Cooper and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 10 apples and bananas altogether. Determine the number of apples, x, and the number of bananas, y, that Cooper bought.

Since equations are expressed as "y=," you can solve for X by setting the equations equal to one another. This is effective because, if two equations have the same unknown y value, then they must also have the same unknown y value.

Imagine that you are tasked with resolving the equations y = 2x + 3, and y = 4x + 1. You can write: 2x + 1 = 4x + 3 since y represents the same number in both equations, proving that both equations must be equal. If this is still unclear, consider y to be a number, let's say 5. Since both equal 5, if 2x+3=5 and 4x+1=5, then (2x+3) must equal 4. 5. by changing the value of y in the second equation to that determined in the first. You can find X by setting the two equations equal to one another. Referring to the problem 2x+3=4x+1 from earlier, you would first try to obtain all the X terms on one side of the equation, Therefore, take 2X off of both sides. 3=2x+1 will be all that is left. Now take one away from both sides to get your X term alone, giving you 2=2x. Lastly, multiply both sides of the equation by two to arrive at the solution, X=1. You can enter the value of X that you just discovered (X=1) into either of your original equations to solve for Y. As a result, y=2(1)+3 and y=4(1)+1 will both result in y=5, which is the same.

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The volume and the surface area of the right cylinder are equal to 175π cubic inches and 120π square inches.

In order to determine the volume (V) in cubic inches and the surface area (A) in square inches of the solid, we must know the dimensions of a right cylinder, whose height (h) in inches and radius (r) in inches are shown in the figure. Below is a description of the formulas:

Here Volume of the cylinder,

V = π · r² · h

Surface area of the cylinder,

A = 2π · r² + 2π · r · h

If we know that r = 5 in and h = 7 in, then the volume and the surface area of the cylinder are, respectively:

Volume is,

V = π · ( 5 in )² · ( 7 in )

V = 175 π in³

Surface area is,

A = 2π · (5 in)² + 2π · (5 in) · (7 in)

A = 120π in²

Therefore volume and surface area of cylinder is 175 π in³ and 120π in².

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Using Conditional Probability,

the probability that the sum of the numbers appearing on the two dice is 8, if 3 appears on the first is 1/5.

We have given that,

Two dice are thrown. Let S be the sample space S={1,2,3,4,5,6×{1,2,3,4,5,6}

Total number of possible outcomes (n(S)) =36

Let A ≡ the event that the sum of the numbers coming up is 8

and B ≡ the event of occurrence of 3 on the first die.

A ≡{(3,5),(6,2),(4,4),(5,3),(2,6)}

favourable cases for A (n(A) )= 5

B≡{(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)}

favourable cases for B (n(B)) = 6

Now, A int B = { (3,5 ) } = 1

favourable cases for AnB (n(An B) )= 1

Probability of event A occur (P(A)) = 5/36

Probability of event B occur (P(B)) = 6/36

Probability of event B occur (P(AnB)) = 1/36

we have to calculate probability the sum of the numbers appearing on the two dice is 8, if 3 appears on the first i.e., P(A/B) --> Conditional Probability

Required probability, P(A/B) = P(ANB)/ P(B)

=> P(A/B) = 1/36/5/36 = 1/5

Hence, the required probability is 1/5.

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Using linear functions, the inequality for the times when Valente is closer than Chiamaka to the university is:

170 + 110t < 149 + 95t

What is a linear function?

Linear functions have a straight line as their graph. The following is the form of a linear function. y = f(x) + a+bx There is one independent variable and one dependent variable in a linear function.

Solution:

Considering the initial distance as the intercept and the velocity as the slope, the linear functions for the distances of each Chiamaka and Valente are given as follows:

C(t) = 149 + 95t

V(t) = 170 + 110t

Valente is closer when:

V(t) < C(t)

Hence the inequality is:

170 + 110t < 149 + 95t

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Step-by-step explanation:

A water park water ride pumps 8,000 gallons of water every 2 minutes, How many gallons of water would the ride pump in 100 minutes?

100/2 = 50

50 * 8,000 = 400,000 gallons in 100 minutes

Answer:

400,000 gallons

Step-by-step explanation:

to find the unit rate or how much per minute we divide 8000 by 2

8000/2

4000 gallons per minute

Now multiply by 100

4000*100

400,000

Hopes this helps please mark brainliest

The two areas at the end of a normal curve that indicate low probability values if the null hypothesis is true are called the critical region.

Critical region: A set of values for the test statistic for which the null hypothesis is rejected is referred to as a critical region, also known as the rejection region. Specifically, we accept the alternative hypothesis and reject the null hypothesis if the observed test statistic is within the critical region.

The probability of rejecting H0, or the Null Hypothesis, is represented by the alpha level. The critical region is the set of z values on a graph that result in the null hypothesis being rejected.

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The answer to the poition will be t²/2 which is the displacement of the car.

What is displacement?

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

The given acceleration is given in the function of velocity, v(t) = t

Let, be the function of velocity v(t) and position is x(t).

So the poition will be ∫v(t) dt = ∫t dt

=t²/2

Hence, the position of the given function will be t²/2

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There are a total of 20 * 6 = 120 numerals when  you form a numeral between 300 and 899, inclusive, using only the digits 1, 4, 5, 6, 8, and 9

Two mathematical ideas, permutation and combination, are used to specify the many ways in which items from a set can be chosen, often without replacement, to produce subsets.Combination is the selection , while permutations is the arrangement.For instance, if we have a group of three letters (A, B, C) inclusive, they may be combined to form the combinations ABC, ACB, BAC, BCA, CAB, and CBA. However, the result of these three letters combined would be ABC, AB, AC, BC, BA, CA, CB, and C. Probability, statistics, and computer science are just a few of the disciplines that benefit from permutation and combination.

How to solve?

We can choose 3 of the 6 digits in a total of 6C3 = 20 ways. Once we have chosen the 3 digits, we can arrange them in a total of 3! = 6 ways. Therefore, there are a total of 20 * 6 = 120 numerals.

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Answer:

The factors of 12 are 1, 2, 3, 4, 6, 12

Step-by-step explanation:

Basically what numbers can be multiplied to equal to 12

Example:

1 x 12 = 12

2 x 6 = 12

3 x 4 = 12

It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.  

A quadrilateral that has two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

Here we have proof of Parallelogram

To get correct statement 6 let's rewrite the whole process from the start

Given that GHIK is a parallelogram, m ∠GHJ = 60° and JKL is a line

Here we need to prove m∠LKG = 120°  

   Statement                                  - Reason

1. GHIK is a parallelogram              -  Given  

2. m ∠GHJ = 60°                             -  Given

3. JKL is a line                                 -  Given

4. m ∠JKL = m∠LKG + m∠JKG       -  On line-segment, ∠JKL is equal to the

                                                           the sum of Non-overlapping parts

                                                            m∠LKG and m∠JKG  

5. m ∠JKL = 180°                            - Angle formed by a straight line is 180°  

6. 180°= m∠LKG + 60°                   - In a parallelogram opposite angles are

                                                         equal i.e m∠JKG = m∠GHJ = 60°

7. m∠JKG = m∠GHJ                       - Transitive/ Substitution

9. m∠LKG =  180° - 60°      

10. m∠LKG =  120°                          - from statement 6

Therefore,

It is proven that m∠LKG = 120°, and the corrected statement 6 is In a parallelogram opposite angles are equal i.e m∠JKG = m∠GHJ = 60°.    

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Answer:

32, 39, 46

Step-by-step explanation:

Given sequence:

Work out the differences between the terms:

[tex]4 \underset{+7}{\longrightarrow} 11 \underset{+7}{\longrightarrow} 18 \underset{+7}{\longrightarrow} 25[/tex]

As the difference between each term in the sequence is constant, the sequence is an arithmetic sequence with common difference of 7.

To find the next three terms in the given sequence, simply add 7 to the previous term:

[tex]\implies 25 + 7 = 32[/tex]

[tex]\implies 32 + 7 = 39[/tex]

[tex]\implies 39 + 7 = 46[/tex]

Answer:

Step-by-step explanation:

Next three terms are 32, 39, 46

As the different in all of them is of 7 so we add 7 with each term to get the next terms :)

At random a baby born in the united states in 2014 is 3.

Part - A:

All probabilities are between 0 and 1. The probabilities also add to 1 and therefore account for all possible birth orders (9th or higher birth order being included in the "g" group)

Probability of event - "A woman gives birth in 2014 to her third child":

P(X = 3) = 0.168

Part - B:

P(X ≤ 2) = P(X = 1) + P(X = 2)

= P(X ≤ 2) = 0.391 + 0.319

= P(X < 2) = 0.710

P(X > 5) = P(X = 6) + P(X = 7) + P(X = 8)

= P(X > 5) = 0.012 + 0.005 + 0.005

= P(X ≤ 2) = 0.022

Therefore, the correct expression is: X = 3.

Hence the answer is, at random a baby born in the united states in 2014 is 3.

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By using the cross multiplication, we can determine the solutions to the equation  w=2 , w=6.

By multiplying the numerator of one side by the denominator of other side and equating the resulting two products, cross multiplying can be used to solve a fractional equation when each side has a fraction with a single denominator.

Given the expression [tex]\frac{w}{2w-4} = \frac{4}{w}[/tex]

By using cross multiplication, we have

[tex]w^{2} = 4(2w-3)\\ w^{2} = 8w-12\\w^{2}-8w+12=0\\(w-2)(w-6)=0\\w=2 and w=6[/tex]

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The conditions of the system of equations to be Non Linear is given below .

In the question ,

we have to find the conditions for which the system of equations is non linear .

the conditions are ,

(1) the Non Linear equations does not form a straight line instead it forms a curve .

(2) the non linear equations have the degree as 2 or more than 2 , but not less than 2 .

(3) the general representation of the non linear equation is ax² + by² = c

(4) The non linear equations forms a curve and if the value of the degree is increased , then the curvature of the graph increases.

Therefore , These are the conditions of the system of equations  to be Non -Linear .

The given question is incomplete , the complete question is

What are the conditions of a system of equations to be nonlinear ?

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The total number of ways/ permutation that A occupies first position is 24 ,  A occupies the first position, and B the second is 6 and a appears before b is 10 ways.

What is permutation ?

Permutation is a meeting of objects in an exceedingly definite order. The members or components of sets square measure organized here in an exceedingly sequence or linear order.

Main body:

A) a occupies the first position-

As A is first, and arrange the remaining letters.  letters (B,C,D,E,F) can be arranged as-

4*3*2*1 = 24 ways

B) a occupies the first position, and b the second

As A is first and b is just after it , there are 5 position out of which 2 are taken by A, B in order , so number of ways they can be arranged is

3*2*1 = 6 ways

C) a appears before b

in this part there is no  condition that a appears just before b , so b can be places anywhere after A.

after fixing A at first place , B can be placed at 4 places.

after fixing A at 2nd place , B can be placed at 3 places.

after fixing A at 3rd place , B can be placed at 2 places.

after fixing A at 4th  place , B can be placed at 1 places.

total ways = 4+3+2+1 = 10

Hence the answer to these parts are 24, 6,10

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Boris should navigate 79.74° to go to Island C.

Given,

Boris is on vacation at a tropical bay that has three islands.

Distance between Island A and Island C = 13 miles

Distance between Island B and Island C = 14 miles

Distance between Island A and Island B = 8 miles

Boris rents a boat on Island A and plans to navigate to Island C.

We have to find that at what angle should she navigate to go to Island C

Here,

14² = 13² + 8² - (2 × 13 × 8) Cos A

Cos A = (13² + 8² - 14²) / (2 × 13 × 8)

Cos A = (169 + 64 - 196) / 208

Cos A = 37/208

A = arc Cos 0.178

A = 79.74°

Therefore,

Boris should navigate 79.74° to go to Island C.

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The given question is incomplete. Completed question is given below;

Boris is on vacation at a tropical bay that has three islands. He rents a boat on Island A and plans to navigate to Island C, which is 13 miles away. Based on the figure below, at what angle θ should he navigate to go to Island C? Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth of a degree . × S

Image is attached;

To prove the sum of all the intercepts = k^2

xi + yj +zk = k^2

The gradient of the function f(x,y,z) = s

f(x,y,z = 1/2sxi + 1/2 syj =1/2 szk

And the tangent plane at the point (xo,yo,zo) is

sx/x +  sy/y +  sz/z

=  sxo/xo +   syo/yo +  szo/zo

=>  sxo/xo +   syo/yo +  szo/zo = k       ........(1)

To find the x intercept , we set y =z=0 and obtain x = ksxo/sx. similarly, y = ksyo/yo and z= kszo/zo. their sum is

ksxo/xo + ksyo/yo + kszo/zo

=k( sx0/xo + syo/yo + szo/zo)

=k.k = k^2   ...from eqn 1

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Linear velocity of a person riding is 5.6 ft/s and time for one revolution of ferries wheel is 31.8 sec.

What is linear velocity?

Linear velocity, v, is defined as the rate of change of linear displacement, s, with respect to time, t.

On a ferries wheel, displacement = circumference of the wheel = 2πr

Hence linear velocity, v = 2πr/T

According to the given question:

Diameter of the wheel is 80 feet

So, radius of wheel = 40 feet

If Ferris wheel makes one revolution is 45 seconds

Then linear velocity

v = 2πr/T = 2 x 3.14 x 40/45

v = 5.6 ft/s

If linear velocity of a person riding on wheel is 8 ft/s then time for one revolution

T = 2πr/v = 2 x 3.14 x 40/ 8

T = 31.8 sec

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Answer:

Step-by-step explanation:

The answer is D

The average number of credit hours per semester for all students at the local college is 9.2.

It is given that,

at the local college a study sound that students earned an average of 9.2 credit hours per semester.

⇒ x = 9.2 credit hours per semester

Therefore by the central limit theorem,

x = μ  = 9.2 credit hours per semester

The central limit theorem states that the distribution of a sample variable approximates a normal distribution as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.

Therefore the average number is 9.2 credit hours per semester for all students at the local college.

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The result of subtracting and simplifying the rational expression in its fully factored form is [tex]\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}[/tex]

From the question, we are to subtract the rational expressions and express in the factored form

The given expression is

[tex]\frac{n^{2} + 5n - 36 }{n^{2} -25} - \frac{n^{2} +8n +15 }{5n^{2} -125}[/tex]

Factor 5n² - 125

[tex]\frac{n^{2} +5n - 36 }{n^{2} -25} - \frac{n^{2} +8n +15 }{5(n^{2} -25)}[/tex]

[tex]\frac{5(n^{2} +5n - 36) - (n^{2} +8n +15) }{5(n^{2} -25)}[/tex]

[tex]\frac{5n^{2} +25n - 180 - n^{2} -8n -15 }{5(n^{2} -25)}[/tex]

Simplify

[tex]\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}[/tex]

Hence, the expression is [tex]\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}[/tex]

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The answer double will be of 8 is 16, by multiplication.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

The fundamental concept of repeatedly adding the same number is embodied in the process of multiplication. The outcome of multiplying two or more numbers is known as the product of those numbers, and the factors that are multiplied are referred to as the factors. The process of repeatedly adding the same number is made easier by multiplication.

So the double of 8 means adding 2 two times. Or multiplying 8 with 2

8*2 = 16

Hence, double will be of 8 is 16

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Answer:

Step-by-step explanation:

C=1.75m+10.50

The correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3

The two given graphs are isomorphic in nature

In the firsts graph, the serial order is u1, u2, u3, u4, u5

wherease in the second graph the order is v1, v2, v4, v5, v3

Upon analysis, it can be seen that  the correct mapping (an isomorphism) between the sets of vertices of the two graphs is

f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3

Then the correct mapping (an isomorphism) between the sets of vertices of the two graphs is f(u1) = v1, f(u2) = v2, f(u3) = v4, f(u4) = v5, and f(u5) = v3.

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The possible key design is 262144.

Algebra is a branch of mathematics that uses mathematical expressions to aid in the representation of problems or situations. In algebra, we use numbers with definite or fixed values, such as 2, -1, 0.5, and so on. In algebra, variables such as x, y, and z are used in addition to numbers.

Given that keys for antique cars had nine parts, with four patterns for each part

We have to determine how many different key designs are possible for these cars

Number of designs possible

= 4x4x4x4x4x4x4x4x4

= 4^9

= 262144

Therefore the possible key design is 262144

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By using completing the square method, the value of x in the given equation (x - 12)(x + 4) = 9 is: D. x - 4 = ±√73

In Mathematics, the standard form of a quadratic equation is given by:

ax² + bx + c = 0.

In this exercise, you're required to determine the value of x in the given equation by using completing the square method. Therefore, we would expand the equation as follows:

(x - 12)(x + 4) = 9

x² - 8x - 48 = 9

Adding 48 to both sides of the equation, we have:

x² - 8x - 48 + 48 = 9 + 48

x² - 8x = 57

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 8x + (8/2)² = 19 + (8/2)²

x² - 8x + 16 = 57 + 16

x² - 8x + 16 = 73

Factorizing the quadratic equation, we have:

(x - 4)² = 73

Taking the square root of both sides of the quadratic equation, we have:

x - 4 = ±√73

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Complete Question:

Use completing the square to solve for x in the equation (x - 12)(x + 4) = 9.

A. x = -1 or 15

B. x = 1 or 7

C. x - 4 = ±√41.

D. x - 4 = ±√73

The value of x for the given geometric figure by similar triangle property will be 4.67.

If two figures look an exact shape but their size could be small or big then both figures are called similar figures.

For example, a square with a side of 10 cm and another with a side of 20 cm both square will be similar.

When anything has identical pieces facing one another or revolving around an axis, it is said to be symmetrical.

The given figure has three parallel lines and two transversals.

By similar triangle property

x/3.5 = 4/3

x = (4/3)3.5 = 4.67

Hence "The value of x by similar triangle property will be 4.67".

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The combined thickness is 7/8 inches.

The installation over the pad indicates they are joined vertically. So, the combined thickness will be sum of individual thickness of carpet and pad. Hence, calculating the thickness now.

The thickness of the carpet and pad = thickness of carpet + thickness of pad

Keep the values in equation

The thickness of the carpet and pad = 3/8 + 1/2

Taking LCM on Right Hand Side, we get 8

Adding the fractions

The thickness of the carpet and pad = (3 + (1×4))/8

The thickness of the carpet and pad = (3 + 4)/8

The thickness of the carpet and pad = 7/8

Hence, the thickness of the carpet and pad is 7/8 inches.

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The equation that help use to find the value of x is h(a+b)/2 = lw.

The value of x if both figure have the same area is 4 in

Area can be defined as the region bounded by a plane shape.

To write and solve an equation to find x, we use the formula of area of a trapeziod and the area of a rectangle

From the diagram,

Where:

From the diagram,

Given:

Substitute these values into equation 1 and solve for x

Hence, the equation is h(a+b)/2 = lw, and the values of x  is 4 in.

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