Help!!!!!! I’ll give 100 points

Given statement solution is :- a) SQ:

Since PQRS is a parallelogram, SQ is the same as the vector opposite to SP. Therefore, SQ is equal to  a+b .

b) PR:

Again, using the properties of parallelograms, PR is the same as the vector opposite to PQ. Therefore, PR is equal to  a-b.

So, the expressions for the vectors are:

a) SQ = a+b

b) PR =  a-b

If two vectors are acting simultaneously at a point, then it can be represented both in magnitude and direction by the adjacent sides drawn from a point.

Parallelogram law of vector addition states that. if two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of the two vectors is given by the vector that is diagonal passing through the point of contact of two vectors.

To express the following vectors in terms of a and/or b, we can use the properties of parallelograms:

a) SQ:

Since PQRS is a parallelogram, SQ is the same as the vector opposite to SP. Therefore, SQ is equal to  a+b .

b) PR:

Again, using the properties of parallelograms, PR is the same as the vector opposite to PQ. Therefore, PR is equal to  a-b.

So, the expressions for the vectors are:

a) SQ = a+b

b) PR =  a-b

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Answer:

\(\frac{11}{5}\)

Step-by-step explanation:

1. isolate x by adding 7 to the other side (7+4)

5x - 7 = 4

5x = 11

2. divide by 5 to get x alone

x = 11/5

Answer:

Step-by-step explanation:

5x - 7 = 4

5x=4+7

5x=11

x=11/5

x=2.2

Answer:

I hope this helps you

:)

To match each number on the left with the correct description on the right, you will need to carefully analyze each option and determine the most appropriate description for each number.

Here are some steps to help you with this task: 1. Read the descriptions on the right side carefully and understand their meanings. It is important to have a clear understanding of the terms before you start matching them with the numbers.

2. Start with the first number on the left and consider each description on the right. Think about the meaning of the number and how it relates to each description.

3. For example, if the first number is 5, and one of the descriptions on the right is "odd number," you can immediately identify that this description matches the number since 5 is indeed an odd number.

4. Continue this process for each number, carefully considering each description and matching it with the appropriate number.

5. Keep in mind that the descriptions on the right may be used more than once. So, you might need to revisit the descriptions to find the best match for each number.

6. Once you have matched all the numbers with their descriptions, double-check your answers to ensure their accuracy and appropriateness. Remember to take your time, think critically, and carefully consider each option before making your final choices.

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Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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Answer:

Step-by-step explanation:

Good luck

Answer:

a

Step-by-step explanation:

heh math

The probability of getting 2 blue is 1/9.

You are choosing replacement marbles. The trials (marble selections) are independent from one another and follow the binomial distribution.

1/3 of the time, a blue marble will be the first one chosen.

(This is due to the fact that 4 out of 12 marbles are blue, therefore 4/12 equals 1/3.

A blue marble is 1/3 more likely to be chosen the second time.

The two probabilities can be multiplied to obtain the following results because the marble selections are independent:

The likelihood of receiving two blues is (1/3)2 =1/9.

Therefore, there is a 1/9 chance of obtaining two blues.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

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Answer:

y = 1/3(x + 5)^2 - 4

Step-by-step explanation:

The general vertex form is;

y = a(x-h)^2 + k

From the question, (h,k) are the coordinates of the vertex which is (-5,-4)

So we have

y = a(x + 5)^2 -4

So we need to get the leading coefficient

Simply substitute the point it passes through

x = -2 and y = -1

-1 = a(-2 + 5)^2 - 4

-1 = a(3)^2 -4

-1 = 9a -4

9a = 4-1

9a = 3

a = 3/9

a = 1/3

So the equation is;

y = 1/3(x + 5)^2 - 4

375 different combinations of pizza Grayson and his friends can create.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

The meat toppings are pepperoni, salami, sausage, chicken, and ground beef.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

They can pick thick, hand-tossed, or deep-dish crust.

Here, n=3 r=1

So, C(n, r) = 3!/1!(3-1)!

= 3

They can also pick garlic, tomato, ranch, pesto, or barbecue sauce.

Here, n=5 r=1

So, C(n, r) = 5!/1!(5-1)!

= 5

Number of ways = 5×5×3×5

= 375

Hence, in 375 ways they can choose pizza.

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Answer: the first term in the sequence is 9.

Step-by-step explanation:

Let the primary term be x.

At that point the moment term is 2x + 4.

And the third term is 2(2x + 4) + 4 = 4x + 12.

Since the third term is given as 48, we will set up an condition and unravel for x:

4x + 12 = 48

4x = 36

x = 9

Given:

The table of values.

To find:

The explicit rule for the given table of sequence.

Solution:

From the given table, it is clear that the 1st ,2nd ,3rd ,4th terms of the sequence are 12, 22, 32, 42.

In the sequence, the difference between two consecutive terms are same and for the sequence,

First term: a=12

Common difference: d= 22- 12 = 10

The explicit rule for an arithmetic sequence is

\(f(n)=a+(n-1)d\)

Where, a is the first term and d is the common difference.

Putting a=12 and d=10, we get

\(f(n)=12+(n-1)10\)

\(f(n)=12+10n-10\)

\(f(n)=10n+2\)

Therefore, the correct option is B.

The first error Emi made in computing the variance is failing to find the difference of 89 - 78 correctly.

This is defined as the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

In this case , sum of given numbers = 87+46+90+78+89 = 390

Divide 390 by the number of numbers which is = 5

390/5 = 78

Therefore Emi failed to find the difference.

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Answer:

emi failed to find the difference of 89 - 78 correctly. 

Step-by-step explanation:

The first derivative of the function `g(u) = u(2u - 3)^3` is `g'(u) = 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u) = 12(u - 1)(2u - 3)^2`.

Given function: `g(u)

= u(2u - 3)^3`

To find the first derivative of the given function, we use the product rule of differentiation.`g(u)

= u(2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g'(u)

= u * d/dx[(2u - 3)^3] + (2u - 3)^3 * d/dx[u]`

Using the chain rule of differentiation, we have:

`g'(u)

= u * 3(2u - 3)^2 * 2 + (2u - 3)^3 * 1`

Simplifying:

`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

To find the second derivative, we differentiate the obtained expression for

`g'(u)`:`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g''(u)

= d/dx[6u(2u - 3)^2] + d/dx[(2u - 3)^3]`

Using the product rule and chain rule of differentiation, we have:

`g''(u)

= 6[(2u - 3)^2] + 12u(2u - 3)(2) + 3[(2u - 3)^2]`

Simplifying:

`g''(u)

= 12(u - 1)(2u - 3)^2`.

The first derivative of the function `g(u)

= u(2u - 3)^3` is `g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u)

= 12(u - 1)(2u - 3)^2`.

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The first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

First, let's find the first derivative:

g'(u) = (2u - 3)³ * d(u)/du + u * d/dx[(2u - 3)³]

Using the chain rule, we can differentiate (2u - 3)³ and u as follows:

d(u)/du = 1

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

Plugging these values back into the equation for g'(u), we have:

g'(u) = (2u - 3)² + u * 3(2u - 3)² * 2

= (2u - 3)³ + 6u(2u - 3)²

Simplifying the expression, we have:

g'(u) = (2u - 3)³ + 6u(2u - 3)²

Now, let's find the second derivative:

g''(u) = d/dx[(2u - 3)³ + 6u(2u - 3)²]

Using the chain rule and product rule, we can differentiate each term:

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

d/dx[6u(2u - 3)²] = 6(2u - 3)² + 6u * d/dx[(2u - 3)²]

= 6(2u - 3)² + 6u * 2(2u - 3)

Plugging these values back into the equation for g''(u), we have:

g''(u) = 3(2u - 3)² * 2 + 6(2u - 3)² + 6u * 2(2u - 3)

= 6(2u - 3)² + 6(2u - 3)² + 12u(2u - 3)

= 12(2u - 3)² + 12u(2u - 3)

Simplifying the expression further, we have:

g''(u) = 12(2u - 3)² + 12u(2u - 3)

Therefore, the first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

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Step-by-step explanation:

cost of 18 apples= 18x6p= 108p

£5-108p= x (will let it be x since i do not know the conversion)

maximum number of banana he can buy= x divide by 40p (rounded down to smallest whole number)= b

The change he have= x-(40×b) = y

apples bought with change= y divide by 6p= a

do the working above to find value for a and b, add a to the 18 apples bought initially and b is number of banana

Answer:

Step-by-step explanation:

82 - 17 + 53

= 188

Answer:

118

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

use pythagorean theorem:

\(12^{2}\) + \(16^{2}\) = \(c^{2}\)

144 + 256 = \(c^{2}\)

400 = \(c^{2}\)

\(\sqrt[ ]{400}\) = c

20 = c

Answer:

1) x = 2 and y = -2

2) x = 6 and y = 5

3) x = 2 and y = -4

Step-by-step explanation:

1) 3x + y = 4

since y = -x subtitute it in the equation

3x + (-x) = 4

3x - x = 4

2x = 4

x = 4\2

x = 2

y = -2

2) 4x - y = 19

since y = x - 1 subtitute it in the equation

4x - (x - 1) = 19

4x - x + 1 = 19

3x = 19 - 1

3x = 18

x = 18\3

x = 6

y = 6 - 1 = 5

3) y = 3x - 10

y - 3x = -10

since 2x + y = 0

thus y = -2x subtitute in equation

-2x - 3x = -10

-5x = -10

x = -10\-5

x = 2

y = -2 * 2 = -4

Answer:

53 packages

Step-by-step explanation:

37.

Add all the distances .

3/4 + 1/2 + 2/3 + 3/4 = 8/3 miles

To add fractions you need equal bottom numbers

find the LCM ( Least common multiple of the denominators )

4 , 2 , 3 , 4 = LCM = 12

Multiply each fraction by the same numerator and denominator, to obtain 12 as a bottom number

(3/4 * 3/3) + (1/2 * 6/6) + (2/3 * 4/4) + (3/4 * 3/3)

9/12 + 6/12 + 8/12 + 9/12

Now that all fractions have the same denominator ( bottom number) you can add them.

Add the numerators ( top numbers ) and put 12 as a denominator.

(9 + 6 + 8 + 9 ) / 12 = 32/12

Simplify ( divide both numbers by 4 )

32/12 = 8/3

The number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x and y be the number of hours for Sophie and Addison:

x + y = 11

20x + 30y = 260

After solving the above two linear equations by substitution:

x = 7 hours

y  = 4 hours

Thus, the number of hours Sophie worked and the number of hours Addison worked are 7 and 4 hours respectively.

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The correct statements from the sample are given as follows:

B About 25% of the students at the high school take painting.

D Next year, 7 out of every 60 students at the high school will take music.

E In a group of 120 students from the high school, about 16 of the students likely take electronics.

The proportion relative to an outcome is given by the number of desired outcomes divided by the number of total outcomes.

15 out of 60 students at the school take painting, hence the proportion is given as follows:

p = 15/60 = 0.25 = 25%.

Out of 60 students, 11 take photography, hence out of 30 students, the amount is given as follows:

30/60 x 11 = 5.5.

For electronics, out of 120 students, we have that:

120/60 x 8 = 16.

The diagram is given by the image presented at the end of the answer.

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Answer:

1

Step-by-step explanation:

The function f(x)=e⁴⁻ˣ   is differentiable for all values of x over the interval (-5,5)

A differential equation is an equation that contains one or more functions with its derivatives.

There are a few ways to tell- the easiest would be to graph it out- and ask yourself a few key questions

Function is continuous over the interval. If it is continuous it is probably differentiable

Does the function have any sharp turns in the interval. A sharp turn means it is not differentiable at that point and therefore not differentiable on the entire interval

f(x)=e⁴⁻ˣ is differentiable over (-5, 5)This is because the exponential function is continuous and infinitely differentiable

Hence, the function f(x)=e⁴⁻ˣ   is differentiable for all values of x over the interval (-5,5)

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a) The cost of 5 boxes of size 1 kg would be: £1.40 × 5 = £7

b) It will cost £6.75 to buy 5 kg of rice in the cheapest way possible.

a)  If the buyer wants 5 kg of rice, then the buyer needs to buy five boxes of size 1kg.

Therefore, the cost of 5 boxes:

£1.40 × 5 = £7

b) In order to buy 5 kg of rice in the cheapest way possible, we need to select the boxes that are cheapest in price. The 1.5 kg box of rice has the lowest cost per kilogram.

Therefore, it is best to buy 2 boxes of 1.5 kg rice and 1 box of 2 kg rice. The cost of 2 boxes of 1.5 kg rice and 1 box of 2 kg rice would be:

2 × £2.05 + 1 × £2.65= £4.10 + £2.65= £6.75

Therefore, it will cost £6.75 to buy 5 kg of rice.

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a)An buying five boxes of 1 kg rice each would cost £7.00.

b)The cheapest way to buy 5 kg of rice would cost £8.70.

To buy 5 kg of rice by purchasing five boxes of size 1 kg each, to calculate the total cost.

The cost of 1 kg of rice in a box is £1.40.

So, the cost of 5 kg of rice would be:

5 kg × (£1.40 per kg) = £7.00

To determine the cheapest way to buy 5 kg of rice,  to consider the prices of different box sizes and their quantities.

From the given information:

1 kg of rice costs £1.40

1.5 kg of rice costs £2.05

2 kg of rice costs £2.65

To find the cheapest way to compare the prices per kg of rice for each box size.

Price per kg for each box size:

1 kg box: £1.40 / 1 kg = £1.40/kg

1.5 kg box: £2.05 / 1.5 kg = £1.37/kg

2 kg box: £2.65 / 2 kg = £1.33/kg

The 2 kg box has the lowest price per kg. So, the cheapest way to buy 5 kg of rice would be by purchasing three boxes of 2 kg each and one box of 1 kg:

3 × 2 kg + 1 ×1 kg = 7 kg

3 × £2.65 (for 2 kg) + £1.40 (for 1 kg) = £8.70

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The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Answer:

P = 90 + 2.50x

Step-by-step explanation:

The equation for P, in terms of x, representing Alexander's total pay on a day on which he sells x computers is:

P = 90 + 2.50x

The set of all 2×3 matrices with entries from ℝ, where each row of entries sums to zero, is indeed a vector space.

To determine if the set of 2×3 matrices with entries from ℝ, where each row sums to zero, forms a vector space, we need to verify if it satisfies the necessary properties of a vector space. These properties include closure under addition and scalar multiplication, associativity, commutativity, existence of a zero vector, existence of additive inverses, and distributive properties.

To check closure under addition, we need to ensure that the sum of any two matrices from the given set is also a matrix in the set. Let's take two arbitrary matrices A and B from the set. Each row of A and B sums to zero. Now, when we add corresponding entries of A and B, the resulting matrix C will also have rows that sum to zero. Thus, the set is closed under addition.

For closure under scalar multiplication, we need to verify that multiplying any matrix from the set by a scalar also produces a matrix within the set. Let's consider an arbitrary matrix A from the set and a scalar c from ℝ. When we multiply each entry of A by c, the resulting matrix cA will also have rows that sum to zero. Therefore, the set is closed under scalar multiplication.

Matrix addition is associative, meaning that for any matrices A, B, and C in the set, (A + B) + C = A + (B + C). This property holds true for matrices in this set since addition of matrices follows the same rules regardless of their row sums.

Matrix addition is commutative, meaning that for any matrices A and B in the set, A + B = B + A. This property also holds true for matrices in this set because the order of addition does not affect the row sums of the resulting matrix.

A zero vector is an element of the set that when added to any other matrix in the set, leaves the other matrix unchanged. In this case, the zero vector is a 2×3 matrix with all entries equal to zero. When we add this zero matrix to any other matrix in the set, the resulting matrix still has rows that sum to zero. Hence, the set contains a zero vector.

For every matrix A in the set, there must exist an additive inverse -A in the set such that A + (-A) = 0. Since each row of A sums to zero, the additive inverse -A will also have rows that sum to zero. Therefore, the set contains additive inverses.

The set needs to satisfy the distributive properties of scalar multiplication over addition and scalar multiplication over scalar addition. These properties hold true for matrices in this set, as the row sums are preserved when performing these operations.

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