A solid is cut by a plane that is perpendicular to its base, forming a two-dimensional cross section in the shape of a rectangle. Which of the following solids could have resulted in that cross section?

Answer: How many students at your school participate in karate.

Step-by-step explanation:

A numerical data is data that will always result in a number.

The depth by which the gardener must increase the depth of his garden to double the area is: 8 m

We have the area of the trapezoid is 60m squared and depth is 8m.

We will let the front width be x so that the back width will be 2x

Here, we will apply the formula of trapezium.

A = ¹/₂(a + b)*h

Plugging in the relevant values, we have:

A = ¹/₂(x + 2x)8

60 = ¹/₂(x + 2x)8

60 = 4(x + 2x)

60/4 = 3x

15 = 3x

x = 15/3

x = 5

We get the front width that is 5 so the back width would be 2 * 5 = 10 m

Now, we will double the area to find the new depth:

120 = ¹/₂(5 + 10)h

240/15 = h

h = 16 m

Thus we have to increase the depth by:

16 - 8 = 8 m

Read more about Area of Trapezoid at: https://brainly.com/question/1463152

#SPJ1

The correct option -D. The Y intercept will be larger and the X intercept smaller.

The points at which a line crosses an axis are known as the x-intercept and the y-intercept, respectively. We set y = 0 and compute the equation for x to determine the x-intercept.

This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve again for intercepts by substituting 0 where necessary and then solving for the final variable. Set x = 0 and then solve for y to find the y-intercept.

Given data:

Y axis- profit from the trucking company

X axis - miles the truck traveled.

driver pay - 0.25 cents a mile.

Thus, The Y intercept will be larger and the X intercept smaller.

know more about the  x and y intercepts:

https://brainly.com/question/24609929

#SPJ1

We can predict that 375 shoppers are likely to return to the mall during the same week.

How to estimate the number of shoppers?

To estimate the number of shoppers who are predicted to return during the same week, we need to use the proportion of shoppers who come to the mall more than once a week in the random survey as an estimate for the proportion of all shoppers who come to the mall more than once a week.

From the random survey, we have:

Number of shoppers surveyed (n) = 120

Number of shoppers who come to the mall more than once a week in the survey (x) = 45

So the proportion of shoppers who come to the mall more than once a week in the survey is p-hat = x/n = 45/120 = 0.375

We can use this proportion to estimate the number of shoppers who come to the mall more than once a week in the population of 1,000 shoppers who visit the mall in one day,

predicted number of shoppers who come to the mall more than once a week = p-hat × population size

= 0.375 × 1000

= 375

Therefore, we can predict that 375 shoppers are likely to return to the mall during the same week.

Learn more about survey here,

https://brainly.com/question/13065787

#SPJ1

Answer:

  (b)  DF = 3.04

Step-by-step explanation:

You want the measure of DF in ∆DEF, which is similar to ∆ABC, given AB=11, AC=7.6, DE=4.4.

Corresponding sides of similar triangles are proportional. This means ...

  DF/DE = AC/AB

  DF/4.4 = 7.6/11

  DF = 4.4×7.6/11 = 3.04

The measurement of DF is 3.04, choice B.

<95141404393>

The monthly payment for an amortized loan if the loan amount is $260,000 at 2.9% APR over a period of 25 years is $1,219.47.

The monthly payment for the amortized loan can be determined using an online finance calculator as follows:

The monthly payment shows the periodic payment that must be made to settle the loan at the end of the loan period.

N (# of periods) = 300 months (25 years x 12)

I/Y (Interest per year) = 2.9%

PV (Present Value) = $260,000

FV (Future Value) = $0

Results:

Monthly Payment (PMT) = $1,219.47

Sum of all periodic payments = $365,840.66

Total Interest = $105,840.66

Learn more about monthly payments at https://brainly.com/question/27926261.

#SPJ1

Lena's total pay if she sells 29 copies of Math is Fun would be $4210.

Lena's total pay (P) to the number of copies of Math is Fun she sells (N) is:

P = 1600 + 90N

This equation shows that Lena's total pay is equal to her base salary of $1600 plus $90 for every copy of Math is Fun she sells.

To find Lena's total pay if she sells 29 copies of Math is Fun, we simply substitute N = 29 into the equation:

P = 1600 + 90(29)

P = 1600 + 2610

P = 4210

Therefore, Lena's total pay if she sells 29 copies of Math is Fun would be $4210.

If the senior classes at High School A and High School B planned separate trips to the indoor climbing gym.  the number of students  a van  can carry is 18 students.

Let's start by using "v" to represent the number of students that can fit in a van, and "b" to represent the number of students that can fit in a bus. We can then set up a system of equations to represent the given information:

For High School A:

14v + 5b = 334 (equation 1)

For High School B:

3v + 10b = 393 (equation 2)

We know that every van has the same number of students as every bus, so we can set v equal to b:

v = b

We can then substitute b for v in either equation:

14v + 5b = 334

14b + 5b = 334

19b = 334

b = 17.58

We can round this to the nearest whole number since we can't have fractional students. So, a bus can carry 18 students.

Since v = b, we know that a van can also carry 18 students.

Therefore the number of students  a van  can carry is 18 students.

Learn more about number of students here:https://brainly.com/question/9273526

#SPJ1

The inverse of the function f(x) = k/x is the expressed derived as; f⁻¹(x) = k/x

A function is said to have an inverse if it is both one-to-one and onto

we replace the function f(x) with y and make x the subject to arrive at the inverse f⁻¹(x) as follows;

Given f(x)= k/x

y = k/x

y × x = k/x × x {multiply both sides by x}

xy = k

xy/y = k/y {divide through by y}

x = k/y

f⁻¹(x) = k/y.

Therefore, the inverse of the function f(x) = k/x is the expressed derived as; f⁻¹(x) = k/x.

Read more about inverse functions here:https://brainly.com/question/3831584

#SPJ1

The lengths of the segments in the drawing, obtained using Thales Theorem are;

1) [AD] = 33.5 cm

2) a) OM ║ AB, therefore, OMAB is a trapezium

b) Thales Theorem indicates that point L is the midpoint of [DE]

c) Rectangle

3) JO ║ IL and IJ ║ OL, therefore, IJOL is a parallelogram

b) [JA] ≅ [AI], therefore; {OD] ≅ [DF] and point D is the midpoint of [OF]

IF = 5.25 cm

5) 1) the point C, which is the point of intersection of the medians is the center of gravity of BJD

2) The parallel sides of the parallelogram ABCD, and Thales Theorem indicates that M and N are the midpoints [BJ], and [DI]

Thales Theorem indicates that MN = DI = IB

Thales Theorem states that a line drawn parallel to one side of a triangle such that it intersects the other two sides, then the line divides the other two sides of the triangle in the same proportion.

1) The the diagonals of a rectangle bisect each other, therefore;

The length of [AD] = Length of [AB] = BE/2

The length of [AD] = 7 cm/2 = 3.5 cm

2) a) Whereby the point M is the midpoint of [AD], then according to the midsegment theorem, [OM] is parallel to [AB], therefore; OMAB is a trapezium, by the definition of a trapezium

b) Whereby [OM] is parallel to [AB], we get;

[OM] is parallel to [BE], therefore;

[OL] is parallel to [DE]

According to the triangle proportionality theorem, which is also known as Thales Theorem, the segment [OL] that divides [BD] in two also divides DE in two, therefore, point L is the midpoint of [DE].

c) Whereby the points A and L are the midpoints of [BE] and [DE], and the point O is the midpoint of [BD], we get;

[AO] is parallel to [DL], and [AL] is parallel to [OD]

[DL] is perpendicular to [BD], by definition of rectangle HBDE, therefore, [AO] is perpendicular to [BD]

Similarly, [AL] is perpendicular to [DE], and the quadrilateral ALDO is a rectangle

3) a) [OL] is parallel to [IJ]

The midsegment theorem indicates that AD is parallel to JO and segment AD is parallel to IL, therefore;

JO is parallel to IL and IJOL is a parallelogram

b) Whereby BD is extended to the point F, and IL cuts BD in F, we get;

JO, AD, and IF cut segment OAI into parts JA and AI of the same length, therefore;

JO, AD, and IF cut segment ODF into parts OD, and DF of the same lengths, therefore, point D is the midpoint of OF

AB = AD = 3.5

FA = 3.5/2 = 1.75

BF = 3.5 + 1.75 = 5.25

IF/5.25 = 3.5/3.5

Therefore, IF = 5.25 cm

5) The center of gravity of a triangle is the point of intersection of the three medians of the triangle

Whereby point J is the symmetric of A with respect to C, we get;

AC = CJ

The parallel sides BA and CD, and the midsegment theorem indicates;

BM = MJ, therefore;

Point M is the midpoint of BJ, and DM is a median of the triangle BJD

Similarly, BN is a median of the triangle BJD

The diagonals of a parallelogram bisect each other, therefore, the point of intersection of the diagonals, I is the midpoint of BD, and JI is a median of the triangle BJD, therefore, the point C is the center of gravity of the triangle BJD

2) The segments AC and CJ are congruent, and the segments CD and BA are parallel. According to the triangle proportionality theorem, segment BM is congruent to segment MJ, and the point M is the midpoint of BJ

Similarly, BC is parallel to AD, therefore, DN is congruent to NJ, and the point N is the midpoint of DJ

The Thales Theorem or midsegment theorem indicates MN = (1/2) × BD, therefore;

MN = DI = BD

Learn more on Thales theorem here: https://brainly.com/question/395481

#SPJ1

The fourth vertex of the rectangle is the point (–2, 3).

To create a rectangle, we need two pairs of opposite sides that are parallel and equal in length.

The line segment connecting the points (–2, 12) and (7, 12) is a horizontal line segment, which means that its opposite side must also be horizontal. The only point with a y-coordinate of 3 is (7, 3).

The line segment connecting the points (7, 12) and (7, –3) is a vertical line segment, which means that its opposite side must also be vertical. The only point with an x-coordinate of –2 is (–2, 3).

So the fourth vertex of the rectangle is the point (–2, 3).

Learn more about vertex at https://brainly.com/question/21185651

#SPJ1

The three inequalities that define the region R are:

y ≤ -2x + 6

x ≤ (2/5)y

x ≥ (3/2)y - (2/3)

An inequality is a statement that two values or expressions are not equal. In other words, it is a statement that one value or expression is greater than or less than another. Inequalities are commonly used to describe relationships between numbers or variables.

To write down the three inequalities that define the region R, we need to identify the equations of the three boundary lines that enclose the shaded region.

From the equations given, we can rearrange them to get the equations of the three lines:

2x + y = 6 => y = -2x + 6

2y = 5x => y = (5/2)x

3y + 2x = 4 => y = (-2/3)x + (4/3)

To determine the inequalities that define R, we need to figure out which side of each boundary line is the shaded region.

The line y = -2x + 6 is the upper boundary of R. To be inside R, we need y to be less than or equal to -2x + 6, so the first inequality is:

y ≤ -2x + 6

The line y = (5/2)x is the right boundary of R. To be inside R, we need x to be less than or equal to 2/5y, so the second inequality is:

x ≤ (2/5)y

The line y = (-2/3)x + (4/3) is the left boundary of R. To be inside R, we need x to be greater than or equal to 3/2y - 2/3, so the third inequality is:

x ≥ (3/2)y - (2/3)

Therefore, the three inequalities that define the region R are:

y ≤ -2x + 6

x ≤ (2/5)y

x ≥ (3/2)y - (2/3)

Each of these inequalities individually describes a half-plane, and their intersection is the shaded region R in the diagram.

To know more about inequalities:

https://brainly.com/question/30231190

#SPJ1

The amount or cubic inches of water present in the aquarium will be: 4096 cubic inches.

To find out how many cubic inches of water will be present in this aquarium, you simply have to multiply all the sides. First, note that the shape of the aquarium is a rectangle. The volume of a rectangle is obtained by multiplying all of the sides.

So, when we multiply all of the sides we will have: 16 in * 8 in * 32 in = 4096 cubic inches. Therefore, we can arrive at the final answer of 4096 cubic inches.

Learn more about volumes here:

https://brainly.com/question/1972490

#SPJ1

Step-by-step explanation:

There are 10 possible outcomes for the digit (0-9) and 26 possible outcomes for the letter (A-Z). Since the choices are independent, the probability of selecting a 6 as the digit and a consonant as the letter is the product of the probabilities of each event occurring separately.

There are 21 consonants in the English alphabet, so the probability of selecting a consonant is 21/26. The probability of selecting a 6 is 1/10.

Therefore, the probability of selecting a 6 and a consonant is:

P(6 and consonant) = P(6) × P(consonant)

= 1/10 × 21/26

= 21/260

= 3/40

Hence, the probability that the number is 6 and the letter is a consonant is 3/40.

The two correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x - 5 < 10 - x and -6x + 15 < 10 - 5x.

What is inequality?

An inequality in mathematics is a statement that indicates the relative size or order of two quantities or expressions, implying that they are not equal.

To solve the inequality, we can simplify it as follows:

-3(2x – 5) < 5(2 – x)

-6x + 15 < 10 - 5x (distribute the negative sign on the left and the positive sign on the right)

-6x + 5x < 10 - 15 (add 6x and subtract 15 from both sides)

-x < -5 (combine like terms)

x > 5 (multiply both sides by -1 and reverse the inequality)

Therefore, x > 5 is the solution to the inequality. The correct representations of this solution are:

-6x - 5 < 10 - x (simplified form of the original inequality)

A number line from 5 to infinity with an open circle at 5 and a bold line pointing to the right (graphical representation)

The options 1, 3, and 4 are incorrect because they do not represent the correct solution to the inequality.

To learn more about inequality visit:

https://brainly.com/question/30238989

#SPJ1

The likelihood that the friend will be late by between 10 and 30 minutes is roughly 0.6667, or 66.67%.

The probability that the buddy will be between 10 and 30 minutes late is equal to the size of the rectangle that exists between x = 10 and x = 30, and below the curve of the probability density function because the probability density function is uniform.

Given that the range of potential values for x is [0, 30] minutes, the height of the rectangle is equal to the greatest value of the probability density function, which is 1/30.

The width of the rectangle is 30 – 10 = 20 minutes, which is the difference between the interval's upper and bottom boundaries.

The likelihood that the friend will arrive between 10 and 30 minutes late is thus:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

To know more about probability follow

https://brainly.com/question/27077702

#SPJ1

Therefore, the solution set for the system of inequalities is all integers less than -5 and less than 3.4.

To solve the system of inequalities, we need to find the values of 'a' that satisfy both of the given inequalities.

First, we will solve the first inequality:

3 - 2a > 13

Subtracting 3 from both sides, we get:

-2a > 10

Dividing both sides by -2 (and flipping the inequality since we are dividing by a negative number), we get:

a < -5

Now, we will solve the second inequality:

5a < 17

Dividing both sides by 5, we get:

a < 3.4

Therefore, the solution set for the system of inequalities is all integers less than -5 and less than 3.4. The integers that are in this solution set are -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55, -56, -57, -58, -59, -60, -61, -62, -63, -64, -65, -66, -67, -68, -69, -70, -71, -72, -73, -74, -75, -76, -77, -78, -79, -80, -81, -82, -83, -84, -85, -86, -87, -88, -89, -90, -91, -92, -93, -94, -95, -96, -97, -98, -99, -100, -101, -102, -103, -104, -105, -106, -107, -108, -109, -110, -111, -112, -113, -114, -115, -116, -117, -118, -119, -120, -121, -122, -123, -124, -125, -126, -127, -128, -129, -130, -131, -132, -133, -134, -135, -136, -137, -138, -139, -140, -141, -142, -143, -144, -145, -146, -147, -148, -149, -150, -151, -152, -153, -154, -155, -156, -157, -158, -159, -160, -161, -162, -163, -164, -165, -166, -167, -168, -169, -170, -171, -172, -173, -174, -175, -176, -177, -178, -179, -180, -181, -182, -183, -184, -185, -186, -187, -188, -189, -190, -191, -192, -193, -194, -195, -196, -197, -198, -199, -200, -201, -202, -203, -204, -205, -206, -207, -208.

Learn more about inequalities here:

brainly.com/question/30231190

#SPJ1

The graph of the given exponential function is as shown in the attached file.

An exponential function is defined as a function with the general form:

y = a(b)^x

where:

a ≠ 0

b is a positive real number and b ≠ 1.

In an exponential function, the base b is a constant. The exponent x is the independent variable where the domain is the set of real numbers.

The given exponential function is:

f(x) = 1(¹/₅)ˣ

The vertical intercept will be the point where x = 0. Thus:

f(0) = 1(¹/₅)⁰

f(0) = 1

Using this value and others, we have the graph as shown in the attached file.

Read more about Exponential Equations Graph at: https://brainly.com/question/2456547

#SPJ1

Answer:where graph

Step-by-step explanation:

Answer:

Step-by-step explanation:

20FT I DID THIS IN 7TH GRADEEEEEEEEEEEEEE

Answer:

C

Step-by-step explanation:

Riding at a constant rate of 15 miles per hour means that the line must be drawn through (1,15) and (2,30).

In one hour, he has traveled 15 miles and in 2 hours, he has traveled 2 times 15 = 30 miles.

The graph which shows the distance that Carmen travelled is option C.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Given that,

Carmen rode his bicycle at a constant rate of 15 miles per hour.

This means that Carmen is riding bicycle at 15 miles for 1 hour, 30 miles for 2 hours, etc.

The general equation for the situation is,

y = 15x

where y is the distance travelled and x is the time taken.

The graph of this function will be a proportional graph passing through points (0, 0), (1, 15), (2, 30), (3, 45), ...

The correct graph is picture number 3.

Hence the correct option is C.

Learn more about Linear functions here :

https://brainly.com/question/20106471

#SPJ2

An expression that can be used to find the amount of the greatest change in one hour include the following: C. -240 - (-80) meters.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Rate of change (slope) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope) = rise/run

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Rate of change (slope) = (y₂ - y₁)/(x₂ - x₁)

Rate of change (slope) = (-204 - (-80))/(2 - 1)

Rate of change (slope) = -124/1

Rate of change (slope) = -124.

Therefore, the required expression is given by;

-240 - (-80) meters.

Read more on slope here: brainly.com/question/3493733

#SPJ1

Answer:

The value of the 8 in the number 1.803 is 0.08.

To find the value of the 8 in 81.30,

we can use the following process:

First, since 1.803 has three digits, we can assume that the value of each digit has a decimal place value of 0.001. So the 8 in 1.803 has a place value of 0.008.

Meanwhile, 81.30 has four digits. Therefore, the value of each digit has a decimal place value of 0.0001. So the 8 in 81.30 has a place value of 0.0008.

Therefore, the value of the 8 in the number 1.803 is greater than the value of the 8 in the number 81.30.

I hope this helps you

1   2/35 miles you run down the slope.

You run 8 2/5 miles in total, and you run 1/2 of that distance on a hill, so you run (1/2) x 8 2/5 = 4 1/5 miles on the hill.

You run down the slope for the last 2/7 of the hill.

To find how many miles that is, we can multiply the total distance on the hill by 2/7:

(2/7) x 4 1/5 = 1  2/35

Therefore, you run down the slope for 1  2/35 miles of your run.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ1

The probability that  the Islanders will win at most one out of five games in a series against the Rangers is P ( A ) = 0.337

Given data ,

The probability that the Islanders will beat the Rangers in a game is 0.4

Now , The probability that  the Islanders will win at most one out of five games in a series against the Rangers is P ( A )

And , from the binomial distribution ,

P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ

On simplifying , we get

p = 0.4 (probability of the Islanders winning a single game)

n = 5 (number of games in the series)

Now we can calculate the probability of winning 0 or 1 game using the binomial probability formula:

P(X=0) = C(5, 0) ( 0.4 )⁰ (1-0.4)⁵

P(X=1) = C(5, 1) ( 0.4 ) (1-0.4)⁴

P(X=0) = 0.6⁵ ≈ 0.078

P(X=1) = 5 x 0.4 x 0.6⁴ ≈ 0.259

Now, to find the probability of winning at most one game, we add the probabilities of winning 0 and 1 game:

P(X ≤ 1) = P(X=0) + P(X=1) ≈ 0.078 + 0.259 ≈ 0.337

Hence , the probability is P ( A ) = 0.337

To learn more about binomial distribution click :

https://brainly.com/question/29350029

#SPJ1

[tex]\underset{ \textit{angle in degrees} }{\textit{area of a regular polygon}}\\\\ A=\cfrac{1}{2}nR^2\sin\left( \frac{360}{n} \right) ~~ \begin{cases} R=\stackrel{\textit{radius of}}{circumcircle}\\ n=\stackrel{\textit{number of}}{sides}\\[-0.5em] \hrulefill\\ n=8\\ R=6 \end{cases}\implies A=\cfrac{1}{2}(8)(6)^2\sin\left( \frac{360}{8} \right) \\\\\\ A=144\sin(45^o)\implies A=144\cdot \cfrac{\sqrt{2}}{2}\implies A=72\sqrt{2}\implies A\approx 101.8[/tex]

The similar rectangle with the dimensions is 4 feet by 8 feet

Given data ,

A rectangle with the dimensions of 2ft by 8ft is similar to a rectangle with the dimensions given by

The scale factor of the rectangle is 2

So , the new dimensions of the rectangle are 4 feet by 8 feet

Hence , the rectangle is having a dimension of 4 feet by 8 feet

To learn more about area of rectangle click :

https://brainly.com/question/15225905

#SPJ1

The complete question is attached below :

A rectangle with the dimensions of 2ft by 8ft is similar to a rectangle with the dimensions of?

With a little bit of effort and persistence, she should be able to come up with a strong list of symmetrical words and be well on her way to winning the competition.

Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used in various fields such as science, engineering, finance, and many others. Number is an abstract concept that can be represented using symbols, such as digits (1, 2, 3) or letters (A, B, C). Number can be used to represent a quantity, an amount, or a certain order. It can also represent relationships between objects, such as combinations, sequences, and patterns.

The best strategy for Lindsay to use to win the competition of who can think of the most symmetrical words is to focus on words that have the same letters in the same positions at the beginning and end of the words. Examples of such words are "civic", "level", and "radar". Lindsay can also focus on words that have the same letters in the reverse order, such as "mom", "noon", and "racecar". Additionally, Lindsay can look for words that have the same letter pattern, but with different combinations of letters, such as "deed" and "feed".

Lindsay can also try to look for words with multiple pairs of symmetrical letters, such as "coconut" or "bobcat". She can also look for words with symmetrical letters in the middle, such as "potato" or "banana". Finally, Lindsay can look for palindromes, which are words that read the same backwards and forwards, such as "racecar" and "kayak".

By focusing on words that have the same letters in the same positions at the beginning and end of the words, as well as words that have the same letters in reverse order, the same letter pattern, multiple pairs of symmetrical letters, and palindromes, Lindsay will be able to increase her chances of winning the competition of who can think of the most symmetrical words. With a little bit of effort and persistence, she should be able to come up with a strong list of symmetrical words and be well on her way to winning the competition.

To know more about number click-
http://brainly.com/question/24644930
#SPJ1

Answer:

Step-by-step explanation: