 2 = -2 + 2 + k

∴ 4 = k

The quadrilateral is down four units.

Let's locate B.

T (x, y) (x + h, y - k) is the translational rule.

∵ B = (-6, 5) (-6, 5)

∵ h = 7 and k = 4

∴ B' = (-6 + 7, 5 - 4)

∴ B' = (1, 1) (1, 1)

Vertex B is located at (1, 1).

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The value of y will be;

⇒ y = 100

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

y varies directly with x and y=20 when x=4,

Now,

Since, y varies directly with x.

Hence, We get;

⇒ y = kx

Where, k is constant of proportionality.

Here, y=20 when x=4,

So, We get;

⇒ y = kx

⇒ 20 = 4k

⇒ k = 5

Thus, For x = 20, The value of y will be;

⇒ y = kx

⇒ y = 5 × 20

⇒ y = 100

Therefore, We get;

⇒ y = 100

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Answer:

Step-by-step explanation:

You want an exponential regression function for the data in the table.

A regression function of most any kind can be found using a graphing calculator or spreadsheet. The attachment shows the function is approximately ...

  y = 371.17 × 1.15^x

where y is the number sold, and x is the month.

Using x=8, the predicted number sold for month 8 is ...

  y = 371.17 × 1.15^8 ≈ 1135.4175 ≈ 1135

Sales for month 8 will be about 1135.

Answer:

A line is defined by two points, and any other point that lies on the same line as those two points will also be on the same line. Therefore, to find the points that lie on the same line as (– 7,– 2) and (– 14,– 7), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

The slope of a line is calculated as the change in y-values divided by the change in x-values between two points on the line. In this case, the slope is (–7 – (–2))/(–14 – (–7)) = –5/–7 = 5/7.

The y-intercept is the point where the line crosses the y-axis, so we can plug in the value of x as 0 to find the y-intercept. Plugging in the values from one of the given points, we get y = (5/7) * (–7) + b = –5 + b, so b = –2.

Therefore, the equation of the line is y = (5/7)x – 2. Any point that satisfies this equation will lie on the same line as (– 7,– 2) and (– 14,– 7).

Some examples of points that lie on this line include (0, –2), (–7, –2), and (–14, –7).

The total amount that will be paid will be $89.70.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, Adryanna got a manicure for $35 and a pedicure for $43 and she plans on leaving a 15% tip

The total amount that will be paid will be:

= ($35 + $43) + (15% × $78)

= $78 + $11.7

= $89.7

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Answer: 3

Step-by-step explanation: schoology whack

Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

What is milk fat?

The percentage of butterfat in milk, as measured by weight, is known as the fat content of milk. To create a range of goods, the fat content, notably of cow's milk, is altered. In order to facilitate instant identification, the milk container is typically marked with the amount of fat present.

Milk is important for the growth of the body. It plays for the growth and development of the body. 100 grams of milk fat has 3.25 % milk fat in it.

100 grams = 3.25 % of milk fat.

10 grams = x

x = 10 * 3.25 / 100

=0.325  %

Milk contains lots of proteins and minerals. It is essential for the growth of the body. It also contains important minerals such as calcium and proteins.

Therefore, Whole milk has 3.25 % milk fat in it. That means 100 grams has 3.25 % of milk fat. so,10 grams of milk has 0.325 milk fat in it.

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A. Width = 16.5 ft             B.Width = 55.25 ft  

   Height  = 9.3 ft                 Height = 91 ft

   Area = 153.45 ft²              Area = 5027.75 ft²  

The area of the rectangle is a place covered by a rectangle in a 2D plane

The formula for Area of the rectangle is given by

Here we have

1 in = 3 feet and  1 cm = 6.5 ft  

Calculation for rectangle A :

In rectangle A

Width  = 5.5 in

=> Width in feet = 5.5 × 3 feet = 16.5 ft

Height =  3.1 in

=> Height in feet = 3.1 × 3 feet = 9.3 ft

By the given formula

Area = 16.5 ft × 9.3 ft = 153.45 ft²    

Calculation for rectangle B :

In rectangle B

Width  = 8.5 cm

=> Width in feet = 8.5 × 6.5 feet = 55.25 ft

Height = 14 cm

=> Height in feet = 14 × 6.5 feet = 91 feet

By the given formula

Area = 55.25 ft × 91 ft =  5027.75 ft²    

Therefore,

 A. Width = 16.5 ft             B. Width = 55.25 ft  

       Height  = 9.3 ft                 Height = 91 ft

       Area = 153.45 ft²              Area = 5027.75 ft²  

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Answer:

Last option:

[tex]\dfrac{4x^4y^2}{z}[/tex]

Step-by-step explanation:

Original expression is

[tex]\dfrac{12x^6y^{-4}z^2}{3x^2y^{-6}z^3}\\\\[/tex]

Let us eliminate the obvious wrong answers

[tex]\dfrac{12}{3} = 4\\\\[/tex]

so the coefficient in the answer should be 4.

We can eliminate first and third choices

Now for each term with the same variable, compute the division
[tex]\dfrac{x^6}{x^2} = x^{6-2} = x^4\\\\[/tex]

Second choice is out so the last choice is the correct one.

We can go further with the other terms

[tex]\dfrac{y^{-4}}{y^{-6}} = y^{-4 - (-6)} = y ^{-4+6} = y^2[/tex]

[tex]\dfrac{z^2}{z^3} = z^{2-3} = z^{-1} = \dfrac{1}{z}[/tex]

Multiplying all these individual terms gives
[tex]4 \cdot x^4 \cdot y^2 \cdot \dfrac{1}{z}\\\\= \dfrac{4x^4y^2}{z}[/tex]