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Evaluate the expression - + y for x=24 and y=17.

42
21
20
41
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Answer:

Step-by-step explanation:

1½ m = 1.5 m

¾ m = 0.75 m

area of rectangle = 1.5×0.75 = 1.125 m²

Each piece is half the rectangle. Area of one piece = 0.5625 m²

Answer:

B) \(4i\sqrt{2}\)

Step-by-step explanation:

\(\sqrt{-2}=i\sqrt{2}\\\sqrt{-18}=i\sqrt{18}=i\sqrt{9*2}=3i\sqrt{2}\\\\\sqrt{-2}+\sqrt{-18}=i\sqrt{2}+3i\sqrt{2}=4i\sqrt{2}\)

Answer:

270

Step-by-step explanation:

15x18

(A)  The system of equations is,

6A + 3S = $51          

9A + 6S = $90    

(B) The price of one adult ticket is $4 and the price of one student ticket is $9.

What is system of equations?

A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.

Given:

Juan's school is selling tickets to the annual talent show.

On the first day of ticket sales the school sold 6 adult tickets and 3 student tickets for a total of $51.

The school took in $90 on the second day by selling 9 adult tickets and 6 student tickets.

Let A be the number of adult tickets sold.

S be the number of students ticket sold.

⇒ 6A + 3S = $51            ..(1)

9A + 6S = $90              ..(2)

Multiply first equation by (2)

12A + 6S = $102            ..(3)

Subtract equation (2) and (3)

   12A + 6S = $102

-   9A + 6S = $90

________________

   3A        = 12

⇒ A = $4

Plug A = 4 in equation (1)

6(4) + 3S = $51

24 + 3S = $51

3S = $51 - $24

3S = $27

S = $9

Hence,

(A)  The system of equations is,

6A + 3S = $51          

9A + 6S = $90    

(B) The price of one adult ticket is $4 and the price of one student ticket is $9.

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Because the graph only intercepts the x-axis only once, the equation has only one solution. The correct option is the second one.

Here we want to see, based on a graph, how many solutions does the cubic equation:

x³ + 6x² + 12x +8 = 0

The graph of the function:

g(x) = x³ + 6x² + 12x +8

Can be seen below, the number of real solutions that the equation:

x³ + 6x² + 12x +8 = 0

has, will depend on how many times the graph intercepts the x-axis.

We can see that there is only one intercept, so there is one real solution.

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The equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6

The coordinates of the point = (-7, -4)

The slope of the line = 10/7

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

The point slope form is

\(y-y_1=m(x-x_1)\)

Where \((x_1,y_1)\) is the coordinates of the point

Substitute the values in the equation

y -(-4) = 10/7(x - (-7))

y + 4 = (10/7)(x + 7)

Convert to slope intercept form

y +4 = (10/7)x + 10

y = (10/7)x + 10 - 4

y = (10/7)x + 6

Hence, the equation of the line that passes through the point (−7,−4) with slope 10/7 is y = (10/7)x + 6

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Answer:

A college student makes a deal with her parents to live at home instead of living on campus. She will pay her parents $0.01

Step-by-step explanation:

Answer:

$1010.33 is the net income

Step-by-step explanation:

1) multiply: $12.50(20 hrs)= $220 per week

2)multiply: $220 (52 wks)= $$11,440 yr

3) then divide: 11,440 yr/ 12mo+$953.33 mo

4) multiply: $953.33 mo (.85)= $810.33 net

5) then add: $810.33 net+100 (withdraws) +$100.00(Parents)=$1,010.33 net income

Answer:

525

Step-by-step explanation:

This is a question involving combinatorics

The number of ways of choosing a subset k from a set of n elements is given by \({n \choose k}\) which evaluates to \(\frac{n!}{k!(n-k)!}\)

n! is the product n × (n-1) × (n-2) x....x 3 x 2 x 1

For example,

4! = 4 x 3 x 2 x 1 = 24

3! = 3 x 2 x 1 = 6

Since we have to choose 4 boys from a class of 6 boys, the total number of ways this can be done is

\({6 \choose 4} = \frac{6!}{4!(6-4)!} = \frac{6!}{4!2!}\)

Note that 6! = 6 x 5 x 4 x 3 x 2 x 1 and 4 x 3 x 2 x 1  is nothing but 4!

So the numerator can be re-written as 6 x 5 x (4!)

We can rewrite the expression \(\frac{6!}{4!2!} \text{ as } \frac{6.5.4!}{4!2!}\)

Cancelling 4! from both numerator and denominator gives us the result

as  (6 × 5)/2! = 20/2 = 15 different ways of choosing 4 boys from a class of 6 boys

For the girls, the number of ways of choosing 3 girls from a class of 7 girls is given by

\({7 \choose 3} = \frac{7!}{3!(7-3)!} = \frac{7!}{3!4!}\)

This works out to (7 x 6 x 5 )/(3 x 2 x 1)  (using the same logic as for the boys computation)

= 210/6 = 35

So total number of committees of 4 boys and 3 girls that can be formed from a class of 6 boys and 7 girls = 15 x 35 = 525

Answer:

Step-by-step explanation:

If the diameter increases by 10%,

new diameter = d+⅒ = 1.1d

also new radius = 0.55r

Height also increasesby 10%,

New height = h+⅒h = 1.1h

hence diameter of larger can =

π*(0.55)²*1.1= 1.0453

hence percentage change in volume

is 4.53% which can be rounded off to

Answer:

the relation between the x-values and y-values of ordered pairs

Answer:

c) 6× (9+8) = (6 × 9) + (6× 8)

Step-by-step explanation:

Distributive property of multiplication

The distributive property of multiplication

a(b+c) = a b + a c

(a+b)c = ac + bc

6× (9+8)  = (6× 9) + (6×8)

if the area of a circle is 36.2 square inches, the radius of the circle to the nearest tenth is 3.4 inches.

The area of a circle is 36.2 square inches and we have to determine the radius of the circle to the nearest tenth.

The formula of the area of the circle is given as:

Area of circle = πR², where R is the radius of the circle.

We are given, Area of the circle = 36.2 square inches

So, πR² = 36.2 square inches

Now, π = 3.14

3.14R² = 36.2 square inches

R² = 36.2/3.14

R² = 11.53

Taking square root on both sides

R = √11.53

R = 3.39 inches

R ≈ 3.4 inch (Rounded to the nearest tenth)

Hence, the radius of the circle to the nearest tenth is 3.4 inches.

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Answer:

B. Researchers working for a company test their new sneaker design to see if it helps athletes run faster.

Step-by-step explanation:

The researchers are testing a hypothesis, and they are also in control of certain variables, they're not just observing like C.

Objects commonly found in a locality include residential buildings, commercial establishments, public facilities, transportation infrastructure, landmarks, natural features, utilities, street furniture, and vehicles.

The type of objects that can be found in a locality can vary greatly depending on the specific location and its surroundings. Here are some common types of objects that can be found in a locality:

Residential Buildings: Houses, apartments, condominiums, and other types of residential structures are commonly found in localities where people live.

Commercial Establishments: Localities often have various types of commercial establishments such as stores, shops, restaurants, cafes, banks, offices, and shopping centers.

Public Facilities: Localities typically have public facilities such as schools, libraries, hospitals, community centers, parks, playgrounds, and sports facilities.

Transportation Infrastructure: Localities usually have roads, sidewalks, bridges, and public transportation systems like bus stops or train stations.

Landmarks and Monuments: Some localities may have landmarks, historical sites, monuments, or cultural attractions that represent the area's heritage or significance.

Natural Features: Depending on the locality's geographical characteristics, natural features like parks, lakes, rivers, mountains, forests, or beaches can be present.

Utilities: Localities have infrastructure for utilities such as water supply systems, electrical grids, sewage systems, and telecommunications networks.

Street Furniture: Localities often have street furniture like benches, streetlights, waste bins, traffic signs, and public art installations.

Vehicles: Various types of vehicles can be found in a locality, including cars, bicycles, motorcycles, buses, trucks, and possibly other modes of transportation.

It's important to note that the objects present in a locality can significantly differ based on factors such as urban or rural setting, cultural context, economic development, and geographical location.

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Answer:

Option B

\(A'(5,5)\)

\(B'(5,1)\)

\(C'(2,1)\)

\(D'(1,5)\)

\(----------\)

hope it helps...

have a great day!!

D 231 = 46w can be used to solve for w, the number of white eggs used last week.

Answer: 3m = 120, 40 minutes

Step-by-step explanation:

3m = 120 (since she works out 3 times a week for a total of 120 minutes)

to solve, divide both sides by 3

m = 40

The sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

To translate the inequality expression "2/3y - 9 < y + 1" into a sentence, we can break it down into smaller parts:

"2/3y" represents two-thirds of a number.

"9" represents the number nine.

"y + 1" represents the number increased by one.

Now let's construct the sentence:

"Nine less than two-thirds of a number" - This refers to the expression "2/3y - 9," indicating that we have subtracted nine from two-thirds of a number.

"is less than" - This is the comparison symbol in the inequality.

"the number" - This refers to the expression "y + 1," representing the number increased by one.

Combining these parts, we form the sentence: "Nine less than two-thirds of a number is less than the number."

Hence, the correct sentence translation of "2/3y - 9 < y + 1" is "Nine less than two-thirds of a number is less than the number."

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Using simple interest, it is found that the principal loan amount was of $156,491.6.

The amount of money after t years in simple interest is modeled by:

\(A(t) = A(0)(1 + rt)\)

In which:

In this problem, she paid $984 monthly for 22 years, hence:

\(t = 22, A(t) = 984(22)(12) = 259776\)

Interest rate of 3%, hence \(r = 0.03\)

Then:

\(A(t) = A(0)(1 + rt)\)

\(259776 = A(0)[1 + 0.03(22)]\)

\(A(0) = \frac{259776}{1 + 0.03(22)}\)

\(A(0) = 156491.6\)

The principal loan amount was of $156,491.6.

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For the given number 4 x 5³/₈. The whole part is 4 and the fraction part is 5³/₈. Both are added together to form a fraction of 43/8.

An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that.

For the given number 4 x 5³/₈.

The whole part is 4.

The fraction part is 5³/₈.

Solving the mixed fraction:

= 5³/₈.

= (5*8 + 3) /8

Both are added together to form a fraction:

= 43/8

The final number becomes:

= 4 x 5³/₈

= 4 x 43/8

= 43/2

Thus, the result of the final number obtained is 43/2.

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The recursive relation of the data distribution a(n) = a ( n - 1 ) x n - ( n - 1 ).

A sequence of values is defined by a mathematical equation termed as a recursive relation, also known as recursive relation. It derives current value(s) through specified initial value(s) and previous value dependent rule(s). In essence, it generates numeric sequences.

Note that every individual unit can be derived by multiplying the preceding one with a rising integer, and subsequently subtracting a descending integer:

1 x 1 - 0 = 1

1 x 2 - 1 = 1

1 x 3 - 2 = 5

5 x 4 - 3 = 17

17 x  5 - 4 = 71

71 x 6 - 5 = 247

We can deduce the relation of a(n) = a ( n - 1 ) x n - ( n - 1 ).

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Answer: 90.93%

Step-by-step explanation:

M= 372

s= 26

n=36

P(365<x<380)

1. Find Z ----> 365-372 \(\sqrt{36}\) = -1.6     Next Z---->  380 - 372 \(\sqrt{36}\)=  1.8

                           26                                               26

2.  plug into calculator to find probablity: normalcdf(-1.6 , 1.8 ) = .90927 or 90.93% that the prob is between 365 and 380

Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

your answer is 3.375

Answer:

26 years old

Step-by-step explanation:

The equation is proved.

G\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`\)

We need to prove the given equation. Solution: Using the identity \(`sin2x=2sinxcosx` and `cos2x=1-2sin^2x`\)

in the given equation, we get

\(`tan(x-1)(sin2x-2cos2x)=2(1-2sinxcosx)`⟹ `tan(x-1)(2sinxcosx-2(1-\)

\(2sin^2x))=2(1-2sinxcosx)`⟹ `tan(x-1)(4sin^2x-2)=2-4sinxcosx`⟹ `2sin(x-1)\)

\((2sin^2x-1)=2(1-2sinxcosx)`⟹ `2sin(x-1)(2sin^2x-1)=2(1-2sinxcosx)`⟹\)

\(`2sinxcos(x-1)(4sin^2x-2)=2(1-2sinxcosx)`⟹ `2sinxcos(x-1)(2sin^2x-1)=1-\)

\(sinxcosx`⟹ `2sinxcos(x-1)(2sin^2x-1)=sin^2x+cos^2x-sinxcosx`⟹\)

`\(2sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-cosx)^2/2`\)

For `LHS`, using identity

\(`sin(90 - x) = cosx`⟹ `sinxcos(x-1)(2sin^2x-1)=(sinx-sin(91-x))^2/2`⟹\)

\(`sinxcos(x-1)(2sin^2x-1)=(-sin(x-1))^2/2`⟹ `sinxcos(x-1)(2sin^2x-1)=sin^2(x-\)

\(1)/2`⟹ `sinxcos(x-1)(4sin^2x-2)=sin^2(x-1)`⟹ `sinxcos(x-1)(2sin^2x-1)=1/2`⟹ `1/2=1/2`.\)

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Answer:

0.000004 = 0.0004% probability of getting 7 or fewer minorities if the jury pool was randomly selected.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either it was a minority, or it was not. The probability of a person being a minority is independent of any other person. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Jury of 90 people:

This means that \(n = 90\)

27% were minorities.

This means that \(p = 0.27\)

Find the probability of getting 7 or fewer minorities if the jury pool was randomly selected.

This is:

\(P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)\)

In which

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{90,0}.(0.27)^{0}.(0.73)^{90} \approx 0\)

\(P(X = 1) = C_{90,1}.(0.27)^{1}.(0.73)^{89} \approx 0\)

\(P(X = 2) = C_{90,2}.(0.27)^{2}.(0.73)^{88} \approx 0\)

\(P(X = 3) = C_{90,3}.(0.27)^{3}.(0.73)^{87} \approx 0\)

\(P(X = 4) = C_{90,4}.(0.27)^{4}.(0.73)^{86} \approx 0\)

\(P(X = 5) = C_{90,5}.(0.27)^{5}.(0.73)^{85} \approx 0\)

\(P(X = 6) = C_{90,6}.(0.27)^{6}.(0.73)^{84} \approx 0\)

\(P(X = 7) = C_{90,7}.(0.27)^{7}.(0.73)^{83} = 0.000004\)

So

\(P(X \leq 7) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 7*0 + 0.000004\)

0.000004 = 0.0004% probability of getting 7 or fewer minorities if the jury pool was randomly selected.

Answer:

60

Step-by-step explanation:

\(a+b+c=180\\\frac{b+c}{2}=a \rightarrow b+c=2a\\\\a+2a=180\\3a=180\\a=60\)

Therefore, the value of a is 60 degrees