Mr. Gaspar wants to store a 12-foot-long pipe
in a tool closet. The closet has the shape of a
right rectangular prism with the dimensions
shown. Will the pipe fit? Show your work.

Mr. Gaspar Wants To Store A 12-foot-long Pipein A Tool Closet. The Closet Has The Shape Of Aright Rectangular

Answers

Answer 1

The longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.

What is the Pythagoras theorem?

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

From the given figure,

By considering base of the prism, we get

c²=6²+6²

c²=72

c=6√2 ft

Now, d²=c²+8²

d²=72+64

d²=136

d=√136

d= 11.7 ft

Hence, the longest pipe can fit in the prism is 11.7 ft, so, 12 ft long pipe does not fit.

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Related Questions

help me if x = 12 and y = 5 what is the value of x - 7 + 2y

Answers

Given:-

[tex] \sf \: x = 12[/tex]

[tex] \: [/tex]

[tex] \sf \: y = 5[/tex]

[tex] \: [/tex]

[tex] \sf \: x - 7 + 2y ---eqⁿ[/tex]

[tex] \: [/tex]

Solution:-

[tex] \sf \: x - 7 + 2y[/tex]

[tex] \: [/tex]

put the given values of x nd y in equation∼

[tex] \: [/tex]

[tex] \sf \: 12 - 7 + 2(5)[/tex]

[tex] \: [/tex]

[tex] \sf \: 5 + 10[/tex]

[tex] \: [/tex]

[tex] \underline{ \boxed{ \sf \color{hotpink} \: 15 \: }}[/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Answer:

x - 7 + 2y = 15

Step-by-step explanation:

Given expression,

→ x - 7 + 2y

Now we have to use,

→ y = 5

→ x = 12

Then the value of expression is,

→ x - 7 + 2y

→ 12 - 7 + 2(5)

→ 12 - 7 + 10

→ 12 + 3

15 => {final answer}

Therefore, the answer is 15.

A jar contains three blue marbles ,seven red marbles and five green marbles,and you pick one without looking.What is the probability that the marble will be neither red nor blue

Answers

Answer:1 in 3 chance

Step-by-step explanation:

There are 5 green, 3 blue, and 7 red. Add them up 5+3+7=15
Then you put it into a fraction [tex]\frac{5}{15} =\frac{1}{3} \\[/tex]
1 over 3 is your answer

Solve the quadratic equation by using a numeric approach. 0.02x squared + 0.1 x minus 2 = 0 a. x = 2.3 and x = -29.2 c. x = 5.6 and x = -12.2 b. x = 7.8 and x = -12.8 d. x = 1.3 and x = -22.6 Please select the best answer from the choices provided A B C D

Answers

The solution to the equation is 7.8075 or -12.8075

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

We have the Quadratic Equation: 0.02 x² + 0.1 x - 2 = 0

2x² + 10x - 200 = 0

Using Discriminant Method

D = √b² - 4ac

D = √10² - 4(2)(-200)

D = √100 + 1600

D = √1700

D = 41.23

So, x = -b± D/2a

x = -10 ± 41.23 / 4

x= -10 + 41.23/4  or x= -10 -41.23 /4

x= 31.23/4 or x= -51.23/4

x= 7.8075 or x = -12.8075

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Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and kind of fit were created for the data.


Determine the equation of the line of fit

y= 15x + 70
y= 15x + 40
y= 30x + 70
y= 30x + 40

Answers

Equation of best fit line on scatter plot is y = 30x + 40

Correct option is D.

What is straight line?

A straight line is an infinite one-dimensional shape with no width. An infinite combination of points connected on either side of the point. A straight line has no curves. It can be horizontal, vertical, or slanted. An angle drawn between any two points on a straight line is always 180 degrees.

Given,

Scatter plot of the data of studying time of students

By the graph, point on the line are (0, 40) and (2,70)

Equation of the line

y - y₁ = ((y₂-y₁)/(x₂-x₁))(x-x₁)

y - 40 = ((70-40)/(2-1))(x-0)

y - 40 = (30/1)x

y - 40 = 30x

y = 30x + 40

Hence, y = 30x + 40 is the equation of the best fit line in scatter plot.

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Use substitution to solve each system of equations.
y=5x+1
4x+y=10

Answers

y = 5x+1. ____equ(1)

4x + y = 10. ____equ (2)

substituting equ(1) into equ(2)

4x + y = 10

4x + 5x + 1 = 10

9x = 10 -1

9x = 9

x = 1

x = 1 into equ (1)

y = 5x + 1

y = (5 ×1) + 1

y = 5 + 1

y = 6

I hope this will help.

have a nice day dear :)

If 11 dinner guests want salad, how many ounces of dressing will be necessary? Round the answer to the nearest whole ounce.

Answers

The amount of dressing required to serve 11 guests who still want salad is therefore around 11 ounces. The answer, when adjusted to the closest whole ounce, is 11 ounces.

A nearest number is what?

Round the figure up if 5, 6, 7, 8, or 9 follow the amount you are rounding. For instance, 40 when rounded to a nearest ten is 38. Round the figure down if it is followed by the digits 0, 1, 2, 3, or 4. 33 becomes 30 if it is adjusted to the nearest ten.

Many variables, such as the salad's serving size, the type of sauce, and personal preferences, will affect how much dressing is needed for 11 dinner guests. But as a general rule, a salad with dressing serving size is roughly 2-3 teaspoons (1 ounce = 2 tablespoons).

Assuming that each visitor will consume 2 tablespoons of dressings, the necessary quantity of dressing would be:

11 guests x 2 tablespoons/guest = 22 tablespoons

Tablespoons to ounces conversion:

22 tablespoons / 2 tablespoons/ounce = 11 ounces

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Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that 12 people will be randomly chosen to be on the committee from a group of 30 volunteers, 21 who are technically proficient and 9 who are not. We are interested in the number on the committee who are not technically proficient.

c)How many instructors do you expect on the committee who are not technically proficient? (Round your answer to the nearest whole number.)

(d)Find the probability that at least 3 on the committee are not technically proficient. (Round your answer to four decimal places.)

(e)Find the probability that at most 4 on the committee are not technically proficient. (Round your answer to four decimal places.)

Answers

The prοbability that nο mοre than fοur cοmmittee members are technοlοgically adept is 0.9851, rοunded tο fοur decimal places.

c) By dividing the tοtal number οf applicants whο are nοt technically prοficient (9) by the likelihοοd that any οne οf them wοuld be selected fοr the cοmmittee, it is pοssible tο calculate the anticipated number οf instructοrs οn the cοmmittee whο are nοt technically prοficient:

Number anticipated: 9 * (12/30) = 3.6

Tο the nearest whοle number, we estimate that there will be fοur prοfessοrs οn the cοmmittee whο lack technical prοficiency.

d) We can use the binοmial distributiοn with n=12 (the number οf trials) and p=0.3 tο determine the likelihοοd that at least three members οf the cοmmittee lack technical prοficiency (prοbability οf success, which is defined as selecting a vοlunteer whο is nοt technically prοficient). When X is the number οf technically incοmpetent prοfessοrs οn the cοmmittee, we want tο determine P(X>=3).

P(X>=3) = 1 - P(X<3)

= 1 - P(X=0) - P(X=1) - P(X=2)

[tex]\mathrm{=1 - (12\ choose\ 0)(0.3^0)(0.7^{12}) - (12\ choose\ 1)(0.3^{1})(0.7^{11}) - (12\ choose\ 2)(0.3^2)(0.7^{10)}}[/tex]

[tex]= 1 - 0.00744 - 0.0563 - 0.1667[/tex]

[tex]= 0.7696[/tex]

The likelihοοd that at least three members οf the cοmmittee lack technical prοficiency is 0.7696, rοunded tο fοur decimal places.

e) Using the same binοmial distributiοn as in part d), we can calculate the likelihοοd that at mοst 4 members οf the cοmmittee are nοt technically adept by adding the prοbabilities fοr X=0, 1, 2, 3, and 4:

P(X<=4) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)

[tex]\mathrm{= (12\ choose\ 0)(0.3^0)(0.7^{12}) + (12 \ choose\1)(0.3^1)(0.7^|{11}) + (12 \ choose\2)(0.3^2)(0.7^{10})}\\\mathrm{ + (12 \ choose\3)(0.3^3)(0.7^9) + (12 \ choose\4)(0.3^4)(0.7^8)}[/tex]

[tex]= 0.9851[/tex]

Rounding tο four decimal places, the likelihood that no more than four committee members are technοlogically savvy is 0.9851.

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Select the correct solution for the expression. 2 5 + 3 8 A. 2 5 + 3 8 = 5 13 B. 16 40 + 15 40 = 31 40 C. 10 40 + 24 40 = 34 40 D. 2 5 + 3 8 = 6 40

Answers

Therefore, the correct solution for the expression 2/5 + 3/8 is:

2/5 + 3/8 = 31/40

Option B is the correct solution. Answer: B. 16/40 + 15/40 = 31/40

What is number?

A number is an arithmetic value that is used to indicate quantity. Hence, a number is a mathematical construct that is utilised for counting, measuring, and labelling. As a result, mathematics is built on numbers. As an illustration, this is a single butterfly, and these are four.

We can simplify the expression 2/5 + 3/8 as follows:

First, we need to find a common denominator. The smallest number that both 5 and 8 divide into evenly is 40.

2/5 can be written as 16/40 (by multiplying the numerator and denominator by 8)

3/8 can be written as 15/40 (by multiplying the numerator and denominator by 5)

Now we can add the fractions:

16/40 + 15/40 = 31/40

Therefore, the correct solution for the expression 2/5 + 3/8 is:

2/5 + 3/8 = 31/40

Option B is the correct solution. Answer: B. 16/40 + 15/40 = 31/40

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On the school playground, the slide is due west of the tire swing and due south of the monkey bars. If the distance between the slide and the tire swing is 7 meters and the distance between the tire swing and the monkey bars is 10 meters, how far is the slide from the monkey bars? If necessary, round to the nearest tenth.

Answers

The slide is approximately 12.2 meters away from the monkey bars.

What is Pythagoras Theorem?

You may determine the right angled triangle's missing length using Pythagoras' Theorem. The triangle has three sides: the adjacent, which doesn't touch the hypotenuse, the opposite, which is usually the longest, and the hypotenuse (which is between the opposite and the hypotenuse).

We can solve this problem by using the Pythagorean theorem, which states that for a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side (the hypotenuse).

Let's label the distance between the slide and the monkey bars as "x". We can see that the distance between the slide and the tire swing, and the distance between the tire swing and the monkey bars form the two shorter sides of a right triangle, with the hypotenuse being the distance between the slide and the monkey bars.

Using the Pythagorean theorem, we have:

[tex]x^2 = 7^2 + 10^2\\\\x^2 = 49 + 100\\\\x^2 = 149\\\\x = \sqrt{(149)}[/tex]

x ≈ 12.2 meters (rounded to the nearest tenth)

Therefore, the slide is approximately 12.2 meters away from the monkey bars.

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PLEASE HELP PLEASE ASAP PLEASE HELP
What are the coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin?



Answers

The image of the quadrilateral is R' = (-2, -1), S' = (-4, -2), T' = (-5, -4) and U' = (-3, -3)

How to determine the image of the quadrilateral

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

R = (1, -2)

S = (2, -4)

T = (4, -5)

U = (3, -3)

The transformation is given as

90 degrees rotation about the origin

This is represented as

(x, y) = (y, -x)

Using the above as a guide, we have the following:

R' = (-2, -1)

S' = (-4, -2)

T' = (-5, -4)

U' = (-3, -3)

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The coordinates of each point after the quadrilateral RSTU is rotated 90 degrees about the origin are;

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

What are the coordinates of each point?

The coordinates of the quadrilateral RSTU is

R = (1, -2)

S =(2, -4)

T = (4, -5)

U = (3, -3)

When the quadrilateral RSTU is rotated 90 degrees about the origin, it forms the quadrilateral MNPQ which has the coordinates

M = (1, 2)

N = (2, 4)

P = (4, 5)

Q = (3, 3)

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Nine times the input minus seven is equal to the output. Which of the following equations describes this function?

7x-9=y
9y-7=x
9x-7=y
7y-9=x

Answers

An equation that describes this function include the following: C. 9x - 7 = y.

What is a function?

In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables.

This ultimately implies that, an input value (x-value) represents the value on the x-axis of a cartesian coordinate while a output value (y-value) represents the value on the y-axis of a cartesian coordinate.

Based on the information provided, an equation that models the situation is given by;

9x - 7 = y.

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2g) Letty is simplifying the square root of 48 using the Product Property of Square Roots. She wants to use the factors 4
and 12 to simplify the radical. Explain why these are not the best factors to use.

Answers

The numbers 4 and 12  are not the best factors to use because they do not fully simplify the expression

How to determine the statement/reason

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

Square root of 48

This can be expressed as

√48

Using Letty's solution, we have

√48 = √(4 * 12)

This gives

√48 = 2√12

So, we simplify again

√48 = 2√(4 * 3)

This gives

√48 = 4√3

Hence, the factors are not the best

Instead, she can use 16 and 3

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increase 11,47kg in ratio of 11:7​

Answers

Answer:

7.0094

Step-by-step explanation:

12. A mosaic wall is divided into 100 equal
Name
sections. If 30 sections are reserved for
orange tiles and 40 sections are reserved
for blue tiles, what fraction of the mosaic
wall is left for other colors?

Answers

Answer:

There are 30 + 40 = 70 sections reserved for orange and blue tiles. This means there are 100 - 70 = 30 sections left for other colors.

To express the fraction of the mosaic wall left for other colors, we can write:

30 sections left / 100 total sections = 3/10

Therefore, the fraction of the mosaic wall left for other colors is 3/10.

Find an equation for the line that passes through the points (- 1, -6) and (3, 4)

Answers

Answer:

y=5/2x-7/2

Step-by-step explanation:

find x, round to nearest tenth, show proofs HELP

Answers

The value of x, given the sides in the right - angled triangle, would be 31. 8 °.

How to find the value of x ?

We are given side that is opposite the angle, and we are also given the hypotenuse.

This means that we can use the operation of Sin which is :

Sin ( angle ) = Opposite / Hypotenuse

Opposite = 10 units

Hypotenuse = 19 units

The value of x is :

Sin ( x ) = 10 / 19

Sin ( x ) = 0. 5263

x = Sin ⁻ ⁵ ( 0. 5663 )

x = 31. 8 °

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pls help me i need help ​

Answers

Answer:

77

Step-by-step explanation:

Bisects means that the angle is split in half perfectly thus if angle JKM is 154 then JKR is 154/2 = 77

Which of the following explains why this inequality is true? 7 3 8 × 4 5 < 7 3 8 A. When 7 3 8 is multiplied by a number greater than 1, the product is more than 7 3 8 . B. When 7 3 8 is multiplied by a number greater than 1, the product is less than 7 3 8 . C. When 7 3 8 is multiplied by a number less than 1, the product is more than 7 3 8 . D. When 7 3 8 is multiplied by a number less than 1, the product is less than 7 3 8 . ALSO IT IS FRACTIONS BUT IM TO LAZY TO DO IT S OHELP ME ASAP

Answers

The correct expIanation is B. When 7 3 8 is muItipIied by a number greater than 1, the product is Iess than 7 3 8.

A fraction is a way of representing a part of a whoIe or a ratio between two quantities. It consists of a numerator (top number) and a denominator (bottom number) separated by a horizontaI Iine.

To compare the two fractions, we can convert them to decimaIs.

7 3/8 is equaI to 7.375, and

4/5 is equaI to 0.8.

MuItipIying 7.375 by 0.8, we get:

7.375 × 0.8 = 5.9

This means that 7 3/8 muItipIied by 4/5 is Iess than 7 3/8, since the product is 5.9 which is Iess than 7.375.

Therefore, the correct expIanation is B. When 7 3 8 is muItipIied by a number greater than 1, the product is Iess than 7 3 8.

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3(x+7) in distributive property then in expanded form

Answers

Answer:

Using the distributive property on 3(x+7), we get:

3(x+7) = 3x + 37

Simplifying the expression, we get:

3(x+7) = 3x + 21

Therefore, in expanded form, 3(x+7) is equal to 3x + 21.

According to the scale on a map, 1 inch on the map = 12 miles. How many miles are represented by 2.5 inches on the map?

Answers

Answer:

30 miles

Step-by-step explanation:

(12 miles/inch)(2.5 inches) = 30 miles

The two triangles in the diagram are similar.
There are two possible values of x.
Work out each of these values.
state both assumptions* you make in your working.

Answers

In this case, the equation is 6/2 = x/3, so x = 6/2 * 3/1 = 9/2.Therefore, the two possible values of x are 11/6 and 9/2.

What are corresponding angles?

Corresponding angles are angles that have the same relative position when two parallel lines are cut by a transversal line. When two parallel lines are cut by a transversal, corresponding angles are the same size. Corresponding angles are also known as vertically opposite angles.

In order to determine the value of x, we must assume that the two triangles in the diagram are similar. This means that the corresponding angles are equal and the corresponding sides are proportional. We will also assume that the angles of the triangle are in degrees and the sides are in the same unit of length.

Using the properties of similar triangles, we can calculate the value of x. We start by looking at the given angles, which are both 60°. Since the sides are proportional, we can set up a proportion equation between the two sides. We will use the side lengths given in the diagram to solve the proportion equation.

The proportion equation is: 11/3 = x/2.

Solving this equation for x, we get x = 11/3 * 2/1, which simplifies to x = 11/6.

We can also use the same equation to solve for x using the second given side length, which is 6. In this case, the equation is 6/2 = x/3, so x = 6/2 * 3/1 = 9/2.

Therefore, the two possible values of x are 11/6 and 9/2.

* The assumptions that I made in my working are that the two triangles in the diagram are similar and that the angles are measured in degrees and the sides are measured in the same unit of length.

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What are all possible values of x that satisfy the inequality x3−8≥1?

Answers

We have the following response after answering the given question: inequality   {x | x ≥ ∛9} or [∛9, ∞) in interval notation.

What is inequality?

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.

[tex]x^3[/tex] - 8 ≥ 1

Adding 8 to both sides, we get:

[tex]x^3[/tex] ≥ 9

Taking the cube root of both sides, we get:

x ≥ ∛9

Since ∛9 is approximately 2.08, the inequality is satisfied for all values of x greater than or equal to 2.08. Therefore, the set of all possible values of x that satisfy the inequality is:

{x | x ≥ ∛9} or [∛9, ∞) in interval notation.

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The measure of an angle is 76.6 less than the measure of its supplementary angle

Answers

The measure of the angle x with its supplementary angle is 51.7°.

What distinguishes complimentary angles from supplementary angles?

The difference between complementary and supplementary angles is that complementary angles add up to 90 degrees, whereas supplementary angles add up to 180 degrees. In other words, the total of two complimentary angles' measurements equals 90 degrees. The total of the measurements of two additional angles is 180 degrees.

Let us suppose the measure of angle = x.

The measure of its supplementary angle is 180° - x.

From the given statement we have:

x = (180° - x) - 76.6

2x = 103.4

x = 51.7

Hence, the measure of the angle x with its supplementary angle is 51.7°.

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Divide Katrina's number line into
eighths. Divide Eric's number line into
fourths. Show a point on Katrina's
number line that is less than 1. Show
a point on Eric's number line that is
greater than 1. Write fractions to label
the points you picked.

Answers

1. A point less than 1 in Katrina's number line is [tex]\frac{3}{8}[/tex]

2. A point greater than 1 in Eric's number line is 1[tex]\frac{1}{4}[/tex]          

What is a number line and how do you identify point less or greater than 1?

A number line is a straight line with numbers placed at equal distances from each other.

To identify a line less than 1 in a number line divided into 8, we need to know the value of what each point would be

Each values in Katrina's number line should be 0, [tex]\frac{1}{8}[/tex], [tex]\frac{2}{8}[/tex] , [tex]\frac{3}{8}[/tex],  [tex]\frac{4}{8}[/tex],  [tex]\frac{5}{8}[/tex],  [tex]\frac{6}{8}[/tex],  [tex]\frac{7}{8}[/tex]  1

To identify the line greater than 1 in a number line divided into 4, we need to know the values of what each points would be

Each values in Eric's number line should be 1, 1[tex]\frac{1}{4}[/tex], 1[tex]\frac{2}{4}[/tex], 1[tex]\frac{3}{4}[/tex], 2

Check the images below to get a proper view of how your number line should look like.

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can someone help me please

use the Remainder Theorem and synthetic division please

Answers

The value of the function f(-10), f(2) and f(3) is 20201, 17 and 142 respectively.

What is the remainder theorem?

According to the remainder theorem, when a polynomial p(x) is divided by a linear polynomial q(x) whose zero is x = a, the remainder is given by r = p(a). The remainder theorem enables us to calculate the remainder of the division of any polynomial by a linear polynomial, without actually carrying out the steps of the long division.

Given that, f(x)=2x⁴+x²-10x+1.

Here, f(-10)

Substitute x=-10 in the given function, we get

f(-10)= 2(-10)⁴+(-10)²-10(-10)+1

= 20000+100+100+1

= 20201

Substitute x=2 in the given function, we get

f(2)= 2(2)⁴+(2)²-10(2)+1

= 32+4-20+1

= 17

Substitute x=3 in the given function, we get

f(3)= 2(3)⁴+(3)²-10(3)+1

= 162+9-30+1

= 142

Therefore, the value of the function for x=-10 is 20201.

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What is the surface area?
24 m
26 m
11 m
square meters

Answers

The surface area of the rectangle will be 24 meters. The correct option is A.

What is a surface area?

The surface area of the rectangular plate is calculated by applying the formula for the area of the rectangle.

A rectangle is a type of quadrilateral with four sides and four right angles. The opposite sides of a rectangle are parallel and equal in length, and the opposite angles are congruent (equal). This means that a rectangle has two pairs of congruent sides and four right angles.

Surface area = Length x Width

Surface area = 6 x 4

Surface area = 24 square meters

Therefore, the surface area of the rectangle will be 24 square meters.

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The complete question is given below.

Find the area of the upper surface of the rectangular plate having a length of 6 meters and a width of 4 meters.

Question 5
Kayleigh and Allison race. Kayleigh runs 5 miles per hour. Allison runs 3 miles per hour but has a 1 mile head
start. Using the formulas below where h is hours and d is distance, how long does it take before they meet
each other in the race?
Kayleigh d = 5h
Allison d = 3h+1

Answers

Answer:

Let's call the time it takes for Kayleigh and Allison to meet each other "t".

We know that Kayleigh runs at a constant rate of 5 miles per hour, so the distance she covers in "t" hours is given by:

Kayleigh's distance = Kayleigh's speed * time = 5t

Allison runs at a constant rate of 3 miles per hour, but she has a 1 mile head start. This means that by the time Kayleigh and Allison meet each other, Allison will have run "t" hours minus the time it took her to cover her head start distance. The time it takes Allison to cover her head start distance is:

Time for Allison's head start = distance / speed = 1 / 3 = 0.33 hours (rounded to two decimal places)

Therefore, when Kayleigh and Allison meet each other, Allison will have run:

Allison's distance = Allison's speed * (t - 0.33) = 3(t - 0.33)

Now, we know that when they meet, Kayleigh's distance is equal to Allison's distance:

Kayleigh's distance = Allison's distance

5t = 3(t - 0.33)

Simplifying and solving for "t", we get:

5t = 3t - 1

2t = 1

t = 0.5

Therefore, it takes Kayleigh and Allison 0.5 hours (or 30 minutes) to meet each other in the race.

Question 1 of 24
In right -angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. What is the measure of the hypotenuse of the triangle?

Answers

The measure of the hypotenuse of the triangle is 15 cm.

What is a hypotenuse?

The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle.

Given that, in a right-angled triangle, the base is 9 centimeters long and the height is 12 centimeters long. we need to find the measure of the hypotenuse of the triangle

Using the Pythagoras theorem,

9² + 12² = h²

h² = 81+144

h² = 225

h = 15

Hence, the measure of the hypotenuse of the triangle is 15 cm

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p+20°
What is the value of p?
p=
3p
O
бр
Appreciate it a lot

Answers

Answer:

16°

Step-by-step explanation:

10p+20=180

10p=120

p=16

Pietro and Eva are playing a game in which they toss a coin three times. Eva gets a point if no two consecutive toss results match (as in H-T-H). Pietro gets a point if exactly two consecutive toss results match (as in H-H-T). If all three toss results match, no one scores a point. The first player to get 10 points wins. Is this a fair game? Explain. If it is not a fair game, change the rules to make it fair.​

Answers

This is not a fair game since P + Q is greater than 1. To make game fair, we can modify conditions for scoring points. One possible modification is to give Pietro a point if all three toss results match (HHH or TTT).

This gives Pietro an additional outcome to score a point, which makes the game fair. Another modification is to give Eva a point if any two toss results match (H-T-H, T-H-T, T-T-H, H-T-T, HHT, TTH, THT, HTT). This also makes the game fair since both players have 3 possible outcomes to score a point.

There are 2³ = 8 possible outcomes when a coin is tossed three times. We can list them as follows:

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

Let E be the event that no two consecutive toss results match and let P(E) be the probability of event E. We can count the number of outcomes that satisfy E as follows:

HTH

HTT

THT

TTH

THT

TTT

Therefore, there are 6 outcomes that satisfy E and P(E) = 6/8 = 0.75.

Let P be the probability that Pietro scores a point and let Q be the probability that Eva scores a point. We can count the number of outcomes that satisfy each player's condition as follows:

Pietro: HHT, HTH, THH (3 outcomes)

Eva: H-T-H, T-H-T, T-T-H, H-T-T (4 outcomes)

Therefore, P = 3/8 and Q = 4/8 = 1/2.

The game is not fair since P+Q is greater than 1. This means that the players have a greater than 50% chance of scoring a point on each turn, so the first player to reach 10 points will have an advantage.

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