At the local dairy mart, you can buy one ice cream sandwich and two ice cream cones for $8 or one ice cream sandwich and one ice cream
cone for $5. this situation can be represented with the system 2x+y = 8 and x + y = 5, where x represents the cost of an ice cream cone
and y represents the cost of an ice cream sandwich use the system of equations to determine the cost of one ice cream sandwich and one ice
cream come

Answer:

x = 1 and x = -3

Step-by-step explanation:

We need to solve the given equation.

\(3+x=x^2+3x\)

Taking all terms together,

\(x^2+3x-3-x=0\\\\x^2+2x-3=0\\\\x^2+3x-x-3=0\\\\x(x+3)-1(x+3)=0\\\\(x-1)(x+3)=0\\\\x=1\ and\ x=-3\)

So, the solution of the above equation is x = 1 and x = -3.

Answer:

\(4=(x+1)^{2}\)

x= -1 ±2

Khan Academy

To find missing coordinates in geometric proofs, you can use various methods such as the distance formula, midpoint formula, and slope formula. These formulas help you calculate the coordinates of a point based on the information you have about other points in the figure.

In geometric proofs, it is often necessary to determine the coordinates of a point based on the given information. One method to find missing coordinates is by using the distance formula. This formula states that the distance between two points (x1, y1) and (x2, y2) is given by the square root of [\((x2 - x1)^2 + (y2 - y1)^2]\). By using the known distances between points and applying this formula, you can solve for the missing coordinates.

Another approach is to use the midpoint formula. This formula allows you to find the coordinates of the midpoint between two given points. It states that the midpoint coordinates (x, y) are given by \([(x1 + x2)/2, (y1 + y2)/2]\), where (x1, y1) and (x2, y2) are the coordinates of the given points. By plugging in the known values and solving for the missing coordinates, you can determine the coordinates of the desired point.

Lastly, the slope formula can be utilized to find missing coordinates. This formula states that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1)/(x2 - x1). By knowing the slope of a line and one point on that line, you can use the formula to find the coordinates of the missing point.

In conclusion, the distance formula, midpoint formula, and slope formula are useful tools in finding missing coordinates in geometric proofs.

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Answer: x = 9

Step-by-step explanation:

The minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

In the question, we are asked to use Lagrange multipliers to find the minimum distance between the origin and the plans 3x + y + 2z = 28.

Lagrange multipliers state that if we want to minimize a function, f(x, y, z), subject to a constraint g(x, y, z) = constant, then ∇f = λ∇g.

We want to minimize the distance, and the distance formula says that the distance from the origin to a point (x, y, z), is given as:

D = √(x² + y² + z²), which can also be shown as:

D² = x² + y² + z².

The gradient of this function is: (2x + 2y + 2z), which needs to be equal to the gradient of the constraint equation multiplied by the constant, λ, that is, λ(3, 1, 2), which gives:

2x = 3λ, or, x = (3/2)λ,

2y = λ, or, y = λ/2, and,

2z = 2λ, or, z = λ.

Substituting these in the equation of the plane, 3x + y + 2z = 28, we get:

3(3/2)λ + λ/2 + λ = 28,

or, 6λ = 28,

or, λ = 28/6 = 14/3.

Thus, we get:

x = (3/2)λ = 7,

y = λ/2 = 7/3, and,

z = λ = 14/3.

Substituting these in the distance formula, we get:

D = √(7² + (7/3)² + (14/3)²) = √(49 + 49/9 + 196/9) = √(686/9) = 8.73.

Thus, the minimum distance between the origin and the plane 3x + y + 2z = 28, using the Lagrange Multipliers is 8.73 units.

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Answer:

f(3)=7

Step-by-step explanation:

just plug in the number

f(3)=2×3+1

=7

Answer:

no

Step-by-step explanation:

52+37+42 should be 180 but its not so it does not form a triangle

I hope you under stand

Answer:

yes

Step-by-step explanation:

use the triangle inequality theorem, where sides are 'a', 'b', and 'c':

all three of these must be true in order to have a triangle:

a+b > c

a+c > b

b+c > a

is 37 + 42 > 52   Yes

is 37 + 52 > 42   Yes

is 52 + 42 > 37   Yes

As a point estimator for, we utilise x-bar (sample mean) (mu, population mean)

The average value in mathematics is the middle number, which is calculated by dividing the total number of numbers by the sum of all the numbers. A set of data's average is calculated by adding up all the values and dividing the result by the total number of values.

We use the x-bar (sample mean) as a point estimator for (mu, population mean). As long as the sample is random, this estimator's impartial long-run distribution is centred at (mu).

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Complete question -

Answer: (1, 34) and (2, 17)

Step-by-step explanation:

Step 1: Divide 34 by the smallest prime factor.

34/2 = 17

Step 2: Since 17 itself is a prime number, therefore, it is divisible by 17 only.

17/17 = 1

Step 3: Now further division is not possible. Thus, we will consider 2 and 7 as the prime factors of 34.

Answer:

C

Step-by-step explanation:

x+x-1-1-1-1-1-1-1 = -x-x-x+1+1+1+1+1+1+1+1+1

2x-7 = -3x +9

5x - 7 = 9

5x = 16

x = 16/5

x= 3⅕

x= 3.2

the answer is 15cm (pls mark brainlest)

Answer:

3:40

Step-by-step explanation:

We need both measurements in the same units.

1 m = 100 cm

2 m = 2 × 1 m = 2 × 100 cm = 200 cm

15 cm to 2 m = 15 cm to 200 m

Divide both numbers in the ratio by 5 cm.

15 cm to 200 cm = 3:40

The number of weak compositions of 2n into 2k parts from which 2 are even and the others are all odd can be found by using the following formula:

C(2n - 2k + 2k - 2, 2k - 2) * C(2k - 2, 2)

Where C(n, k) is the binomial coefficient, which can be calculated as:

C(n, k) = n! / (k! * (n - k)!)

So, for the given example where n = 4 and k = 3, the number of weak compositions would be:

C(2 * 4 - 2 * 3 + 2 * 3 - 2, 2 * 3 - 2) * C(2 * 3 - 2, 2) = C(8, 4) * C(4, 2) = 70 * 6 = 420

Therefore, the number of weak compositions of 2n into 2k parts from which 2 are even and the others are all odd is 420.

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The given sample is a cluster sample because cluster sampling separates the population into non-overlapping subgroups (clusters), some of which are then included in the sample.

In a cluster sample, the population is divided into clusters or groups, and a random selection of clusters is chosen to represent the entire population. In this case, the population consists of all 10th-grade students in the state. The high schools are the clusters, and a random sample of 15 high schools was selected.

Once the clusters (high schools) are chosen, all 10th-grade students within those selected high schools are included in the sample. Therefore, every 10th-grade student in the selected high schools is part of the sample.

Cluster sampling is often used when it is impractical or expensive to sample individuals directly from the entire population. It allows for more efficient data collection by grouping individuals together based on their proximity or some other characteristic.

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To gather information about the validity of a new standardized test for 10th-grade students in a particular state, a random sample of 15 high schools was selected from the state. The new test was administered to every 10th-grade student in the selected high schools. What kind of sample is this?

The game is based purely on chance, the moves and decisions made by each player during the game will require strategic thinking and planning.

Russell has the first throw, he will need to roll two dice and hope that the numbers add up to 12.

The probability of rolling a 12 with two dice is relatively low, at only 1/36.

This means that Russell may need to roll several times before he is able to achieve a sum of 12 and begin the game.
Peter, on the other hand, will also have to throw two dice and hope to achieve a sum of 12.

If Russell is unable to roll a 12, Peter will have the opportunity to roll and try to beat Russell's highest sum.
Once the game begins, Russell and Peter will take turns rolling the dice and moving their game pieces around the board.

The outcome of each turn will depend on the numbers rolled on the dice and the rules of the game.
It is important to note that the probability of rolling different numbers with two dice varies.

For example, the probability of rolling a 7 is much higher than the probability of rolling a 2 or a 12.

This means that certain numbers may be more advantageous to roll in the game, depending on the rules and strategies involved.
Overall, the game will be determined by a combination of luck and skill.

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Answer:

one solution

Step-by-step explanation:

the solution to a system of equations given graphically is at the point of intersection of the 2 lines, that is (1, 2 )

Since there is only 1 point of intersection then there is only one solution.

Answer:

Circumference of the smaller circle = 2.1x units

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA ?

Radius of the larger circle OB = x units

Radius of the smaller circle OA = y units

Circumference of larger circle = 2πx units

Circumference of smaller circle = 2πy units

Since circumference of larger circle is 3 times the circumference of smaller circle,

2πx = 3(2πy)

2πx = 6πy

x = 3y

y = \(\frac{x}{3}\)

Therefore, circumference of the smaller circle = \(2\pi (\frac{x}{3})\) units

                                                                             = \(\frac{2\pi x}{3}\) units

                                                                             = 2.094x

                                                                             ≈ 2.1x

Circumference of the smaller circle circle = 2.1x units

\(4( \frac{1}{5} x + 7) = 2x - 2\)

\(x = 25\)

Answer:

The movie was found to be delightful and entertaining by viewers.

Answer:

D. The movie was found to be delightful and entertaining by viewers.

Hope this helps.

The kingdom is the widest category, it includes other categories such as phylum, genus, order, and many more.

Taxonomy is defined as the scientific method of classifying, identifying, and naming living organisms.

In the hierarchy of living organisms, the largest group of organisms is the Kingdom. This is followed by:

Phylum

Class

Order

Family

Genus and

Species (which is lowest in the hierarchy).

The species is the smallest unit of classification.

The kingdom is the widest category, it includes other categories such as phylum, genus, order, and many more.

It is the most specific because the individuals within a species are:

Therefore, species are the most specific in modern taxonomy.

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Answer:

I believe it is genus

Step-by-step explanation:

In situation a, the predictor variable is age, as it is being tested to see if it affects the outcome variable, which is the number of risky behaviors. So, age is the independent variable and the number of risky behaviors is the dependent variable.

In situation b, the predictor variable is the number of family members, as it is being tested to see if it affects the outcome variable, which is the level of education of children. So, the number of family members is the independent variable and the level of education of children is the dependent variable.

It is important to identify the predictor variable and the outcome variable in any study as this helps in understanding the relationship between the two variables and in interpreting the results accurately.

For situation A, the predictor variable is "age," and the outcome variable is "number of risky behaviors." As age increases, the study aims to see if the number of risky behaviors changes.

For situation B, the predictor variable is "number of family members," and the outcome variable is "level of education of children." The study examines whether the children's level of education changes based on the number of family members.

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The earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

How do I calculate a circle's circumference?

A circle's diameter is multiplied by to determine its circumference (pi). You can also determine the circumference by multiplying 2radius by pi (=3.14).

Given: theta angle (central) = 7.2°; arc length S = 800 km

This indicates that an 800 km long arc is extending a circle with a 7.2° center angle ( earth in this case).

By definition, "An arc's length is a portion of a circle's diameter."

Therefore, we must first establish what percentage of the circle the specified arc length represents.

360° is a complete circle.

Thus, the fraction equals 7.2°/360°, or 1/50.

As a result, the stated arc length (800km) with a 7.2° central angle is 1/50th of the entire circle.

Thus, the whole circumference is 800 x 50, or 40000 km.

Alternately, you can calculate circumference using the formula below:

360° center angle x arc length as the circumference (theta)

Values substituted: circumference 800 = 360° 7.2°

circumference = 360°, 800°, and 7.2°, or 40000 kilometers

Therefore, the earth is 40000 kilometers around. There is no need to round off because the circumference already contains significant figures.

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Answer:

A kid leaping happily to home after school

The graph represents the relationship between height and time.

Given that,
A curve has been shown we have to explain the behavior of the curve.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here,
The curve is shown, where the vertical axis represents the height above the ground and the horizontal axis represents the time. Let's assume a plane of paper is flying, the plane getting a rise and then a certain down and again rise and down as according to the height of the plane.

Thus, the graph represents the relationship between height and time.

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add -7x to the other side so the equation is

y=7x-2

slope is 7

y-int is -2

Answer:

B is the correct option.

Hope it helps!!!

Answer:

1.33333333quarts

1.3(repeating) quarts

Step-by-step explanation:

Answer: 67

Step-by-step explanation:

We see a pattern where we multiply the number we added by previously by two.

For example, from 5 to 7, it is 2.

From 7 to 11, we add by 4.

From 11 to 19, we add by 8.

From 19 to 35, we add by 16.

This means the next number would be 32, adding 35 by 32 gives us 67,

Answer: 360

Step-by-step explanation:

done

To show that `(n + 3)7 ∈ Θ(n7)`, we need to prove that `(n + 3)7 = Θ(n7)`.This can be done by showing that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)` .Now, let's prove the two parts separately:

Proof for `(n + 3)7 = O(n7)`.

We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≤ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≤ n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + n7
≤ 2n7 + 21n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6
≤ 2n7 + 84n6 + 441n5 + 2205n4 + 10395n3 + 45045n2 + 153609n + 729
```Thus, we can take `c = 153610` and `k = 1` to satisfy the definition of big-Oh notation. Hence, `(n + 3)7 = O(n7)`.Proof for `(n + 3)7 = Ω(n7)`We want to prove that there exists a positive constant c and a non-negative constant k such that `(n + 3)7 ≥ cn7` for all `n ≥ k`.Using the Binomial theorem, we can expand `(n + 3)7` as:```
(n + 3)7
= n7 + 7n6(3) + 21n5(3)2 + 35n4(3)3 + 35n3(3)4 + 21n2(3)5 + 7n(3)6 + 37
≥ n7
```Thus, we can take `c = 1` and `k = 1` to satisfy the definition of big-Omega notation. Hence, `(n + 3)7 = Ω(n7)`.

As we have proved that `(n + 3)7 = O(n7)` and `(n + 3)7 = Ω(n7)`, therefore `(n + 3)7 = Θ(n7)`.Thus, we have shown that `(n + 3)7 ∈ Θ(n7)`.From the proof, we can see that we used the Binomial theorem to expand `(n + 3)7` and used algebraic manipulation to bound it from above and below with suitable constants. This technique can be used to prove the time complexity of various algorithms, where we have to find the tightest possible upper and lower bounds on the number of operations performed by the algorithm.

Hence, we have shown that `(n + 3)7 ∈ Θ(n7)` for non-negative integer n.

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The velocity vector v(t) = -3 sin (3t) i + 3 cos (3t) j + 3t k.

The acceleration vector is

a(t)=⟨−9cos(3t),−9sin(3t),3t⟩.

The initial velocity is

v(0)=<1,0,1>,

and the initial position vector is

r(0)=<1,1,1>.

Compute: (A) The velocity vector v(t)

Let v(t) be the velocity vector.

Therefore, the velocity can be computed by integrating the acceleration:

v(t) = ∫a(t) dt

Integrating with respect to x, we get:

vx(t) = ∫−9cos(3t) dt

= -3 sin (3t) + C1

Taking the initial velocity to be

v(0) = <1,0,1>,

we can find the value of C1:

vx(0) = -3 sin (0) + C1 = 1

⇒ C1 = 1

Integrating with respect to y, we get:

vy(t) = ∫−9sin(3t) dt

= 3 cos (3t) + C2

Taking the initial velocity to be

v(0) = <1,0,1>,

we can find the value of C2:

vy(0) = 3 cos (0) + C2

= 0

⇒ C2 = -3

So, the velocity vector is given by:

v(t) = vx(t) i + v y(t) j + vz(t) k

v(t) = -3 sin (3t) i + 3 cos (3t) j + 3t k

The velocity vector

v(t) = -3 sin (3t) i + 3 cos (3t) j + 3t k

Answer: The velocity vector v(t) = -3 sin (3t) i + 3 cos (3t) j + 3t k.

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Given statement solution is :- The mass of x refers to the probability mass function (PMF) values for each value of x.

Plot of the probability mass function (PMF):

The PMF plot represents the probabilities of the different values of x.

css

Copy code

x  |  P(X=x)

---|--------

0  |  0.362

1  |  0.442

2  |  0.153

3  |  0.037

4  |  0.006

5  |  0.0005

The cumulative distribution function (CDF) of x is a function that gives the probability that X takes on a value less than or equal to a given x-value.

a. The possible values of x are 0, 1, 2, 3, 4, and 5. This represents the number of hearts you can get from the 5 cards dealt.

b. The mass of x refers to the probability mass function (PMF) values for each value of x. We can calculate the mass as follows:

P(x = 0) = (39/52) * (38/51) * (37/50) * (36/49) * (35/48)

P(x = 1) = 5 * (13/52) * (39/51) * (38/50) * (37/49) * (36/48)

P(x = 2) = 10 * (13/52) * (12/51) * (39/50) * (38/49) * (37/48)

P(x = 3) = 10 * (13/52) * (12/51) * (11/50) * (39/49) * (38/48)

P(x = 4) = 5 * (13/52) * (12/51) * (11/50) * (10/49) * (39/48)

P(x = 5) = (13/52) * (12/51) * (11/50) * (10/49) * (9/48)

Note: The coefficients in front of each probability correspond to the different ways of selecting x hearts from the available hearts in the deck.

c. Plot of the probability mass function (PMF):

The PMF plot represents the probabilities of the different values of x.

css

Copy code

x  |  P(X=x)

---|--------

0  |  0.362

1  |  0.442

2  |  0.153

3  |  0.037

4  |  0.006

5  |  0.0005

d. The cumulative distribution function (CDF) of x is a function that gives the probability that X takes on a value less than or equal to a given x-value.

The CDF of x can be calculated by summing up the probabilities of all the values less than or equal to x.

CDF(x = 0) = P(x = 0)

CDF(x = 1) = P(x = 0) + P(x = 1)

CDF(x = 2) = P(x = 0) + P(x = 1) + P(x = 2)

CDF(x = 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)

CDF(x = 4) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

CDF(x = 5) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5)

e. Plot of the cumulative distribution function (CDF):

The CDF plot represents the cumulative probabilities for the different values of x.

scss

Copy code

x  |  CDF(X<=x)

---|-----------

0  |  0.362

1  |  0.804

2  |  0.957

3  |  0.994

4  |  1.000

5  |  1.000

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