Find the first term and common ratio for the geometric sequence a2=-15 a4=-375

Answer:

Step-by-step explanation:

(a)

The sample space is

{(1,1), (2,2), (3,3), (4,4), (1,2), (1.3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2) (3,4), (4,1),(4,2), (4.3)}

(b)

i  {(2,2), (4,4), (2,4), 4,2)}

ii {(1,1), (1,2), (3,3), (1,3), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1), (4,3)}}

iii {(1,1)}

iv {3,4), (4,3)}

v {(3,3), (2,4), (4,2), (3,4), (4, 3), (4,4)}

vi {(1,1), (2,2), (3,3), (4,4)}

vii  {(1,2), (1,3), (2,1), (3,1), (2,2), (2,4), (3,3), (3,4), (4,2), (4,3)}

viii {(1,1), (2,2), (3,3), (1,2), (1.3), (2,1), (2,3), (3,1), (3,2)}

The additional acres that the parks occupy will be 33.75 acres.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, the additional acres that the parks occupy will be:

= (12.5 × 3) - 3.75

= 33.75 acres.

Note that the information is incomplete and the complete information is given below.

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A city is building 3 parks in a new subdivision. Each park will be 1.25 acres. How many total acres will the 3 parks be? 3.75 acres

The city acquired more land next to the subdivision. If it decides to make each park 12.5 acres, how many additional acres would the parks occupy?

Answer:

the slope intercept form is   y = (1/2)x - 1

Step-by-step explanation:

The slope-intercept form is, y = mx + b

We see from looking at the graph that,

at x = 0, y = -1

So, from this we find that b = -1

at x = 2, y = 0,

now, we find the slope m,

using,

\(m = \frac{y_{2} -y_1}{x_2-x_1}\)

Using x_2 = 2, y_2 = 0,

x_1 = 0, y_1 = -1, we get,

m = (0-(-1))/(2-0)

m = 1/2

So, the slope intercept form is,

y = (1/2)x - 1

Roland's percent error is approximately 3.889%.

This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.

The positive sign indicates that Roland's measured value is slightly lower than the actual value.

To calculate Roland's percent error, we can use the formula:

Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100

Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:

Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100

Simplifying the expression within the absolute value:

Percent Error = (|-0.007| / 0.180) \(\times\) 100

Since the absolute value of -0.007 is 0.007, we have:

Percent Error = (0.007 / 0.180) \(\times\) 100

Calculating the division:

Percent Error = 0.03889 \(\times\) 100

Percent Error = 3.889%.

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Given Information:

Cost price = $4

Selling price = $10

Salvage value = $1.50

Average demand = μ = 250 boxes

Standard deviation = σ = 34 boxes

Required Information:

Number of lettuce boxes = ?

Answer:

The supermarket should purchase 268 boxes  of lettuce

Step-by-step explanation:

The required number of lettuce boxes that supermarket should purchase is given by

Number of lettuce boxes = μ + (z*σ)

Where μ is the average demand of lettuce boxes, σ is the standard deviation, and z is the z-score which is given by

p = C_us/(C_us + C_os)

The z-score corresponding to probability p will be obtained.

The cost of under stocking is given by

C_us = Selling price - Cost price

C_us = $10 - $4

C_us = $6

The cost of over stocking is given by

C_os = Cost price - Salvage value

C_os = $4 - $1.50

C_os = $2.50

p = C_us/(C_us + C_os)

p = 6/(6 + 2.50)

p = 0.7058

p  = 70.58%

The z-score corresponding to 70.58% probability is approximately 0.54

Number of lettuce boxes = μ + (z*σ)

Number of lettuce boxes = 250 + (0.54*34)

Number of lettuce boxes = 250 + (18.36)

Number of lettuce boxes = 268.36

Number of lettuce boxes ≈ 268

Therefore, the supermarket should purchase 268 boxes of lettuce.

How to use z-table?

Step 1:

In the z-table, find the probability you are looking for and note down the two-digit number of the given row. (e.g 0.5, 2.2, 0.5 etc.)

Step 2:

Then look up at the top of z-table and note down the value in the column for the remaining decimal point in the range of 0.00 to 0.09.

Step 3:

Finally, add the numbers obtained from step 1 and step 2.

The equivalent sine and cosine values are as follows:

The relationship between sine and cosine angles is:

sinθ = cos(90 - θ)

This equation is known as the complementary angle identity for sine and cosine. It states that the sine of an angle is equal to the cosine of its complementary angle (90 degrees minus the original angle).

For example, if we have an angle theta = 30 degrees, its complementary angle would be 90 - 30 = 60 degrees.

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Out of the 400 surveyed students, 327 were either seniors or commuters.

To find the number of students who were either seniors or commuters out of the 400 surveyed students, we need to add the number of seniors and the number of commuters while avoiding double-counting those who fall into both categories.

According to the information given:

There were 262 seniors.

There were 215 commuters.

150 of the seniors were also commuters.

To avoid double-counting, we need to subtract the number of seniors who were also commuters from the total count of seniors and commuters.

Seniors or commuters = Total seniors + Total commuters - Seniors who are also commuters

= 262 + 215 - 150

= 327

Therefore, out of the 400 surveyed students, 327 were either seniors or commuters.

It's important to note that in this calculation, we accounted for the overlap between seniors and commuters (150 students who were both seniors and commuters) to avoid counting them twice.

This ensures an accurate count of the students who fall into either category.

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The distance to second base is approximately 127.28 feet. Round to the nearest hundredth

Since the angle is 45 degrees, the other side of the right triangle are equal, hence we have two sides of 90 ft to be used to find the hypotenuse

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 90² + 90²

x² = 16200

x = √16200

x = 90√2

x = 127.28 ft (to the nearest hundredth)

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When an isοsceles right triangle has a base οf x-2 and a height οf x-2. The area οf the triangle is 50 square inches then Using A=1/2 bh tο find the area οf a triangle is 1/2 (x-2)(x-2) = (x-2)²/2, and  12 inches is the value οf x?

An isοsceles right triangle has twο equal legs and the length οf the hypοtenuse is \(\sqrt{(2)\) times the length οf a leg. In this case, bοth legs have the length x-2, sο the length οf the hypοtenuse is (x-2)*sqrt (2).

The area οf the triangle is given by A=1/2 bh, where b is the base and h is the height. In this case, b=h=x-2, sο the area is:

A = 1/2 (x-2)(x-2) = (x-2)²/2

Area is 50, sο we can set up an equatiοn:

(x-2)²/2 = 50

Multiplying bοth sides by 2 gives:

(x-2)² = 100

Taking the square rοοt οn bοth sides gives:

x-2 = 10 οr x-2 = -10

The negative sοlutiοn dοesn't make sense in this cοntext, sο we discard it. Therefοre, we have:

x-2 = 10

Adding 2 tο bοth sides gives:

x = 12

Therefοre, the value οf x is 12 inches.

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When an isοsceles right triangle has a base οf x-2 and a height οf x-2. The area οf the triangle is 50 square inches then Using A=1/2 bh tο find the area οf a triangle is 1/2 (x-2)(x-2) = (x-2)²/2, and  12 inches is the value οf x.

An isοsceles right triangle has twο equal legs and the length οf the hypοtenuse is  times the length οf a leg. In this case, bοth legs have the length x-2, sο the length οf the hypοtenuse is (x-2)*sqrt (2).

The area οf the triangle is given by A=1/2 bh, where b is the base and h is the height. In this case, b=h=x-2, sο the area is:

A = 1/2 (x-2)(x-2) = (x-2)²/2

Area is 50, sο we can set up an equatiοn:

(x-2)²/2 = 50

Multiplying bοth sides by 2 gives:

(x-2)² = 100

Taking the square rοοt οn bοth sides gives:

x-2 = 10 οr x-2 = -10

The negative sοlutiοn dοesn't make sense in this cοntext, sο we discard it. Therefοre, we have:

x-2 = 10

Adding 2 tο bοth sides gives:

x = 12

Therefοre, the value οf x is 12 inches.

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If you don't know the value of sigma (population standard deviation), then you must use the T distribution instead of the Z distribution. However, if the sample size n is greater than 30, then the T distribution is approximately the same as the Z distribution.

This means that even if you don't know sigma, you can use the Z distribution if n > 30.

-----------------------------------

In short, you use T over Z if you don't know sigma and n = 30 or smaller

Answer
2 (9 x + 4 y)

Hope this helps :)

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

Option A is the correct answer.

We have,

The problem states that a student must work on i-Ready for at least 4 hours per month to receive a grade of 100.

Since Sophia received a math grade of 100, it means that she has met the requirement of working on i-Ready for at least 4 hours in the last month.

And,

The symbol "≥" means "greater than or equal to," indicating that Sophia worked for at least 4 hours.

Therefore,

The inequality that represents the number of hours Sophia spent working on i-Ready last month is h ≥ 4.

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Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

Answer:

2

Step-by-step explanation:

The first term is our fifrth and 13th is our 9th term in the new sequence. So each step has to be 2. 2 * 8 = 16

Applying the formula for the area of triangle using sine, we have:

sin A = 1/3 (A ≈ 19.5°).

Given that a triangle has the following parameters:

Area of triangle ABC = 21 square units

Side b = 14 units

Side c = 9 units

Thus, applying the area of a triangle using the sine rule, we have the following formula:

Area = 1/2 * b * c * sin A

Plug in the values:

21 = 1/2 * 14 * 9 * sin A

2 * 21 = 126 * sin A

42 = 126 * sin A

42/126 = sin A

sin A = 1/3

A = sin^(-1)(1/3)

A ≈ 19.5°

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ANSWER

x = 20

EXPLANATION

The equation given can be express as

y = 0.25x + 50

y = 0.30x + 40

Since, both equations are functions

Equate the two functions together

0.25x + 50 = 0.30x + 40

Collect the like terms

0.25x - 0.30x = 40 - 50

x(0.25 - 0.30) =-10

x(-0.5) = -10

-0.5x = -10

Divide both sides by -0.5

-0.5x / -0.5 = -10/-0.5

x = 10/0.5

x = 20

When collecting the like terms, we isolate values with the same variables from values with a different variables.

If a positive sign crosses an equality sign it automatically becomes a negative sign and if a negative sign crosses an equality operator it automatically becomes a positive sign

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

Answer:

Step-by-step explanation:

b 35

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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The length of segment AB is,

AB = 9 units

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

In triangle ADC,

AC = 9

AD = 16

Hence, We have;

Line l is divide the base AC in two equal parts.

Hence,

⇒ AB = AC

This gives,

AB = 9 units.

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\( \frac{7}{9} \times (8 \frac{3}{7} + 5 \frac{11}{14}) = \\ \)

\( \frac{7}{9} \times (8 \frac{6}{14} + 5 \frac{11}{14} ) = \\ \)

\( \frac{7}{9} \times (13 \frac{6 + 11}{14}) = \\ \)

\( \frac{7}{9} \times (13 \frac{17}{14}) = \\ \)

\( \frac{7}{9} \times (14 \frac{3}{14}) = \\ \)

\( \frac{7}{9} \times ( \frac{14 \times 3 + 3}{14}) = \\ \)

\( \frac{7}{9} \times ( \frac{42 + 3}{14}) = \\ \)

\( \frac{7}{9} \times ( \frac{45}{14}) = \frac{7 \times 45}{9 \times 14} = \frac{5}{2} \\ \)

_________________________________

And we're done.

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Answer:

\(\displaystyle \frac{199}{18}\)

Step-by-step explanation:

Fraction Operations

Before attempting to operate with the given fractions, we need to express all of them in the form a/b, because the last 2 fractions are in mixed form.

\(\displaystyle 8\frac{3}{7}=8+\frac{3}{7}=\frac{8*7+3}{7}=\frac{59}{7}\)

\(\displaystyle 5\frac{11}{14}=5+\frac{11}{14}=\frac{5*14+11}{14}=\frac{81}{14}\)

Now for the sum of the last two fractions:

\(\displaystyle \frac{59}{7}+\frac{81}{14}\)

Make both denominators equal by multiplying by 2 both parts of the first fraction:

\(\displaystyle \frac{59}{7}+\frac{81}{14}=\frac{118}{14}+\frac{81}{14}\)

\(\displaystyle =\frac{118+81}{14}=\frac{199}{14}\)

Now multiply by 7/9:

\(\displaystyle \frac{199}{14}*\frac{7}{9}=\frac{199}{18}\)

The value for the square root of 121 is 11.

We have,

The square root of 121 is 11.

To find the square root of 121, we can use a method called "prime factorization."

Begin by finding the prime factors of 121:

121 = 11 x 11

Since both factors are the same, we can pair them together:

11 x 11 = 11²

The exponent 2 indicates that the number 11 is repeated twice.

Therefore,

The value for the square root of 121 is 11.

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Answer:

18 T-shirts

Step-by-step explanation:

1gram = 1000milligrams

1gram × 156000milligrams ÷ 1000milligrams

The milligrams unit cancel out each other thus grams remains as the main unit.

=156grams

1 T-shirt = 156grams

1 T-shirt × 2808grams ÷156grams

The grams unit cancel out each other thus T-shirt remains as the main unit.

=18 T-shirts

Answer:

18

Step-by-step explanation:

The solution set for the quadratic equation (2x - 7)² = 25 is 6 and 1.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

The solution set for a quadratic equation is the roots of the quadratic equation.

Given, (2x - 7)² = 25.

2x - 7 = ± 5.

2x = ± 5 + 7.

x = (± 5 + 7)/2.

x = 12/2 Or 2/2.

x = 6 or 1.

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Answer:

Y(0,13)

X(13,0)

Answer:

nu tg hi yum

Step-by-step explanation: