______1. 2 + 3 = 9 ______2. 4 > 5 + 7 ______3. 9 = 12 + 2 ______4. 2 − 3 ≥ 2 ______5. 61 ≠ 5 − 12

The three lowest values of x are 30, 31 and 32.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

The statement "x is a whole number if three quarters of x is subtracted from 62. the result is less than 40" can be written as:

62 - (3/4)x < 40

- (3/4)x < 40 - 62

-3x/4 < -22

-3x < -22 × 4

-3x < -88

x > -88/-3

x > 29.33

Since x > 29.33 and x is a whole number, the three lowest values of x are 30, 31 and 32.

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a) 2,4,8 b) 1,3,9

A has a total sum of 16, and B has a total sum of 13.

Answer:

The new slope is 1 and the line is shifted flatter.

Step-by-step explanation:

Line A slope is 4.

Line B slope is 1.

The y-intercept rose up 3

As far as slope, it became flatter because the line only rises 1 'square' for every 1 'square' it travels to the right. It was rising 4 'squares' for every 1 to the right.  

The yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

To calculate the yearly deposits needed, we can use the concept of future value of an annuity. The future value formula for an annuity is given by:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity

P = Yearly deposit amount

r = Interest rate per period

n = Number of periods

In this case, the future value needed is $2 million, the interest rate is 8% (0.08), and the number of periods is 30 years. We need to solve for the yearly deposit amount (P).

Using the given formula:

2,000,000 = P * [(1 + 0.08)^30 - 1] / 0.08

Simplifying the equation:

2,000,000 = P * [1\(.08^3^0 -\) 1] / 0.08

2,000,000 = P * [10.063899 - 1] / 0.08

2,000,000 = P * 9.063899 / 0.08

Dividing both sides by 9.063899 / 0.08:

P = 2,000,000 / (9.063899 / 0.08)

P ≈ 2,000,000 / 113.298737

P ≈ 17,650.23

Therefore, the yearly deposit needed to achieve the retirement goal is approximately $17,650.23. None of the given options match this amount, so the correct answer is not provided in the given options.

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The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

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

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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The probability that the difference between the sample means will be within 0.05 units of the difference between the population means μ₁ − μ₂ is required.

a) The difference between the sample means, X - Y, is approximately normally distributed with mean μ₁ − μ₂ and variance (σ₁²/n₁) + (σ₂²/n₂), where σ₁² and σ₂² are the variances of populations A and B, respectively. In this case, σ₁² = 0.01 and σ₂² = 0.02. The probability can be found by calculating the area under the normal distribution curve between -0.05 and 0.05. Using the known parameters and the z-score formula, the probability can be determined.

b) If n₁ = n₂ = n, the variance of the difference between the sample means is (σ₁²/n) + (σ₂²/n) = (0.01/n) + (0.02/n). We want this variance to be within 0.04 units with a probability of 0.9. By setting up the appropriate equation and solving for n, we can find the required sample size that satisfies this condition.

The calculations involve applying the properties of the normal distribution and solving equations to find the desired probabilities and sample sizes.

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Step-by-step explanation:

(18x-44) is x and the answer is: -792

and (13 y -38) you would have to Remove the parentheses.

Answer:

(x + 3)² + (y - 5)² = 20

Step-by-step explanation:

Equation of a circle is (x - a)² + (y - b)² = r²,

where a is the x-coordinate of the centre of the circle, b is the y-coordinate of the centre of the circle, r is the circle's radius.

so we have  (x - -3)² + (y - 5)² = r²

(x + 3)² + (y - 5)² = r²

r = the line from (1,7) to (-3, 5).

length of this is √[(-3 - 1)² + (5 - 7)²]

= √(16 + 4)

= √20

so r² = (√20)² = 20.

equation of circle is  (x + 3)² + (y - 5)² = 20

Answer:

18, 36, 54

Step-by-step explanation:

Find the least common multiple of 6 and 9:

Multiples of 6: 6, 12, 18, ......

Multiples of 9: 9, 18, 27, ......

We see that 18 is the least common multiple of 6 and 9.

Additional multiples of 18 are 36 and 54.

If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.

Consider the statement as a contradiction.

The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.

Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product \($2 \times 3 \times 3=18$\) exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of \($2 \times 2 \times 3 \times 3=36$\) which exists also not divisible by 54.

Therefore, the correct answer is option e) 54.

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Answer:

Each angle measures 90 degrees.

Step-by-step explanation:

By definition, in a square, each angle measure is 90 degrees, and all side lengths are equal lengths.

I hope this helps!

In a post office, the mailboxes are numbered from 61001 to 61099. These numbers represent quantitative data. The correct answer is A. quantitative data.

The post office mailboxes are numbered from 61001 to 61099. These numbers represent quantitative data. Quantitative data is defined as data that is numerical in nature and can be quantified or measured.

It is a type of data that can be easily calculated and evaluated by performing mathematical operations such as mean, median, mode, standard deviation, etc. Because these mailboxes are numbered sequentially, the data is still considered quantitative because they represent numerical values.

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Given:

The expression is

\(0.3+0.6ab+0.5b\)

To find:

The terms and the coefficients.

Solution:

In an expression, the variables, constants and product of variable and constant separated by positive sign "+" are called terms.

We have,

\(0.3+0.6ab+0.5b\)

Here, the terms are 0.3, 0.6ab and 0.5b. The coefficients of variables are 0.6 and 0.5 respectively and 0.3 is a constant.

Answer:

  no; the weight is greater than 600 lbs

Step-by-step explanation:

You want to know if a 4' by 2' by 2' aquarium filled 80% with water at 62 lb/ft³ should be placed on a table with a capacity of 600 lb.

The weight of the aquarium water will be its volume multiplied by its density. The volume is 80% of the product of the aquarium dimensions, so the weight of the water is ...

  (4 ft)(2 ft)(2 ft)(0.80)(62 lbs/ft³) = 793.6 lbs

This weight is somewhat greater than the maximum weight the table will support. The aquarium should not be placed on the table.

__

Additional comment

If the aquarium were filled to 60% capacity, the weight of the water would be about 595 lb. The table could support that with no safety margin. The weight of the aquarium itself, and any rocks or other decoration placed in it could cause the capacity of the table to be exceeded.

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Answer:

Scalene triangle or right scalene triangle is correct

Step-by-step explanation:

The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.

a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.

b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.

c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.

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There are 1540 ways can five members be selected for a search and rescue mission such that at least one officer is included.

What is a combination?

Combinations are mathematical operations that count the variety of configurations that can be made from a set of objects, where the order of the selection is irrelevant. You can choose any combination of the things in any order.

Formula to calculate combination

ⁿCₓ = n!/x!(n-x)!

Here, we have

The total count of members is 14.

The total number of officers is 3.

So, the count of non-officers will be

14−3 = 11

Now, 5 members are selected including at least one officer. So, the count of officers and non-officers in the team of 5 members is as follows:

(a) 1 officer and 4 non-officers

(b) 2 officers and 3 non-officers

(c) 3 officers and 2 non-officers

To find the ways for each of the three cases above, we use combinations

ⁿCₓ = n!/x!(n-x)!

where

n: is the total count of objects and

x: is the count of selected objects.

Number of ways when 1 officer and 4 non-officers can be selected, we have possible combinations

³C₁ ×¹¹C₄ = 3!/1!(3-1)! × 11!/4!(11-4)!

              = 3!/2! ×  11!/4!(7)!

              = (3 × 2!)/ 2!  × (11×10×9×8×7!)/(4! × 7! )

             =  3 × (11×10×9×8)/(4×3×2×1)

             =  990

Number of ways when 2 officers and 3 non-officers can be selected, we have possible combinations

³C₂ ×¹¹C₃ = 3!/2!(3-2)! × 11!/3!(11-3)!

              =  3!/2! ×  11!/3!(8)!

              =  (3 × 2!)/ 2!  × (11×10×9×8!)/(3! × 8! )

               =  3 × (11×10×9)/(3×2×1)

              = 495

Number of ways when 3 officers and 2 non-officers can be selected, we have possible combinations

³C₃ ×¹¹C₂ = 3!/3!(3-3)! × 11!/2!(11-2)!

              =  1! ×  11!/2!(9)!

              = 1 × (11×10×9!)/(2! × 9! )

               = 55

The total number of ways when 5 members can be selected including at least one officer is calculated as follows:

³C₁ ×¹¹C₄+ ³C₂ ×¹¹C₃+ ³C₃ ×¹¹C₂ = 990 + 495 +55 = 1540

Hence, there are 1540 ways can five members be selected for a search and rescue mission such that at least one officer is included.

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From given data:

The number of blocks that could fit in one box is:

Now the number os blocks could fit in three box is:

Answer:

x = 2, 4

Step-by-step explanation:

Hi there!

x=√(2x-4)+2

Move 2 to the left:

x-2 = √(2x-4)

Square both sides:

x²-4x+4 = 2x-4

Combine like terms:

x²-6x+8 = 0

Factor:

(x-2)(x-4) = 0

Therefore, x = 2, 4.

I hope this helps!

The consumer testing group has confirmed that the samples were randomly selected and independent, and the populations have normal distribution and the population variances are equal and test Statistic for this example is 8.90b and the P-value for this example is 0.011

The null hypothesis and alternative hypothesis are:H0: μ1 = μ2 = μ3HA: At least one μi differs from the rest of the means.The level of significance is α = 0.05The test statistic used for this example is the F distribution (ANOVA).a. Calculation of the Test Statistic:

Test Statistic = MSR / MSEWhere,MSR = mean square due to regression = SSTR / 2 = 190.66MSE = mean square due to error = SSE / 12 = 21.43Therefore, the test statistic F = MSR / MSE = 8.90b.

Calculation of the P-value:P-value = P(F > 8.90)The degrees of freedom for numerator is k-1 = 3 - 1 = 2 and the degrees of freedom for the denominator is N-k = 15 - 3 = 12.The p-value of the F distribution with 2 and 12 degrees of freedom at 5% level of significance is 0.011. Therefore, P-value < α.

Thus, we reject the null hypothesis. We conclude that at least one μi differs from the rest of the means. Therefore, the average battery lifetimes are not statistically the same for the three brands.

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an angle in radians corresponding to 0.25 rotations around the unit circle is π/2 radians or 90 degrees.

An angle in radians corresponding to 0.25 rotations around the unit circle is π/2 radians or 90 degrees.π radians correspond to a half-turn and the whole turn is 2π radians, which is 360 degrees. Therefore, 0.25 rotations around the unit circle is equal to 0.25*2π radians, which is equal to π/2 radians.

However, if you need a 100-word answer, here's a more detailed explanation:

In trigonometry, the unit circle is a circle with a radius of one unit that is centered at the origin of a Cartesian plane. The unit circle is an essential tool for understanding the relationships between the angles in trigonometry and the values of the trigonometric functions of those angles. An angle in radians corresponding to 0.25 rotations around the unit circle is a quarter of a turn around the circle. A full turn is 2π radians, which corresponds to 360 degrees. Thus, 0.25 rotations are equal to 0.25*2π radians, which is equal to π/2 radians. Therefore, an angle in radians corresponding to 0.25 rotations around the unit circle is π/2 radians or 90 degrees.

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Answer:

fh. = 40h + 120,  fh. = $200

200 = 40h + 120

200 - 120 = 40h

80 = 40h

80/40  = h

 2 = h

h = 2 hours.

Step-by-step explanation:

Assuming question is:

3(0)= -2x+9

and we have to solve for x:

0 = -2x + 9

We take x to one side, so it becomes:

2x = 9

Now we divide by 2 on both sides:

2x/2 = 9/2

x = 9/2

The correct answer is:

6x+16=136[vertically opposite angle]

6x=136-16

6x=120

X=120/6

X=20

Answer:

$37.50

Step-by-step explanation:

22 x 2.50 = 55

92.50 - 55 = 37.5

the purchase of the burgers cost

$37.50

(im not sure if its correct tho so im sorry if im wrong)

Example of perfect square trinomial is: x² + 6x + 9 it is expressed as

(x + 3)²

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Example:

  x² + 6x + 9

= x² + 3x + 3x + 9

= (x +3) (x + 3)

= (x + 3)²

so, this is a perfect square trinomial.

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The solutions to the trigonometric equation:

cos(x)*(cos(x) - 1) = 0

Are the ones in option B;

x = ± n*π , π/2 ±  2πn,  3π/2 ±  2πn

Where n is a natural number.

Here we have the trigonometric equation:

cos(x)*(cos(x) - 1) = 0

Remember that a product A*B = 0 either if A or B (or both) are equal to zero, so the solutions of the given equation are the values of x such that:

cos(x)=  0

cos(x) - 1 = 0

The solution of the first one is trivial, it is just π/2 and  3π/2

And for the second one:

cos(x) - 1 = 0

cos(x) =1

The solutions are x = 0 and x =  π

Now we can extend that tho the whole range by writting:

x = ± n*π for the second equation.

x = π/2 ±  2πn   and   3π/2 ±  2πn  for the first equation.

That is what we can see in option B.

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Answer:

1.......c

2.....a

3.....b

4......e

5.....d

Because of the size of the black section,