Find an
expression which represents the sum of (-X – 7) and (-9x + 6) in
simplest terms.

Answer:

28% .................

Answer:

28%

Step-by-step explanation:

100%/x%=160/44.8

(100/x)*x=(160/44.8)*x       - we multiply both sides of the equation by x

100=3.5714285714286*x       - we divide both sides of the equation by (3.5714285714286) to get x

100/3.5714285714286=x

28=x

x=28

now we have:

44.8 is 28% of 160

Answer:36

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Turn the percent into a decimal (.90), then multiply by 40. 40 times .90 is 36.

The expression that can be used to approximate the expression below is\(log_a x = \frac{log_{b}a}{log_{b}x}\)

\(log_a x = \frac{log_{10}a}{log_{10}x}\)

This is similar to the option c where the base of "b" was used as \(log_a x = \frac{log_{b}a}{log_{b}x}\)

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Answer: C

Step-by-step explanation:

If you don't want to read it all

The number of combinations or ways to choose 8 non-defective and 2 defective parts from a group containing 24 non-defective and 9 defective parts is 13,860,776.

To solve this problem, we need to use the formula for combinations, which gives the number of ways to choose r items from a set of n items without regard to order. The formula is:

nCr = n! / r!(n-r)!

where n! is the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. The symbol ! denotes the factorial function.

Using this formula, we can find the number of ways to choose 8 non-defective parts from the 24 non-defective parts in the group:

24C8 = 24! / 8!(24-8)! = 735471

Similarly, we can find the number of ways to choose 2 defective parts from the 9 defective parts in the group:

9C2 = 9! / 2!(9-2)! = 36

Now we can combine these two values to get the total number of ways to choose 8 non-defective and 2 defective parts from the group:

(24C8 × 9C2) / 33C10 = (735471 × 36) / 193536720 = 13,860,776

Therefore, there are 13,860,776 ways to choose 8 non-defective and 2 defective parts from the given group of parts.

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We can estimate that approximately 35 gas stations sell a gallon of regular gas for no more than $2.01.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%". The percentage can be calculated by dividing the value by the total value and then multiplying the result by 100.

a) To find the percentage of gas stations that sell regular gas for less than $1.973, we need to calculate the z-score corresponding to this value:

z = (1.973 - 2.05) / 0.47 = -0.164

Using a standard normal distribution table or calculator, we can find that the percentage of gas stations selling regular gas for less than $1.973 is approximately 44.38%.

b) To find the percentage of gas stations selling regular gas for at least $2.17, we can calculate the z-score corresponding to this value:

z = (2.17 - 2.05) / 0.47 = 0.255

Using a standard normal distribution table or calculator, we can find that the percentage of gas stations selling regular gas for at least $2.17 is approximately 40.86%.

c) To find the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05, we can calculate the z-scores for each value:

z1 = (1.97 - 2.05) / 0.47 = -0.164

z2 = (2.05 - 2.05) / 0.47 = 0

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to each z-score:

P(z < -0.164) = 0.4364

P(z > 0) = 0.5 - 0.5(0) = 0.5

To find the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05, we can add these probabilities:

P(z < -0.164 or z > 0) = P(z < -0.164) + P(z > 0) = 0.4364 + 0.5 = 0.9364

Therefore, the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05 is approximately 93.64%.

d) To find the number of gas stations that sell regular gas for no more than $2.01, we can calculate the z-score corresponding to this value:

z = (2.01 - 2.05) / 0.47 = -0.085

Using a standard normal distribution table or calculator, we can find the probability corresponding to this z-score:

P(z < -0.085) = 0.4664

Multiplying this probability by the total number of gas stations (75), we can estimate the number of gas stations that sell regular gas for no more than $2.01:

0.4664 * 75 ≈ 35

Therefore, we can estimate that approximately 35 gas stations sell a gallon of regular gas for no more than $2.01.

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Complete question:

The price of a gallon of regular gasoline at 75 What percent of gasoline gas stations sell gallons of gas stations across the state is normally regular gas for less than $1.973 distributed with & a mean of $2.05 and a standard deviation of 47. b) What percent of gas stations sell a gallon? regular gas for at least $2.17? c) What is The probability that gas station sells gallons of regular gas for less than $1.97 or greater than $2.05? About how many stations sell a gallon of regular gas for no more than $2.01?

There are indeed 48 triangles that can be chosen from the rectangular array shown .

To find the 48 triangles, you should use the Combination formula which will show you the number of ways to pick 3 points when given 8 points.

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

C ( 8 , 3 ) = 8 ! / (3 ! x ( 8 - 3 ) ! )

C ( 8, 3 ) = 336 / 6

C ( 8, 3) = 56

Now, there are technically 56 ways to pick the points but some of these ways are collinear and these cannot form triangles. Each row will have 4 such points so the number of ways to pick triangles is:

= 56 - ( 4 x 2 )

= 48 triangles

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Answer:

y = -3

Step-by-step explanation:

Add 2 to each side to isolate the -3y. Doing this leaves you with -3y=9. You then divide each side leaving you with y = -3

Answer:

The equation has one solution at which y = -3.

Step-by-step explanation:

To find the value of y, we need to isolate it from the rest of the equation.

\(\displaystyle{-3y-2=7}\\\\-3y = 9\\\\\bold{y = -3}\)

We can check to make sure that y = -3 by substitution.

\(\displaystyle{-3(-3)-2 = 7}\\\\9-2=7\\\\7= 7 \ \checkmark\)

Because we got a true statement, we can determine that y = -3.

Given that Ben bowled 134 and 213 at his first two games.

Let Ben bowled x in his third game, then the average of his three bowling would be

If Ben has an average of at least 160, then the value of x is as calculated below:

Hence, Ben must bowl at least 133 to have an average of at least 160

Answer:

See below

Step-by-step explanation:

Use the roots given to make this :

(x+3) (x-1/2)  = 0

   you can do the multiplication (if required) to get

x^2 + 2.5x - 1.5 = 0      now you can multiply by 2 to get rid of the decimals

2x^2 + 5x - 3 = 0

   All three are correct......pick the format you want ....

====================================================

Explanation:

Set each factor equal to zero and solve for x. I'm using the zero product property which says A*B = 0 leads to either A = 0 or B = 0.

Let's apply that idea to the first factor.

x^2+4x+3 = 0

(x+1)(x+3) = 0

x+1 = 0 or x+3 = 0

x = -1 or x = -3  are two roots

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

Do the same for the other factor as well.

x^2 - 4 = 0

(x-2)(x+2) = 0  .... difference of squares rule

x-2 = 0 or x+2 = 0

x = 2 or x = -2  are another two roots

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

In total, the four roots are:

Side note: The term "root" is the same as the zeros of a polynomial. Visually, this corresponds to the x intercepts. Plugging any of those four items into p(x) will lead to p(x) = 0.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

In the Social Exchange Theory of interpersonal relationship satisfaction, you would feel happiest in relationships when you feel that the rewards of the relationship equal or exceed its costs.

The Social Exchange Theory states that people evaluate their relationships in economic terms, with rewards being the benefits of the relationship and costs being the negatives. Rewards can include affection, attention, emotional support, sex, and companionship. Costs can include time, effort, money, and negative emotions such as stress, anxiety, and sadness.

According to the theory, individuals will be motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

The opposite is also true; if individuals feel that the costs of the relationship are greater than the rewards, they will be motivated to leave the relationship.

Therefore, people are constantly evaluating their relationships to determine whether they are getting what they need from the relationship and whether it is worth continuing.

The Social Exchange Theory of interpersonal relationship satisfaction suggests that individuals are motivated to stay in a relationship as long as they feel that the rewards of the relationship are greater than the costs.

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The wooden made triangle is that it is a Isosceles Right Angled Triangle

Triangle: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted ΔABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

it is given that a piece of wood is cut into a triangle with sides that measure 17 cm , 17cm and 24cm the angles of the triangle measure 45 degrees, 45 degrees, and 90 degrees.

sides of the triangles=17 cm , 17cm and 24cm

two sides are equal so we can say it is an isosceles triangle

because isosceles triangle has two equal measured sides

if we get into the angles of that triangle they are 45 degrees, 45 degrees, and 90 degrees.

triangle with 90 degrees angle is called as right angled triangle

so we can finally conclude about the wooden made triangle is that it is a Isosceles Right Angled Triangle

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The triangle is made of wood and is an isosceles right triangle.

What does Triangle mean?

A triangle is a polygon that has three vertices and three edges. It is one of the fundamental geometric shapes. The symbol for a triangle containing the vertices A, B, and C is ABC. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Given that a piece of wood is carved into a triangle with sides that measure 17, 17, and 24, and angles that measure 45, 45, and 90 degrees, the triangle's dimensions are as follows.

triangles have sides of 17, 17, and 24 cm.

It is an isosceles triangle since its two sides are equal.

since an isosceles triangle has two sides with equal lengths

When it comes to that triangle's angles, they are 45, 45, and 90 degrees.

Right-angled triangles are triangles with an angle of 90 degrees.

Finally, we may say that the triangle is an isosceles right triangle because it is composed of wood.

The correct answer is: making it harder to reject H0.

By selecting a smaller alpha level (significance level), the researcher is increasing the threshold for rejecting the null hypothesis (H0). This means that stronger evidence is required to reject H0 and conclude that there is a significant treatment effect or difference. A smaller alpha level makes it harder to reject the null hypothesis because it reduces the chance of making a Type I error (incorrectly rejecting H0 when it is true). Type I error is the risk of concluding there is a significant effect or difference when there is none in the population. Therefore, selecting a smaller alpha level improves the ability to control the risk of Type I error, but it also makes it more difficult to detect a treatment effect.

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1. The Complete table is shown below.

2. The graph likes like parabola whose equation is y= 50x - x².

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve. The topic of conic sections includes parabola, and all of its principles are discussed here.

Given:

Length  Width  Area

10            40      400

20             30      600

25             25       625

35             15        525

40              10       400

So, x+ y= 50

y= 50- x

so, area of figure is

= x (50- x)

= 50x - x²

So, we get parabola which is opened downward.

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Answer:

Answer would be 7.

Step-by-step explanation:

5 x 7 = 35

Answer:

\(6n - 5\)

Step-by-step explanation:

\(7 - 1 = 6\)

\(6n - 5\)

to check whether your answer is correct.

\(n = 1 \\ 6 \times 1 - 5 \\ 6 - 5 \\ = 1\)

\(n = 2 \\ 6 \times 2 - 5 \\ 12 - 5 \\ = 7\)

yes, it's correct

hope this helps you

The determination of the method of the painting will be done according to the cost of painting each method incurs.

To determine which painting method is cheaper, you will need to consider the following values:

A: $8.99, the cost of primer per gallon

B: $15.99, the cost of paint per gallon

C: $26.99, the cost of special paint per gallon

G: 200 square feet, the coverage of primer per gallon

H: 400 square feet, the coverage of paint and special paint per gallon

L: 1964 square feet, the total wall space to be painted

D: 15 hours, the estimated time for the special paint method

E: 30 hours, the estimated time for the primer and paint method

Using these values, you can calculate the cost and time for each method and compare them to determine which one is cheaper.

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The probability that Peter will pass the quiz is given by the option 3: 0.0035

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

\(X \sim B(n,p)\)

The probability that out of n trials, there'd be x successes is given by

\(P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

For the considered case, the problem's statement is missing some facts.

They are:

Number of multiple choice questions in test = 10

Peter uses guessing for answering the questions.

To pass the test, Peter needs to get at least 7 correct answers.

Some probabilities on left are:

Let X be the number of questions peter gets correct in his test.

Then, the probability that he will pass the test is denoted as:

\(P(X \geq 7)\)

This can be rewritten as:

\(P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\\P(X \geq 7) =0.0031 + 0.000386 + 0.0000286 + 0.000000954 = 0.003515554\)

This is approximately 0.0035

Thus, the probability that Peter will pass the quiz is given by the option 3: 0.0035

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We need to multiply the numerator and denominator by 3-√5 to rationalize the denominator of the fraction. Therefore, the correct answer is option B

To rationalize the denominator of the fraction 6−2√3+√5, we need to eliminate any radicals present in the denominator. We can do this by multiplying both the numerator and denominator by an expression that will cancel out the radicals in the denominator.

In this case, we can observe that the denominator contains two terms with radicals: -2√3 and √5. To eliminate these radicals, we need to multiply both the numerator and denominator by an expression that contains the conjugate of the denominator.

The conjugate of the denominator is 6+2√3-√5, so we can multiply both the numerator and denominator by this expression, giving us:

(6−2√3+√5)(6+2√3-√5) / (6+2√3-√5)(6+2√3-√5)

Simplifying the numerator and denominator, we get:

(6 * 6) + (6 * 2√3) - (6 * √5) - (2√3 * 6) - (2√3 * 2√3) + (2√3 * √5) + (√5 * 6) - (√5 * 2√3) + (√5 * -√5) / ((6^2) - (2√3)^2 - (√5)^2)

This simplifies to:

24 + 3√3 - 7√5 / 20

Therefore, the correct answer is option B.

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Part A:

Best graphical representation to display data will be line graph.

Given,

Scores of basketball team during the first 13 games of the season

{85, 94, 101, 118, 107, 110, 114, 96, 117, 105, 121, 88, 125}.

Now.

Part B:

We can create line graph with a very simple technique.

Firstly,

On x - axis take the number of season the team has played. In our case the number is 13 so take 13 distinct points on the x - axis.

Secondly,

On y -axis take the scores of the team in each of the 13 seasons corresponding to their values at x - axis.

Then,

Plot the points on the graph for all 13 seasons .

Last step,

Join all the points in the graph with the help of ruler. This will form the required line graph of the question.

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x = 8

Step-by-step -e-x-p-l-a-n-a-t-i-o-n- below

The angles shown are vertical angles

Vertical angles are congruent (equal to each other)

This means that 8x + 36 = 5x + 60

Using this equation we can solve for x

8x + 36 = 5x + 60  

==> subtract 36 from both sides

8x = 5x + 24

==> subtract 5x from both sides

3x = 24

==> divide both sides by 3

x = 8

Answer:

\(\huge\boxed{\sf x = 8}\)

Step-by-step explanation:

8x + 36 = 5x + 60 (Vertically opposite angles are equal)

Subtract 5x to both sides

8x - 5x + 36 = 60

3x + 36 = 60

Subtract 36 to both sides

3x = 60 - 36

3x = 24

Divide 3 to both sides

x = 24/3

\(\rule[225]{225}{2}\)

Answer:

Hello! answer: 22

Step-by-step explanation:

10 + 2 + 2 × 5 = 22 HOPE THAT HELPS!

Answer:

28

Step-by-step explanation:

The T-Shirts are 5.

The Socks are 2.

The Ties are 10.

The last image shows 1 tie, 3 socks twice and a t-shirt.

10 + 3 + 3 · 5 = 28

An Experiment is repeated 10 times compared to just 3 times, the results from the 10 repetitions would generally be considered more reliable.

True.

In general, conducting an experiment multiple times increases the reliability of the results. The more times an experiment is repeated, the greater the opportunity to collect data and observe patterns or trends. This allows for a more robust analysis and reduces the impact of random variations or errors that may occur in a single trial.

When an experiment is repeated multiple times, it helps to reduce the effects of outliers or anomalies that may occur in a single trial. By averaging the results over multiple repetitions, the overall outcome tends to be more representative and reliable.

In the context of statistical analysis, increasing the sample size (number of repetitions) can lead to more precise estimates of parameters and reduce the margin of error. It provides a better understanding of the underlying phenomenon being studied and allows for more confident conclusions.

Therefore, if an experiment is repeated 10 times compared to just 3 times, the results from the 10 repetitions would generally be considered more reliable. The larger sample size provides a stronger basis for drawing conclusions and making inferences about the population or phenomenon under study.

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The length of the smallest part of the line segment is 12 cm.

The line segment of length 96 cm is divided into 3 parts with the ratio of 2:9:5. The given ratio is a part-to-whole ratio. We can find the lengths of the parts by applying the formula:

Part = Whole × Ratio

Part 1 = 96 cm × (2/16)

= 12 cm

Part 2 = 96 cm × (9/16)

= 54 cm

Part 3 = 96 cm × (5/16)

= 30 cm

Therefore, the length of the smallest part of the line segment is 12 cm.

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Answer:

x = -48

Step-by-step explanation:

The equation is,

→ x/4 = -12

Let's solve for the value of x,

→ x/4 = -12

→ x = -12 × 4

→ [ x = -48 ]

Hence, the value of x is -48.

The average time a molecule spends in its reservoir is known as the residence time.

Residence time is an important concept in environmental science, particularly in the study of water quality and pollution. It refers to the average amount of time that a substance, such as a molecule or a pollutant, spends in a particular environment before it is either removed or transformed. For example, in a river, the residence time of a pollutant would be the amount of time it takes for that pollutant to be either broken down by natural processes or transported downstream to another location. By understanding residence time, scientists can better predict how pollutants will move through the environment and where they are likely to accumulate.

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To find the length of the diagonal of square C, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Since square C has equal sides, we only need to find the length of one side and then multiply it by the square root of 2 to get the length of the diagonal.

Using the coordinates given, we can find the length of one side by subtracting the x-coordinate of one vertex from the x-coordinate of the other vertex (11 - 1 = 10). We then multiply this by the conversion factor given in the problem (1 square unit = 25 feet) to get the length in feet (10 * 25 = 250). Finally, we multiply this by the square root of 2 to get the length of the diagonal (250 * sqrt(2) ≈ 353.55 feet).

Therefore, if square C has an area of 2500 square units and each unit is equal to 25 feet, then a square with a diagonal length of approximately 353.55 feet would be an accurate representation of square C.

Answer:

Least common denominator is 120.

5/8 = 75/120

-11/15 = -88/120

17/(-24) = -85/120

7/12 = 70/120

75 > 70 > -85 > -88

5/8 > 7/12 > 17/(-24) > -11/15

Step-by-step explanation:

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