Word problems ( put solution )

1. John mixed 10.84 liters of honey water with 12.2 liters of
lemon juice to make a drink. Then he poured the mixture
into 0.75-liter bottles.
a) How many bottles could he fill completely with the mixture?
b) How many liters of the mixture were left

2.Mr. Alai bought a digital music player at $76.55 and a
memory card at $10.95 before sales tax. If the sales tax
was 10%, find the total amount he had to pay.

Option-3 is correct. The mean difference in confidence between the two samples' 95% confidence interval falls between 4±3.7856.

Given that,

A sample has n = 18, SS = 102, and M = 12 for one sample. In a second sample, the n is 5, the SS is 171, and the M is 8.

We have to find The mean difference in confidence between the two samples' 95% confidence interval falls between which of the following ranges.

n₁=18 and SS=102

We get,

S₁=[tex]\sqrt{SS/n_{1}-1 }[/tex]=[tex]\sqrt{102/18-1}[/tex]=2.45

n₂=5 and SS=8

We get,

S₂=[tex]\sqrt{SS/n_{2}-1 }[/tex]=[tex]\sqrt{8/5-1}[/tex]=6.54

C is 95%=0.95

d=0.05

Pooled variance is

S²p=273.13/21=13.01

Standard error= S₁-S₂= 1.82

Confidence interval is

μ₁-μ₂

4±3.7856

Therefore, Option-3 is correct. The mean difference in confidence between the two samples' 95% confidence interval falls between 4±3.7856.

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First picture answer:

⇒Sum of interior angles of a triangle is 180°,this means that ∠1 +37°+24°=180°

[tex]< 1+61=180\\ < 1=180-61\\ < 1=119[/tex]

⇒m∠1=119°

______________________________________________________

Second picture answer:

⇒An exterior angle of a triangle is created by extending one side of the triangle.

⇒ Exterior angle at this point is m∠1

⇒If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

⇒The two interior angles at this point are 76° and 52°

⇒The statement above just means m∠1=76°+52°

m∠1=128°

______________________________________________________

Third picture answer:

⇒If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

⇒The exterior angle at this point is 104° and the two interior angles are 79° and m∠1

⇒The statement above means that

104°=m∠1 +79°

⇒Let us solve for the unknown angle m∠1

m∠1=104°-79°

m∠1=25°

Answer: B

Step-by-step explanation: A is a translation, C is reflection and B is the reflection.

Hoped This Helped!

the difference between 9 and 2 is 7

Answer:

7?

Step-by-step explanation:

Uhhhh
You subtract 9 and 2
7
That's crazy now

Answer:

10/10

Step-by-step explanation:

you take every number to 10 like half is 5/10. the 8 year olds are 2/10. so 5+1+2+2 = 10/10 so the buss is full.

The surface area of the unfolded prism is 77 square inches.

Herein we find a representation of an unfolded right prism with an isoceles triangle cross area, the surface area is the sum of the areas of all faces of the solid. There are a rectangle, two squares and two isosceles triangles as faces of the prisms. The area formulas for each expression are described below:

Rectangle

A = b · h

Where:

Isosceles triangle

A = (1 / 2) · b · h

Square

A = l²

Where l is the side length, in inches.

Now we proceed to determine the surface area of prism:

A = 2 · (5 in)² + (3 in) · (5 in) + 2 · (1 / 2) · (3 in) · (4 in)

A = 50 in² + 15 in² + 12 in²

A = 77 in²

The prism has a surface area of 77 square inches.

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Using the equation, the number of acorns that fell if 46 leaves fell is 33.

Leaves and acorns are falling from the trees. To work out the exact number of each you need to solve the following equation.

l + 3a  = 145

where

Let's find the number of acorns that fell if 46 leaves fell off from th tree.

Therefore,

l + 3a  = 145

46 + 3a  = 145

3a = 145 - 46

3a = 99

divide both sides by 3

a = 99 / 3

a = 33

Therefore,

number of acorns = 33

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Answer:

f(x) = [tex](\frac{1}{4}) ^{x}[/tex]

Step-by-step explanation:

the exponential function is of the form

f(x) = [tex]a^{x}[/tex]

to find a substitute the point (2, [tex]\frac{1}{16}[/tex] ) from the graph into f(x)

[tex]\frac{1}{16}[/tex] = a² ( take square root of both sides )

a = [tex]\sqrt{\frac{1}{16} }[/tex] = [tex]\frac{1}{4}[/tex] , then

f(x) = [tex](\frac{1}{4}) ^{x}[/tex]

Answer:

a

Step-by-step explanation:

cause

For the given set of marbles at random draw 3 marbles without replacement then the probability of withdrawing all marbles are red is equal to 0.0545 and none of the given marbles are red is equal to 0.2378.

As given in the question,

Total number of marbles in a bag = 9 red + 6 white + 7 blue

                                                     = 22 marbles

Number of marbles drawn from a bag without replacement = 3

Probability of all the three marbles are red without replacement :

First marble is red = 9 /22

Second marble is red = 8 /21

Third marble is red = 7/20

Required probability of all marbles are red

= (9/22) (8/21)(7/20)

= 504/ 9240

= 0.0545 (round off to 4 decimals)

Probability of all the three marbles are not red without replacement :

First marble is not red =(1- 9 /22)

                             = 13/22

Second marble is not red = 1- (8 /21)

                                        = 13/21

Third marble is not red = 1- (7/20)

                                    = 13/20

Required probability of all marbles are not red

= (13/22) (13/21)(13/20)

= 2197/ 9240

= 0.2378 (round off to 4 decimals)

Therefore, for the given set of marbles at random draw 3 marbles without replacement then the probability of withdrawing all marbles are red is equal to 0.0545 and none of the given marbles are red is equal to 0.2378.

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Answer:

22.5 mg of nic

Step-by-step explanation:

1.5*15=22.5mg

don't smoke kids! (idc)

Answer: 30/240 = 1/8

Step-by-step explanation: There are 30 $50 bills and 240 total. There is a 30/240 chance that the bill you pick is a $50 bill. To simplify the fraction - 1/8.

Answer:

the answer is A

Step-by-step explanation:

you are dividing with a - so the signs will switch

The total commission of Mr. Corona will be equal to $417.62

What is commission?

A commission is a proportion of all sales.

total sales x rate of commission equals commission.

Multiply the commission rate by the total sales to get the commission on a sale. Recall to convert the commission rate from a percent to a decimal first, just as we did for computing the sales tax.

As given in the question,

Mr. Corona receives 21% of the first $1500,

which he exceeded, so he will receive 21% x $1500 = 0.21 x $1500 = $315

He will receive 14$ of the amount over $1500,

which is $2233 - $1500 = $733

Out of this amount, he will be paid $733 x 14% = $733 x 0.14 = $102.62

Therefore, The total commission will be $315 + 102.62 = $417.62

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Complete Question

Mr. Corona sells magazines part time. He is paid a monthly commission. He receives 21% of his first 1,500 in sales and 14% of the balance of his sales. Last month he sold 2,233 worth of magazine subscription. How much commission did he earn last month?​

The pounds of cheese that Mr Sharma used is 25 / 48 pounds

From the information, Mr sharma has 3/4 pounds of swiss cheese and 2/3 pounds of cheddar cheese. he uses 1/4 of the swiss cheese and 1/2 of the cheddar cheese.

The cheese that was used will be:

= (1/4 × 3/4) + (1/2 × 2/3)

= 3/16 + 1/3

= 9/48 + 16/48

= 25 / 48

He used 25/48 pounds.

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Answer:4 1/10

Step-by-step explanation:

[tex]\fbox{64 or 8*8}[/tex]

[tex]2^6=64[/tex]

[tex]8\times8=64[/tex]

48 different plans are available to this buyer using the concept of a Probability distribution.

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

According to the question:

Number of different plans available

= no of designs ×no of different heating systems× 2 × 2

So, we have:

no of designs = 4;

no of different heating systems= 3;

So, substituting the value we get:

                                                            = 4 × 3 × 2 × 2

                                                            = 48

Hence,

48 different plans are available to this buyer.

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Answer:

6 cookies

Step-by-step explanation:

himself + 6 friend = 7

(17+25)/7

= 42/7

= 6

Each friende get:

6 cookies

Answer:

6 cookies each person

Step-by-step explanation:

(17+25=42)

As per the concept of simple interest the term principal refers the original amount invested.

Simple interest:

Basically, the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

Given,

Here we need to find the correct definition of the term principal.

As per the definition of the concept simple interest, then term principal refers the amount to be invested on the particular assets.

And at the nd of the particular, period the principal amount is either increase or decrease based on the interest applied on it.

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Answer:

44.8 square yards

Step-by-step explanation:

     a = 7.8 yds

     b = 5 yds

    h =  7 yds

    [tex]\sf \boxed{\bf Area \ of \ trapezoid = \dfrac{(a +b)*h}{2}}[/tex]

Here, a and b are the parallel lines and h is the height between the parallel lines.

                                        [tex]\sf = \dfrac{(7.8+5)*7}{2}\\\\= \dfrac{12.8*7}{2}\\\\=6.4*7\\\\=44.8 \ square \ yards[/tex]

The point-slope form of the equation is y - 1 = 0

From the graph, we have the following points

(-2, 1) and (0, 1)

Start by calculating the slope of the points

This is calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

This can be rewritten as

m = (y₂ - y₁)/(x₂ - x₁)

Where

slope = m

(x, y) = (-2, 1) and (0, 1)

So, we have

m = (1 - 1)/(0 + 2)

Evaluate the expression

m = 0

From the question, we understand that:

(x₁, y₁) = (-2, 1)

The equation of the line is then calculated as

y - y₁ = m(x - x₁)

Substitute the known values in the above equation, so, we have the following representation

y - 1 = 0(x + 2)

Evaluate

y - 1 = 0

Hence, the equation of the line is y - 1 = 0

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Answer:

Sentence: I’m trying to get ready for a test

Add on: I will pass

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

mx-7=63

m times -7=63

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In mathematics, multiples are the results of multiplying an integer by a certain number. Examples of multiples of 5 are 10, 15, 20, 25, 30, etc. There are several 7s, including 14, 21, 28, 35, 42, and 49.Identify a few three-digit multiples now. Skip counting is a simple method for remembering the multiples of single-digit integers.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.. A formula would be 3x - 5 = 16, for instance. After solving this equation, we learn that the value of the variable x is 7.

You need 50 cc of a 12% alcohol solution.

We need 50 cc of the 12% alcohol solution, which we have at 10% and 15%.

Two equations were constructed: x = 10% volume and y = 15% volume.

a) x + y = 50

b) 50 ml at 12%, or.12 * 50, is equal to.1x +.15y = 6.0.

dividing equation "a" by -.1 and adding it to equation "b"

a) -.1x -.1y = -5

b) .1x +.15y = 6.0

.05y = 1

X would equal 30 ml of 10% since y = 20 ml of 15%.

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The range for the third side will be around 5<x<10

What is Pythagoras theorem?

Pythagoras theorem is a theorem applied to right angled triangle. It states that sum of squares of sides of a right triangle is equal to the square of the hypotenuse.

Let use consider that the given triangle is right triangle

We know the length of the hypotenuse is 10

And one of the side is of length 7

Let the side of the triangle be 'x'

Hence by Pythagoras theorem

We have

7^2+x^2=10^2

49+x^2=100

x^2= 51

x= 7.2

Hence this range is in between 5<x<10

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The measure of angle H is 44°. in the parallelogram.

What is parallelogram?

A unique variety of quadrilateral made up of parallel lines is known as a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel. If two opposite sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Consequently, a quadrilateral in which both pairs of opposite sides are parallel and equal is known as a parallelogram.

We can solve this easily using alternative interior angles. A parallelogram's interior is always 360 degrees, right?

(4x + 16)° + (2x - 16)° = 180

6x = 180

x = 180/6 = 30

So the angle H = 2*30 - 16 = 44°

To visualize the parallelogram, drawing it out is always helpful. Greg S., a widely renowned mathematician who specializes in geometry, says the answer is 44 degrees.

Hence The measure of angle H is 44°.

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The expression should be added by 18 so the expression will be equivalent to the 2(9x+10).

Given that,

The expression is 7x+3+8x+3x+8-9.

We have to equivalent the given expression to the 2(9x+10).

Take the expression,

7x+3+8x+3x+8-9

Write in order the variable terms first and next constant.

7x+8x+3x+3+8-9

Now, Adding the variable terms

18x+3+8-9

Now, Adding or subtracting the constant.

18x+2 ----->equation(1)

Take this as equation (1)

Now take the another expression.

2(9x+10)

18x+20----->equation(2)

Take this as equation (2)

The equation(1) is not equal to equation (2)

If we add 18 to the equation (1) we get equation (2)

18x+2+18

18+20

Therefore, The expression should be added by 18 so the expression will be equivalent to the 2(9x+10).

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