Find the surface area of the prism.

The correct answer regarding the volume of the pyramid has been explained and given below.

The volume of the pyramid shape is given by the product of its base area and its height and then the product is divided by 3.

i.e.V = (1/3)a²h

So, the options which are correct are, (a) XY and ST , (b) VU and TW  and (d) TX and WX.

From the given figure we can clearly see that,

a=XY=YZ=ZU=UV=VW=WX

h=ST

Firstly, the volume of the pyramid can be easily determined by XY and ST.

and also, VU and WX can be used to calculate the area of the base and YZ and TX can be used to calculate height.

Learn more about volumes on

https://brainly.com/question/13338592?referrer=searchResults

#SPJ4

Answer:

An algebraic expression is a statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations.

Step-by-step explanation:

An example could include x^3 + 1, or something more complicated, like (y^4x^2 + 2xy – y)/(x – 1) = 12

Answer:

Step-by-step explanation:

These are equations which have an = sign and have a variable that needs to be found.

E.g x + 3 = 24

To value of volume 750 ml after converting to cups is 3.17 cups.

The conversion is useful when you need to measure liquids in cups instead of milliliters, especially if you are following a recipe that is written in cups instead of milliliters.

To convert 750ml to cups, you need to know that one cup is equal to 236.6ml. Knowing how to make the conversion can help you get the right measurements and produce accurate results in your cooking or baking. To do the conversion, divide 750 by 236.6 to get the answer in cups.

So, 750ml / 236.6ml per cup = 3.17 cups (rounded to the nearest hundredth).

Therefore, volume of 750ml is equivalent to 3.17 cups.

To know more about volume:

https://brainly.com/question/23409099

#SPJ4

The slope of the tangent line to the graph g(x) = 2x⁴ at (-2,32) is -64.

Given the function in the question;

g(x) = 2x⁴

Slope of the tangent line at (-2,32) = ?

Since 2 is constant with respect to x, the derivative of 2x⁴ with respect to  x will be;

2 d/dx [x⁴]

Now, differentiate using power rule.

d/dx[ xⁿ ] = nxⁿ⁻¹ where n = 4

2( 4x³ )

8x³

Next, evaluate the derivative at x = -2

8( -2 )³

8 × -8

-64

Therefore, the slope of the tangent line is -64.

Learn more about power rule here: https://brainly.com/question/30117847

#SPJ1

The height of Amber's scale model of the Washington Monument should be 2.775 feet.

To find the height of Amber's scale model, we need to multiply the actual height of the Washington Monument by the scale factor:

Scale factor = 1/200

Height of Amber's model = (1/200) * 555 feet

Height of Amber's model = 2.775 feet

Therefore, the height of Amber's scale model of the Washington Monument should be 2.775 feet.

In mathematics, scale refers to the ratio between measurements of the real world and measurements of a model or a drawing. It is a way of representing an object or a phenomenon that is too large or too small to observe directly, by creating a scaled-down or scaled-up representation of it.

For example, in maps, the scale represents the ratio between distances on the map and distances in the real world. A scale of 1:50,000 means that 1 unit on the map represents 50,000 units in the real world. Similarly, in architectural drawings, the scale represents the ratio between the size of the drawing and the size of the actual building.

Scales are used in many fields, including engineering, architecture, cartography, and model making. They allow us to represent objects and phenomena in a way that is more manageable and easier to visualize, while preserving the important proportions and relationships between the different elements of the object or phenomenon.

To know more about scale visit :

https://brainly.com/question/105644

#SPJ1

The area of the shaded region is 5π  

The sector of a circle refers to the region enclosed by two radii of a circle and the arc between them. It is a part of the whole circle, and its area can be calculated using the following formula:

where θ is the central angle (in degrees) of the sector, r is the radius.  

Here we have

The length of arc FG = 5/3 π  and measure of ∠FEG = 50°

As we know Arc Length = θ × (π/180) × r  

=> Length of arc FG = 50 × (π/180) × r

From the given data,

=> 50 × (π/180) × r = 5π/3

=> 5 × (1/18) × r = 5/3

=>  (1/6) × r = 1

=> r = 6 units  

Hence, the radius of the circle is 6 units

By using the formula,

Area of a Sector of Circle = (θ/360°) × πr²

Area of shaded region = (50/360) × π(6)²  

= (5/36) × π(36)

= (5/36) × π(36)

= 5π  

The area of the shaded region is 5π  

Learn more about Area of Sector at

https://brainly.com/question/7512468

#SPJ1

The correct answer is option (c): They are both solid lines.

In mathematics, an inequality is a statement that two values are not equal. Instead, one value is either greater than or less than the other value. Inequalities are represented by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, the inequality 5 < 8 means that 5 is less than 8, while the inequality x + 3 > 7 means that the sum of x and 3 is greater than 7.

Inequalities can be graphed on a number line, which is a horizontal line that represents the set of real numbers. To graph an inequality on a number line, you can draw a closed or open circle at the value of the variable that satisfies the inequality, and shade the region to the left or right of the circle, depending on the direction of the inequality.

For example, to graph the inequality x < 3, you would draw an open circle at 3 on the number line, and shade the region to the left of the circle, because x is less than 3. Similarly, to graph the inequality y ≥ -2, you would draw a closed circle at -2 on the number line, and shade the region to the right of the circle, because y is greater than or equal to -2.

Graphing inequalities on a number line is a useful tool for solving problems and visualizing the solutions to inequalities in one variable.

The inequality y ≤ 3x + 5 can be written as y = 3x + 5 or y > 3x + 5. Similarly, the inequality y ≤ (2/3)x + 5 can be written as y = (2/3)x + 5 or y > (2/3)x + 5. Since the inequality symbols are less than or equal to, the lines representing these inequalities will be solid lines.

Also, since the coefficients of x and y are positive in both the inequalities, the lines will have a positive slope and will slant upwards from left to right. The y-intercept of both lines is 5.

Hence, the correct answer is option (c): They are both solid lines.

To know more about intercept visit:

https://brainly.com/question/14180189

#SPJ1

The lines will have a positive slope and slant upward from left to right since the coefficients of x and y in both inequalities are positive. Both lines have a y-intercept of 5.

Hence, option (c) is the appropriate response: Both of them are solid lines.

In mathematics, an inequality is a statement that two values are not equal. Instead, one value is either greater than or less than the other value. Inequalities are represented by symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

For example, the inequality 5 < 8 means that 5 is less than 8, while the inequality x + 3 > 7 means that the sum of x and 3 is greater than 7.

Inequalities can be graphed on a number line, which is a horizontal line that represents the set of real numbers. To graph an inequality on a number line, you can draw a closed or open circle at the value of the variable that satisfies the inequality, and shade the region to the left or right of the circle, depending on the direction of the inequality.

For example, to graph the inequality x < 3, you would draw an open circle at 3 on the number line, and shade the region to the left of the circle, because x is less than 3. Similarly, to graph the inequality y ≥ -2, you would draw a closed circle at -2 on the number line, and shade the region to the right of the circle, because y is greater than or equal to -2.

Graphing inequalities on a number line is a useful tool for solving problems and visualizing the solutions to inequalities in one variable.

The inequality y ≤ 3x + 5 can be written as y = 3x + 5 or y > 3x + 5. Similarly, the inequality y ≤ (2/3)x + 5 can be written as y = (2/3)x + 5 or y > (2/3)x + 5. Since the inequality symbols are less than or equal to, the lines representing these inequalities will be solid lines.

Also, since the coefficients of x and y are positive in both inequalities, the lines will have a positive slope and will slant upwards from left to right. The y-intercept of both lines is 5.

Hence, the correct answer is an option (c): They are both solid lines.

To know more about intercept visit:

brainly.com/question/14180189

#SPJ1

A binomial theorem calculator is an online tool that calculates the expansion of a binomial expression raised to a power

The binomial theorem, also known as the binomial expansion, describes the algebraic expansion of a binomial expression, which is a mathematical expression that consists of two terms. A binomial theorem calculator is an online tool or a software program that calculates the expansion of a binomial expression raised to a power. The binomial theorem calculator can quickly and easily perform this expansion for any given binomial expression and power.

For example, if we have the binomial expression (a + b) raised to the power of 3, the binomial theorem calculator will provide the expanded form:

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3

This expansion can be useful in many mathematical calculations and applications, such as probability theory, combinatorics, and algebraic equations.

Learn more about binomial theorem here

brainly.com/question/27813780

#SPJ4

The region (labelled A) corresponding to all values of x and y that is added as an attachment

Based on the given information, we can write the following system of inequalities:

Lashonda exercises for at least 7 hours:

x + y ≥ 7

She spends at most 5 hours on weight training:

y ≤ 5

She spends at most 11 hours doing cardiovascular work:

x ≤ 11

So the system of inequalities can be written as:

x + y ≥ 7

y ≤ 5

x ≤ 11

Read more about inequalities at

https://brainly.com/question/30728087

#SPJ1

The true statement is, 3) Each bag must contain at least 20 marbles.

We know The expected value, also known as the expectation, average, is a generalization of the weighted average in the field of probability theory.

The anticipated value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.

1. From the table, Piper's bag has definitely more pink marbles than Kai's.

2. If Piper chooses 15 more marbles he can expect (4/30)×15 = 2 orange marbles.

3. There can be green marbles in Kai's bag as the process is repeated only 20 times.

4. So, The true statement is each bag must have at least 20 marbles,

As the sum of different colored marbles is 20.

learn more about expected value here :

https://brainly.com/question/29574962

#SPJ1

Answer:

If Piper chooses 15 more marbles, she can expect 3 to be orange.

It should be noted that the geometrical constraint is that the average of the top and bottom lines will be the middle line thus the value of length XY is 18 units.

A quadrilateral is a geometrical 2d shape in which there are four sides and each side is connected and makes a close polygon.

The average of the top and bottom lines will be the middle line.

So, (6s + 1 + s)/2 = (4s - 2)

7s + 1 = 8s - 4

5 = s.

So,

XY = 4(5) - 2

= 20 - 2

= 18.

Learn more about quadrilateral on:

https://brainly.com/question/23935806

#SPJ1

Answer:

$42.12

Step-by-step explanation:

if tip is 17% then she should pay 117% (this is 1.17)

$36 * 1.17 = $42.12

The quartic polynomial in standard form is:

f(x) = x^4 - 4x^3 - 19x^2 + 106x - 300

Since the zeros of the quartic function are -5, -2, 5, and 6, we can write the function as:

f(x) = a(x + 5)(x + 2)(x - 5)(x - 6)

where a is the leading coefficient of f(x).

Since the leading coefficient of f(x) is assumed to be 1, we have:

f(x) = (x + 5)(x + 2)(x - 5)(x - 6)

To write this in standard form, we need to expand the product:

f(x) = (x^2 + 7x + 10)(x^2 - 11x + 30)

Multiplying out the terms, we get:

f(x) = x^4 - 4x^3 - 19x^2 + 106x - 300

Therefore, the quartic polynomial in standard form is:

f(x) = x^4 - 4x^3 - 19x^2 + 106x - 300

Learn more on quartic polynomials here https://brainly.com/question/22433922

#SPJ1

Once data has been collected through Qualtrics, it can be downloaded in a variety of formats, including a CSV file that can be imported into SPSS for data analysis.

Qualtrics is a popular web-based survey tool used to create and distribute online surveys.

To import Qualtrics data into SPSS, follow these steps:

Open SPSS and create a new data file.

Go to "File" > "Import Data" > "CSV File" and browse to find the Qualtrics data file you want to import.

In the import wizard, select the CSV file and choose the appropriate options for handling missing values and delimiters.

Specify the variable properties, including the variable name, label, and measurement level.

Click "Finish" to complete the import process.

Once the data has been imported into SPSS, you can use various statistical analyses to explore the relationships between variables, test hypotheses, and generate charts and tables to summarize the data.

The exact analysis methods used will depend on the research questions and the nature of the data, but common techniques include descriptive statistics, correlations, regression analysis, and factor analysis.

To learn more about analysis click on,

https://brainly.com/question/18233448

#SPJ4

The explanation is in the picture

To use back substitution to solve a system of equations, work backwards from the last equation to the first.

Back replacement is a strategy for settling frameworks of conditions by working in reverse from the last condition to the first. To settle an arrangement of conditions utilizing back replacement, follow these means:

Begin with the last condition in the framework and tackle for the variable with the biggest coefficient.

Substitute this worth into the second-to-last condition and tackle for the relating variable.

Keep subbing values from the tackled conditions into the excess conditions, working in reverse until all factors are settled.

Actually look at the arrangement by subbing the qualities into the first conditions.

Back replacement is a valuable technique for tackling frameworks of conditions, particularly when the conditions are in three-sided structure or when Gaussian disposal has been applied. Be that as it may, it may not be the most proficient technique for bigger frameworks, and different strategies, for example, grid reversal or Cramer's standard might be more suitable

To learn more about back substitution, refer:

https://brainly.com/question/17053426

#SPJ4

Answer:

Step-by-step explanation:

The book is $56.56.

The rand to dollar exchange rate is R17.25 = $1

To find the price of the book in rands, simply multiply 56.56 x 17.25

= 975.66

The book would be R975.66 in rands.

Step-by-step explanation:

The answer is mentioned in above pdf. so for bad handwriting

The measure of angle x is 70°  

For a triangle, the exterior angle is the angle formed by extending one of the sides of the triangle

The Triangle Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

Here we have

A triangle where 105° is an exterior angle

And 'x' is an interior angle

Name the given triangle as given below

If we take AC as Transversal which cuts AB and DC  

=> ∠A = 35°    [ Alternate Interior Angles ]      

In a triangle,

The measure of an exterior angle will equal to the sum of measures of opposite interior angles.  

=> x° + 35° = 105°  

=> x° = 105° - 35°  

=> x° = 70°  

Therefore,

The measure of angle x is 70°

Learn more about Triangle Exterior Angle Theorem at

https://brainly.com/question/956912

#SPJ1    

The following equation after completion gives us the result which are given below :

An equation is made up of two expressions joined by an equal sign ("="). The two expressions on each side of the equals sign are referred to as the equation's "left" and "right" sides. The right-hand side of an equation is usually assumed to be zero. This will not limit generality since we can balance it by subtracting the right-hand side expression from the expressions on both sides.

Algebra examines two major groups of equations: polynomial equations and linear equations. P(x) = 0, where P is a polynomial and axe + b = 0 is the generic form of linear equations, can be used to write polynomial equations with one variable. a and b are parameters in this case. To solve these equations, we can use geometric or computational approaches from linear algebra or mathematical analysis. There are also several sorts of equations, such as:

Learn more about Equations:

https://brainly.com/question/22688504

#SPJ4

herefore, the area of the triangle is approximately 2.58 square yards.

Area = (1/2) * a * c * sin(B)

where B is the angle opposite to the side of length b, and a and c are the lengths of the other two sides.

In this case, we have:

B = 47 degrees (given)

a = 2 yards (given)

c = 4 yards (given)

To use the formula, we first need to find the length of the third side, b, using the Law of Cosines:

[tex]b^{2}[/tex] = [tex]a^{2}[/tex]+ ^[tex]c^{2}[/tex] - 2accos(B)

b^2 = 2^2 + 4^2 - 224cos(47)

b^2 ≈ 13.37

b ≈ 3.657

Now we can substitute the values into the formula for the area:

Area = (1/2) * a * c * sin(B)

Area = (1/2) * 2 * 4 * sin(47)

Area ≈ 2.58 square yards

To more about measurement visit :

#SPJ1

14 kilometers is approximately equal to 8.699 miles

The conversion factor from kilometers to miles is 0.621371.

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

So, to convert kilometers to miles you can multiply the number of kilometers by 0.621371.

The distance in kilometer = 14 kilometers

The distance in miles = conversion factor × The distance in kilometer

Substitute the values in the equation

The distance in miles = 14 × 0.621371

Multiply the numbers

=  8.699 miles (to three decimal places).

Therefore, the 14 km is 8.699 miles

Learn more about conversion factor here

brainly.com/question/5056146

#SPJ4

The rate of change of the area is equal to -3 * 8^2 = -12.694 in2/min.

The rate of change of the area is the rate at which the area is increasing or decreasing over a given period of time. It is calculated by taking the difference between the initial and final area values and dividing it by the amount of time it took for the change to occur.

For example, if the area of a square increases from 10 square meters to 12 square meters over a period of two days, then the rate of change of the area would be (12-10)/2 = 1 square meter per day.

The rate of change of the area of a circle is equal to the negative of the product of the rate of change of the radius and the square of the radius. The rate of change of the radius is given as -3 inches per minute, and the radius is given as 8 inches. So, the rate of change of the area is equal to -3 * 8^2 = -12.694 in2/min.

To know more about Rate of change of the area, visit:

https://brainly.com/question/28520282

#SPJ1

The value of x that makes lines e and f parallel and intersected by transversal b is x = 25. Answer choice (c) is correct.

Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.

When parallel lines e and f are cut by a transversal, the corresponding angles are congruent. Using this fact, we can set up an equation involving the angles formed by the intersection of lines e and f with transversal b:

2x + 10 = 3x - 15

Solving for x, we get:

x = 25

Therefore, the value of x that makes lines e and f parallel and intersected by transversal b is x = 25. Answer choice (c) is correct.

for such more question on Parallel lines

https://brainly.com/question/30195834

#SPJ4

To find the sum of the squared differences, you first need to calculate the mean of the data set. Then, you need to subtract the mean from each score to get the difference. Finally, you need to square each difference and add them all together to get the sum of the squared differences.

Here are the steps to find the sum of the squared differences:

1. Calculate the mean of the data set by adding up all the scores and dividing by the number of scores.
2. Subtract the mean from each score to get the difference.
3. Square each difference.
4. Add up all the squared differences to get the sum of the squared differences.

For example, if the data set is {1, 2, 3, 4, 5}, the mean is (1+2+3+4+5)/5 = 3. The differences are (-2, -1, 0, 1, 2), and the squared differences are (4, 1, 0, 1, 4). The sum of the squared differences is 4+1+0+1+4 = 10.

So, the sum of the squared differences for this data set is 10.

https://brainly.com/question/22871228

#SPJ1

Roots of the given quadratic equation are

x = -4/9 + 6.86i/9 and x = -4/9 - 6.86i/9

A quadratic equation is a second-order algebraic equation in x. The quadratic equation in standard form is ax² + bx + c = 0.

where a and b are the coefficients, x is the variable, and c is the constant term.  

Given, equation

9x² + 10x + 16 = 2x + 9

taking 2x + 9 to left side

9x² + 10x + 16 - 2x - 9 = 0

Subtracting like terms

9x² + 8x + 7  = 0

here, a = 9, b = 8, c = 7

Quadratic formula for the solution

x = (-b ± √(b² - 4ac))/2a

x = (-8 ± √(8² - 4 . 9 . 7))/2 . 9

x = (-8 ± √(64 - 252))/18

x = (-8 ± √- 188)/18

x = -4/9 + 6.86i/9 and x = -4/9 - 6.86i/9

Hence, x = -4/9 + 6.86i/9 and x = -4/9 - 6.86i/9

are the roots of the given equation.

Learn more about quadratic equation here:

https://brainly.com/question/17177510

#SPJ1

Answer:

Step-by-step explanation:

If functions h(x)= f(x)+g(x), the point (2, 2) is on h(x) and The point (–2, 0) is on h(x).

In mathematics, a function is a rule or a set of rules that assigns a unique output to each input of a given set of inputs. It is a type of mapping or transformation in which each member of one set (the inputs) is associated with a unique member of another set (the outputs). Functions are often represented by equations or graphs, and they can be used to describe relationships between different variables.

For example, the equation y = x2 describes the function that assigns to each number x its square y.

The point (2, 2) is on h(x) since h(x) = f(x) + g(x) = 2 + 0 = 2. The point (–2, 0) is on h(x) since h(x) = f(x) + g(x) = 0 + 0 = 0. The point (0, –3) is not on h(x) since h(x) = f(x) + g(x) = 0 + 2 = 2, which does not equal –3.

To know more about Function Calculations, visit:

https://brainly.com/question/17043948

#SPJ1

The difference between original loan and unsubsidized loans at the time of graduation is =  8302.57 - 7855 = $447.57

What is meant by a loan?

A loan is a type of debt that a person or other entity incurs. The lender advances the borrower a certain amount of money, typically on behalf of a business, financial institution, or government. The borrower accepts a specific set of terms in return, which may include any economic costs, interest, a repayment schedule, and other requirements.

The lender may occasionally need collateral to protect the loan and guarantee repayment. Major purchases, investments, renovations, debt reduction, and company endeavours are just a few uses for loans. Loans aid in the expansion of already existing businesses. The growth of an economy's total money supply and fostering competition are made possible by loans to new enterprises.

Given,

 Time to graduate = 18 months

Amount of loan for 3 semesters = $7855

Unsubsidized loan

rate of interest = 3.7%

Subsidized Stafford Loan

rate of interest = 4.7%

Amount after 6 months for each loan

P = $7855

r1 =  3.7%

r2 = 4.7%

t (in years) = 18 months = 1.5 years

Number of times compounded in a year n = 12

Amount of  Unsubsidized loan at the time of graduation

= [tex]P(1 + \frac{r}{n})^{nt}[/tex]

= [tex]7855(1 + \frac{0.037}{12})^{12*1.5}[/tex]   = $8302.57

Amount of the Subsidized Stafford Loan at the time of graduation

= [tex]P(1 + \frac{r}{n})^{nt}[/tex]

= [tex]7855(1 + \frac{0.047}{12})^{12*1.5}[/tex]   = $8427.60

Therefore the difference between the balance amount of the original loan and the unsubsidized loan at the time of graduation is

=  8302.57 - 7855 = $447.57

To learn more about loans, follow the link.

https://brainly.com/question/28704618

#SPJ1