please help me this is geometry

The probability that at least one person will receive the correct letter is 2/3.

Given data,

Let's say that the letter matching to the envelope is A, B, and C.

Each envelope has exactly one letter inside it once the letters are randomly placed inside.

Aa, Bb, Cc, Aa, Bc, Cb, Ab, Ba, Cc, Ab, Bc, Ca, Ac, Bb, Ca, Ac, Ba, Cb, are all possible combinations.

Thus, the total number of scenarios is 6 (n(S)).

A=(Aa, Bb, Cc), (Aa, Bc, Cb), (Ac, Bb, Ca), (Ab, Ba, Cc), n(A)=4

let A be an event that at least one letter is in its right envelope.

So,

The probability that at least one letter is in the right envelope P(A) = n(S) / n(A) = 4 / 6

= 2 / 3

​

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Jessica bought [tex]2\frac{1}{4}[/tex] yards of fabric more than Derek.

According to the question,

We have the following information:

Jessica bought 5 yards of fabric, plus 20% extra fabric. Derek bought 3 yards of fabric, plus 25% extra.

Now, we will find first the extra fabric they both bought:

For Jessica, we have:

20% of 5

20*5/100

1 yard

Now, the total fabric Jessica has:

5+1

6 yards

For Derek, we have:

25% of 3

25*3/100

3/4 yards

Now, the total fabric Derek has:

3 + 3/4

Taking 4 as the least common factor and adding the fractions:

15/4 yards

Now, we will subtract the fabric Derek has from the fabric Jessica has:

6 - 15/4

(24-15)/4

9/4

Converting this into mixed fraction:

[tex]2\frac{1}{4}[/tex] yards

Hence, the correct option is B.

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The volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex]. It can be obtained by using the formula of the volume of the sphere.

What is the formula of the volume of the sphere?

Volume of any object is the amount of 3 dimentional space occupied by that object. Volume of the sphere is given by the following expression:

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

Here, V is the volume of the sphere and r is the radius of the sphere.

Substitute x-1 for r in the above formula.

[tex]V=\frac{4}{3}\pi r^3\\V=\frac{4}{3}\pi (x-1)^3[/tex]

This is the simplest form.

In the above equation, you can apply the formula [tex](a-b)^3=a^3-3a^2b+3ab^2-b^3[/tex] but that will make the equation difficult and lenthy. Hence, there is no need to apply this formula.

Hence, the volume of the sphere is [tex]\frac{4}{3}\pi (x-1)^3[/tex].

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For the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to

7 : 3.

As given in the question,

Probability of any particular event occurring is equal to 7 /10

Probability of any particular event not occurring is = 1- (7/10)

                                                                                    = (10 -7) /10

                                                                                    = 3/10

Probability of the odds favoring the events which are not occurring

= (7 /10) / (3/10)

= ( 7 × 10) / (3 × 10)

= 7 /3

Odds favoring the events which are not occurring in the form a: b

= 7 : 3

Therefore, for the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to 7 : 3.

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Answer:

k = [tex]\frac{fr^2}{90}[/tex]

Step-by-step explanation:

f = k [tex]\frac{90}{r^2}[/tex] ( multiply both sides by r² to clear the fraction )

fr² = 90k ( divide both sides by 90 )

[tex]\frac{fr^2}{90}[/tex] = k

The solution to the linear equation is (-1, 3).

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable.

2x + y = 1 …… (1)

3x - y = -6 …… (2)

To solve the linear equations in two variables

By adding both the equations

5x = -5

x = -1

Substitute the value of x in equation (1)

2 (-1) + y = 1

-2 + y = 1

y = 1 + 2 = 3

y = 3

Therefore, the solution to the linear equation is (-1, 3).

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Depreciation expense in year 2 = 2/4 x $225,000 = $112,500.

acc to our question-

hence,Depreciation expense in year 2  = $112,500.

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The correct option is, Mickey should have added –4 and 2 when combining the coefficients of the x terms.

Given,

The expression;  2x² - 4x - 9 - x² + 2x + 3

We have to simplify the expression;

To group and arrange an expression in such a way that it is easier to understand and solve is to simplify the expression.

We first group and find like terms and then add and cancel out

2x²-x²- 4x+2x - 9+ 3

=x²-2x-6

Mickey did not add the coefficients -4 and +2 for x terms in the expression, instead it looked like he added 4+2 as the coefficients

Therefore the correct option is

Mickey should have added –4 and 2 when combining the coefficients of the x terms.

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Answer:

[tex]3( - 7x - 3) + 4x = - (x - 3)[/tex]

[tex] - 21x - 9 + 4x = - x + 3[/tex]

[tex] - 21x + 4x + x = 9 + 3[/tex]

[tex] - 16x = 12[/tex]

[tex] - 16 \div ( - 16x = 12)[/tex]

[tex]x = - \frac{3}{4} [/tex]

Step-by-step explanation:

it is negative 3/4 not positive 3/4

Camel can drink 21 gallons of water in 14 minutes.

Given in question,

Gallons of water camel can drink in 10 minutes = 15

 Gallons of water camel can drink in 1 minutes = 15/10

                                                                              = 1.5

Gallons of water camel can drink in 14 minutes = 1.5 * 14

                                                                              = 21

Hence, camel can drink 21 gallons of water in 14 minutes.

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Answer:

12.5 hours a week

Step-by-step explanation:

So far this week, you have worked 10 hours at your part-time job. This is 80% of the number of hours you work each week. How many hours do you work each week?

10 hours = 80%

80% = 0.8

10/0.8 = 12.5 hours a week

The solution of the expression is 2√5x(√2-1).

From the question, we have

√5x ( √8x² - 2√x)

= √5x ( 2√2x - 2√x)

= √5x(√2-1)(2√x)

= 2√5x(√2-1).

The solution of the expression is 2√5x(√2-1).

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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Answer: ITS D

Step-by-step explanation:

2x sqrt 10x - 2x sqrt 5

Answer:

y= 1/4x+5

Step-by-step explanation:

y=mx+c

to calculate gradient: change in y/change in x

-3/-12 = 0.25

y = 1/4x+c

4 * 1/4 = 1

6-1 = 5

c= 5

Totally:
y= 1/4x+5

The value of x in complementary angle is 12.5⁰.

We need to know about complementary angles to solve this problem. The complementary angle is the angle that can make another angle has a value of 90⁰. It can be written as

A + B = 90⁰

where A and B are the complementary angles.

From the question above, the given parameters are

A = 18⁰

B = (8x - 28)⁰

By substituting the given parameters, we can calculate the x value

A + B = 90⁰

18⁰ + (8x - 28)⁰ = 90⁰

8x = 90 - 18 + 28

8x = 100

x = 12.5⁰

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Answer: 12.5

Step-by-step explanation:

18+8x-28=90

18-18

90-18

8x-28=72

28+28

72+28

8x=100

8x/8

100/8

x=12.5

Answer:

Step-by-step explanation:

D

75÷100=0.75

0.75×5=3.75

3.75×4=15

75+15=90

According to the Centroid Ratio Theorem , we have:

                    x = 37 , DG = 22,

                   AG = 44  and AD = 66

Centroid Ratio Theorem:

The Centroid ratio theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the mid point of the side.

according to the centroid ratio theorem, we have,

                        AG = 2/3 (AD)       ----------------------------- (1)

                        AG = x + 7

                        DG = x - 15

                        AD = x + 7 + x- 15 = 2x - 8

Putting the values in equation (1)

     x + 7 = 2/3 (2x - 8)

⇒ 3(x + 7) = 2( 2x - 8)

⇒3x + 21 = 4x - 16

⇒ -x = -37

⇒ x = 37

Putting the value of x= 37

DG = 37 - 15 = 22

AG = 37 +7 = 44

AD= 2×37 - 8 = 66

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We need to multiply equation 2 with 3 and result is x = 1.25. The cost of one apple and one banana is $1.25 and $0.75 respectively.

Forming the equation using given variables x and y. Firstly writing the equation based on Lydia's items.

5x + 3y = 8.50 : Equation 1

Now writing the equation based on Ari's items.

3x + 2y = 5.25 : Equation 2

Now we need to equate one variable to find the other variable. So, multiplying equation 1 with 2 and equation 2 with 3.

10x + 6y = 17 : Equation 3

9x + 6y = 15.75 : Equation 4

Subtracting equation 4 from equation 3. We get the result -

x = 1.25

Keep the value of x in equation 1 to find the value of y

5×1.25 + 3y = 8.50

6.25 + 3y = 8.50

3y = 8.50 - 6.25

3y = 2.25

y = 2.25/3

y = 0.75

Thus, the cost of one apple is $1.25 and cost of one banana is $0.75.

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The complete question is -

lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. this system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas. 5x 3y = 8.5 3x 2y = 5.25 if you multiply the first equation by 2, what number should you multiply the second equation by in order to eliminate the y terms when making a linear combination? complete the multiplication and add the equations. what is the result? what is the price per pound of apples? what is the price per pound of bananas?

Answer: x = 140°

Step-by-step explanation:

The sum of all interior angles in a pentagon is 540°.

Since you have every other angle except for one, you can subtract them from the total:

540°-120°-118°-89°-73° = 140°

Therefore the x angle is equal to 140°.

Step-by-step explanation:

4x - 9 ≥ 17

4x ≥ 17 + 9

4x ≥ 26

4x/4 ≥ 26/4

x ≥ 13/2

x ≥ 6.5

Answer:

1018.25

----------------------------------------------------------------------

hope you do well on the quiz/test/assignment!

The confidence interval for the proportion of left-handed golfers is of:

(0.12, 0.18).

A confidence interval is calculated as the sample mean plus/minus the margin of error, hence the bounds of the confidence interval are given as follows:

In the context of this problem, these parameters are given as follows:

Hence the lower bound of the confidence interval for the proportion of left-handed golfers is:

0.15 - 0.03 = 0.12.

The upper bound of the confidence interval for the proportion of left-handed golfers is:

0.15 + 0.03 = 0.18.

Then the interval is:

(0.12, 0.18).

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Answer:

s=1

Step-by-step explanation:

Slope formula is

Δy/Δx

Substitute in:

7-6/s-10=-1/9

cross multiply

7-6=-1/9s+10(1/9)

7-6=-1/9s+10/9

1-10/9=-1/9s

-1/9=-1/9s

divide both sides by -1/9

thus:

1=s

s=1

(check by plugging back in)

7-6/1-10=-1/9

The percent change of the worth is 3.26%.

Apples were for sale from a fruit vendor. He has 420 apples and sells 40% of them. How many apples did he have in total when he first started?

Solution: Assume a fruit vendor had x apples in stock.

According to the query,

(100 – 40%) of x = 420

60% of x = 420

60/100 x = 420

X = 700

The fruit vendor, therefore, had 700 apples in all.

Let , the worth is $x.

according to the question, $x + $5 =$158

∴ $x= $153

∴ percent change= (5/153)×100

                             =3.26%

The percent change of the worth is 3.26%.

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Answer:

17 = 5 + b

b = 12

y = x + 12

The correct statement that regarding the angles of triangle is option (C)  m∠C > m∠A > m∠B

The value of p ≥ 3

Consider the value p = 3

The length of the side AB = 4p - 1

= 4×3 - 1

= 12 - 1

= 11 units

The length of side BC = 3p

= 3×3

= 9 units

The length of the side AC = p + 4

= 3 + 4

= 7 units

Then length of AB > length of BC > length of AC

The angles opposite to the side AB, BC and AC are m∠C , m∠A and m∠B

Then  m∠C > m∠A > m∠B

Hence, the correct statement that regarding the angles of triangle is option (C)  m∠C > m∠A > m∠B

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The base of the triangle is 15 meters.

Here, we are given that the height of a triangle is 5 m longer than the base.

Let the height of the triangle be h

Then, the base of the triangle will be = h - 5

Further, we are given that area of the triangle = 150 meter square

We know that area of a triangle = 1/2 × base × height

⇒ 150 = 1/2 × h × (h-5)

150 × 2 = h(h-5)

300 = [tex]h^{2}[/tex] - 5h

[tex]h^{2}[/tex] - 5h - 300 = 0

Now, we solve the above quadratic equation by splitting the middle term.

[tex]h^{2}[/tex] + 15h - 20h - 300 = 0

h( h + 15) - 20( h + 15) = 0

(h - 20) (h + 15) = 0

Thus, h = 20 or -15

But since height cannot be negative, h = 20

⇒ base = h - 5

= 20 - 5

= 15 meters

Thus, the base of the triangle is 15 meters.

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Answer:

B

Step-by-step explanation:

In a positive correlation, an increase in the independent variable has a corresponding increase in the dependent variable.

What is correlation?

Correlation is a statistical measure that expresses the extent to which two variables are linearly related. We know a positive correlation—when the correlation coefficient is greater than 0 signifies that both variables move in the same direction. Also, A positive correlation exists when one variable decreases as the other variable decreases or one variable increases while the other increases.

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