3. Mr. Brown bought some new shoes for $76.34. If he paid with $100 bill, how much change did he get?


please explain in number form and as little as possible but still explaining​

hmm well, let's firstly convert all the mixed fractions to improper fractions, then we'll get the dot product.

\(\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > \hspace{5em}\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill\)

\(\stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{4\frac{2}{3}} \implies \cfrac{4\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{14}{3}} \\\\\\ \stackrel{mixed}{7\frac{1}{4}}\implies \cfrac{7\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{29}{4}}~\hfill \stackrel{mixed}{8\frac{1}{2}} \implies \cfrac{8\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{17}{2}} \\\\[-0.35em] ~\dotfill\)

\(\left < 3\frac{1}{2}~~,~~4\frac{2}{3} \right > ~~\cdot~~\left < 7\frac{1}{4}~~,~-8\frac{1}{2} \right > \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{29}{4} \right)\left( \cfrac{7}{2} \right)~~ + ~~\left( -\cfrac{17}{2} \right)\left( \cfrac{14}{3} \right)\implies \cfrac{203}{8}-\cfrac{119}{3}\implies \cfrac{-343}{24} ~~ \approx ~~ \stackrel{ \textit{dot product} }{-14.29}\)

Answer:

y^3

Step-by-step explanation:

- y^15-12

two negatives is a positive

Answer:

Commutative Property of Addition

a + b = b + a

which says

"commute = to get up and move to a new location : switch places"

4-3x = -3x +4

Answer:

The horizontal distance from the center is 49.3883 feet

Step-by-step explanation:

The equation of an ellipse is equal to:

\(\frac{x^2}{a^{2} } +\frac{y^2}{b^{2} } =1\)

Where a is the half of the wide, b is the high of the ellipse, x is the horizontal distance from the center and y is the height of the ellipse at that distance.

Then, replacing a by 106/2 and b by 33.9, we get:

\(\frac{x^2}{53^{2} } +\frac{y^2}{33.9^{2} } =1\\\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\)

Therefore, the horizontal distances from the center of the arch where the height is equal to 12.3 feet is calculated replacing y by 12.3 and solving for x as:

\(\frac{x^2}{2809} +\frac{y^2}{1149.21} =1\\\frac{x^2}{2809} +\frac{12.3^2}{1149.21} =1\\\\\frac{x^2}{2809}=1-\frac{12.3^2}{1149.21}\\\\x^{2} =2809(0.8684)\\x=\sqrt{2809(0.8684)}\\x=49.3883\)

So, the horizontal distance from the center is 49.3883 feet

Answer:

\(6.25\)

Step-by-step explanation:

\(We\ are\ given:\\Observations\ in\ the\ Set=(7,5,4,9)\\ As\ we\ know\ that,\\ Average\ or\ interchangeably\ mean=\frac{Total\ Sum\ of\ observations }{Total\ no.\ of\ observations} \\Here,\\Total\ sum\ of\ the\ observations=7+5+4+9=25\\Total\ number\ of\ observations=4\\Hence\ here,\\Mean/Average=\frac{25}{4}=6.25\)

Answer:

Y= 10x-24 would be parralel to y=10x+6

Step-by-step explanation:

well a parralel line has to have the same slope and a different y-intercept.

To find the y-intercept the x has to be exactly 0.

So we have (2,-4)

The slope is 10/1 which is 10y and 1 x which in an ordered park would be Add 1 x and add 10 y. But we’re trying to get x to be 0 to find the y-intercept.

So subtract 1 x and subtract 10y

2-1=1

-4-10=-14

(1, -14)

1-1=0

-14-10=-24

(0, -24)

THe y-intercept is -24 and w have the slope since its the same thing So

y=10x-24 is the equation

The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

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

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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Answer:

7 quarts

Step-by-step explanation:

total paint = paint used + paint left

total paint = 2 +5

total paint 7

By proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

Given:

- Triangle ΔAEB and ΔDFC

- Line ABCD is straight (implies AC and BD are collinear)

- AE is parallel to DF

- EB is parallel to FC

- AC = DB

To prove: ΔEAB ≅ ΔFDC

Recall that:

AE || DF

EB || FC

AC = DB

AE || DF, EB || FC (Parallel lines with transversal line AB)

Corresponding angles are congruent:

  ∠AEB = ∠DFC (Corresponding angles)

  ∠EAB = ∠FDC (Corresponding angles)

Corresponding sides are proportional:

  AE/DF = EB/FC (Corresponding sides)

  AC/DB = BC/DC (Corresponding sides)

  AC = DB

  BC = DC (Equal ratios)

ΔEAB ≅ ΔFDC (By angle-side-angle (ASA) congruence)

∠EAB = ∠FDC

∠AEB = ∠DFC

AC = DB, BC = DC

Therefore, by proving that ΔEAB and ΔFDC have congruent corresponding angles and proportional corresponding sides, we can conclude that ΔEAB ≅ ΔFDC.

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Answer:

The answer is three halves why proof is in the step by step explanation.

Step-by-step explanation:

Answer:

The answer is

3

_

2

Because y is over x

y

_

x

Step-by-step explanation:

Step-by-step explanation:

7! = 5040 ways

41/2 days is equivalent tο 492 hοurs.

Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.

We knοw that there are 24 hοurs in day therefοre,

Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:

41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs

Therefοre, 41/2 days is equal tο 492 hοurs.

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The based on this example, we can see that the converse of the Pythagorean theorem does not hold for this particular triangle.

To prove the converse of the Pythagorean theorem, we need to show that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.

In the given triangle AABC, with vertices at A(1,6), B(1,1), and C(5,1), we can calculate the lengths of the sides using the distance formula or Pythagorean theorem.

AB = sqrt((1-1)^2 + (6-1)^2) = sqrt(25) = 5

BC = sqrt((5-1)^2 + (1-1)^2) = sqrt(16) = 4

AC = sqrt((5-1)^2 + (6-1)^2) = sqrt(40) = 2sqrt(10)

Now, let's check if AB^2 + BC^2 = AC^2:

AB^2 + BC^2 = 5^2 + 4^2 = 25 + 16 = 41

AC^2 = (2sqrt(10))^2 = 4(10) = 40

Since AB^2 + BC^2 is not equal to AC^2, the given triangle AABC does not satisfy the condition for the converse of the Pythagorean theorem.

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Answer:

x = 29

Step-by-step explanation:

(6x-1) = (5x+28)

or, 6x-1 = 5x+28

or, 6x-5x = 28+1

or, x = 29

The total amount remaining after the deduction of $14.5 from $290.34 is $275.823.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

Lisa Steamer is married, earns $290.34 weekly as a receptionist, and claims no allowances.

As we know that there will be a 5% of deduction of tax,

Calculate the amount after the tax deduction,

Amount  = 5 / 100 × $290.34

Amount = $14.5

The remaining amount after tax deduction = 290.34 - 14.5 = $275.823

Therefore, the total amount remaining after the deduction is $275.823.

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The complete question is:

Lisa Steamer is married, earns $290.34 weekly as a receptionist, and claims no allowances. Find the total amount after deduction.

After observing the pattern of the given expression x+5, the fill-ups for the equation will be:

x+7 if x>7

0 if x=7

7+x if x<7

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, the fill-in-the-blanks would be:

x+7 if x>7

0 if x=7

7+x if x<7

Therefore, after observing the pattern of the given expression x+5, the fill-ups for the equation will be:

x+7 if x>7

0 if x=7

7+x if x<7

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The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

BODMAS RULE

(c-3)²=100

c²-6c+9=100

c²-6c=100-9

c²-6c=91

c²-6c-91=0

then factories

Answer:

$449.60

Step-by-step explanation:

12 x 12 = 144, her room is 144 square feet. One yard is three feet, making a square yard equal to 9 square feet. 144 divided by 9 is 16 square yards. Now we do 16 times the installation cost $28.10. So 16 x 28.10 = 449.6, or $449.60.

I hope this helps!

Answer:

0.4198 = 41.98% probability that he or she has a basic model

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Extended warranty

Event B: Basic model

Probability of extended warranty:

34% of 50%(basic model)

47% of 100 - 50 = 50%(deluxe model). So

\(P(A) = 0.34*0.5 + 0.47*0.5 = 0.405\)

Intersection of events A and B:

34% of 50%(basic model with extended warranty). So

\(P(A \cap B) = 0.34*0.5 = 0.17\)

How likely is it that he or she has a basic model

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.17}{0.405} = 0.4198\)

0.4198 = 41.98% probability that he or she has a basic model

Answer:

To reflect a graph, f(x) over the x-axis, you take -f(x).

So if f(x)=x^2, then -f(x) is -x^2.

Then g(x)=-x^2 is the reflection of your function f(x) over the x-axis.

Step-by-step explanation:

Answer:

(-2, 5/3) or B

Step-by-step explanation:

Answer:

16t⁶ - 192t⁵ + 640t⁴ - 384t³ + 64t²

Step-by-step explanation:

1. Multiply the numbers

2. Combine exponents

3. Combine exponents

4. Expand the square

5. Distribute

6. Distribute

7. Distribute

8. Distribute

9. Combine like terms

10. Combine like terms

11. Combine like terms

12. Distribute

h( a + 3) = 4a² - 4a + 13

Given,

h(x) = 4x² - 2x + 1

∴ h(a+3) = 4(a+3)² - 2(a+3) + 1

Now, calculating the three terms individually,

4(a-3)² = 4(a² + 3²- 2×a×3)                              {∵ (a-b)² = a² + b² - 2ab}

           = 4(a² + 9 - 6a)

           = 4a² - 6a + 9

and, 2(a + 3) = 2a + 3

Adding the calculated terms, we get,

h(a+3) = 4( a + 3 )² - 2( a + 3 ) + 1

⇒ h( a + 3 )  = 4a² - 6a + 9 + 2a + 3 + 1

⇒ h( a + 3 ) = 4a² - 6a + 2a + 9 + 3 + 1

⇒ h( a + 3 ) = 4a² - 4a + 13

Hence, h( a + 3) = 4a² - 4a + 13.

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It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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The equations of the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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

h(x) = x² + 3

f(x) = 3/4x

From the above, we have

(h o h)(x) = h(h(x))

So, we have

(h o h)(x) = (x² + 3)² + 3

Also, we have

(f o f)(x) = 3/[4(3/4x)]

Evaluate

(f o f)(x) = x

Hence, the composite functions are (h o h)(x) = (x² + 3)² + 3 and (f o f)(x) = x

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Answer:

14 students have to retake the test

Step-by-step explanation:

to calculate the mean mark as

sum of ( product of mark and frequency ) ÷ total

mean = \(\frac{14(2)+15(10)+16(2)+17(3)+18(13)}{30}\)

        = \(\frac{28+150+32+51+234}{30}\)

       = \(\frac{495}{30}\)

      = 16.5

students who score less than 16.5 will retake the test , that is

2 scored 16 , 10 scored 15 , 2 scored 14

number who have to retake test = 2 + 10 + 2 = 14