What word is missing from this true mathematical statement: Twelve is congruent to 60 ______ 8 because both 12 and 60 have 4 as a remainder when divided by 8?

The statement "the leftmost end point of a line segment must be specified as the start point of the line." is true because it extends infinitely in both directions and does not have a starting or ending point.

To specify a line segment, we must indicate the points that define its endpoints. The leftmost endpoint of a line segment is significant because it establishes the relative position of the segment in space.

Furthermore, it is essential to remember that the order of the endpoints of a line segment matters. Reversing the order of the endpoints changes the direction of the line segment. For instance, the line segment AB is not the same as the line segment BA.

Therefore, specifying the leftmost endpoint is critical because it establishes the direction of the line segment.

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Answer:

So we know that if we have an unknown variable that is not stated in the question we can always say Meg buys X vintage T-shirts.

The cost of X vintage T-shirts can be expressed as 16X.

Meg's remaining birthday money after purchasing X vintage T-shirts may be computed by subtracting the cost of the T-shirts from the total amount of birthday money received:

Amount of money Meg has left = Total amount of birthday money - Cost of X vintage T-shirts

= $200 - $16X

So, the function that describes the amount of birthday money Meg has left after purchasing X vintage T-shirts is:

f(X) = $200 - $16X

This is a linear function with a negative slope of -16, indicating that the amount of money Meg has left decreases as she buys more T-shirts.

The vertical angle theorem and the angle addition postulate indicates;

m∠PMK = 39°

m∠NMP = 18°

Vertical angles are the non adjacent angles formed when two lines or line segment intersect.

The measures of the angles are;

m∠JMG = 39°

m∠LMN = 72°

∠PMK and ∠JMG are vertical angles, therefore;

∠PMK ≅ ∠JMG (Vertical angles theorem)

m∠PMK = m∠JMG = 39°

∠LMP = ∠LMN + ∠NMP (Angle addition property)

The angle marking indicates that the measure of the angle m∠LMP = 90°, therefore;

m∠LMP = m∠LMN + m∠NMP

90° = 72° + m∠NMP

m∠NMP = 90° - 72° = 18°

m∠NMP = 18°

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Answer:

42

Step-by-step explanation:

[tex]48° + x = 90(angle \: at \: a \: right \: angle)[/tex]

[tex]therefore \: x = 90°- 48°\\ = 42°[/tex]

Answer:

B = 42

Step-by-step explanation:

B + 48 = 90 ... because they are complement angles

B = 90 - 48

B = 42 ...... so the unknown angle is 42

The equation of the line that passes through the points (6.4, 2.6) and (5.2, 9) is y = 5.333x - 30.178

To find the equation of the line that passes through the points (6.4,2.6) and (5.2,9), we need to determine the slope (M) of the line and the y-intercept (b).

The slope of a line can be found using the formula

M = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

Using the points (6.4, 2.6) and (5.2, 9), we have:

M = (9 - 2.6) / (5.2 - 6.4)

M = (-6.4) / (-1.2)

M = 5.333

Now, we can use the point-slope form of the equation of a line, which is

y - y₁ = M(x - x₁)

where (x₁, y₁) is any point on the line and M is the slope we just calculated.

We can choose either point (6.4, 2.6) or (5.2, 9) as (x₁, y₁). Let's use (6.4, 2.6)

y - 2.6 = 5.333(x - 6.4)

Simplifying, we get:

y = 5.333x - 30.178

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"How many times have you been to the library in the last month?" is an example of a natural metric response format. So option (b) is true.

A natural metric field format. Natural metric and synthetic metric types.

Natural measure response format, the respondent specifies the category name that best describes it. The five response groups are generally considered to represent assessment levels. Natural Metric Scales measure things that have quantity in them. Synthetic metrics are metrics that use human definitions or numbers. We have a metric response type problem when the response is a number that represents how much of the behavior is being measured. Accordingly, the correct answer is option (b).

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Complete question:

How many times have you visited the library in the last month?" is an example of:

a) A natural but non-metric response format.

b) A natural metric response format.

c) A natural synthetic response format.

d) A synthetic metric format.

Answer:

A, B, C, D

Step-by-step explanation:

First of all, logically, an exponential function should change faster than a linear function (linear functions increase/decrease at a constant rate while exponential functions increase/decrease at an increasing/decreasing rate). Thus, if an exponential function is growing, it increases faster than a linear function at one point. Also, looking at all of the graphs, note how every exponential function is able to surpass the linear function in height (y-values). This also shows how all of the exponential functions will exceed the linear functions.

Factoring the expression -48x gives 2⁴ * 3 * -x

From the question, we have the following parameters that can be used in our computation:

-48x

Expand -48

So, we have

-48x = -2 * 2 * 2 * 2 * 3 * x

Express 2 as exponent expression

So, we have

-48x = 2⁴ * 3 * -x

Hence, the factored expression is 2⁴ * 3 * -x

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For a sample of rating of an automobile manufacturer's van regarding rating of 28.3 miles/gallon (mpg), the Z-test statistic value is equals to the -1.631.

Z-test is a parametric test. When the sample size is sufficiently large, it is mostly used. This test statistic is computed a standard normal distribution. It is then compared with the critical value (obtained from z-table). If the test statistic value is greater than it, there is evidence to reject the null hypothesis. We have an automobile manufacturer with its van rating. A sample of 200 vans is randomly considered. Sample size, n = 200

Mean of rating = 28

Standard deviations = 2.6

Lavel of significance= 0.01

To test the firm'claim we have to consider hypothesis testing here. Since it is claimed by an automobile manufacturer that its car has a 28.3 miles/gallon (MPG) rating, therefore, the null hypothesis and alternative can be stated as:

[tex]H_0 :μ = 28.3[/tex]

[tex]H_a :μ≠28.3[/tex]

Now, to determine the value of the test statistic, consider the Z-test : [tex] z = \dfrac{{M - \mu }}{{\dfrac{\sigma }{{\sqrt n }}}}[/tex]

where, M -> mean

n --> sample size

Substitute all known values in above formula, [tex]= \dfrac{{28 - 28.3}}{{\dfrac{{2.6 }}{{\sqrt {200} }}}}\\[/tex]

[tex]= \dfrac{{-0.3}}{{\dfrac{{0.26 }}{{\sqrt {2} }}}}\\[/tex]

=> z = - 1.631

Hence, required test statistic value is -1.631.

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Answer:

4.32 cm

Step-by-step explanation:

let x = scale length of the car

1/100 = x/4.32

100x = 4.32

x = 4.32/100 = 0.0432 m

convert to m to cm:  0.0432 m x 100 cm/m = 4.32 cm

A seasonality index of 0.7 for the summer season means that the company's demand during the summer is 70% of the average demand for all seasons.

The seasonality index is a tool used by businesses to analyze the variations in demand during different periods. It measures how the demand for a particular season compares to the average demand for all seasons. An index value above 1 indicates higher than average demand, while a value below 1 signifies lower than average demand. In this case, a seasonality index of 0.7 implies that the company experiences 30% lower demand during the summer compared to the average demand across all seasons.

The company should be aware of the lower demand during the summer season and plan its production, inventory management, and marketing strategies accordingly to maximize efficiency and profitability.

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The Senate minority leader was younger relative to their group (with a mean age of 62 and standard deviation of 10 years) as they were 66 years old.

To determine which leader was older relative to their group, we need to calculate the number of standard deviations away from the mean age for both the Senate minority leader and the House of Representatives minority leader. This is also known as the z-score. Here are the steps:

Step 1: Calculate the z-score for the Senate minority leader.

z = (age of the leader - mean age of the group) / standard deviation of the group

z = (66 - 62) / 10

z = 4 / 10

z = 0.4

Step 2: Calculate the z-score for the House of Representatives minority leader.

z = (age of the leader - mean age of the group) / standard deviation of the group

z = (76 - 58) / 11

z = 18 / 11

z = 1.64

Step 3: Compare the z-scores.

The House of Representatives minority leader has a higher z-score (1.64) compared to the Senate minority leader (0.4).

Therefore, Relative to their group, the House of Representatives minority leader was older.

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Relating to their group, the House Minority Leader is older than the Senate Minority Leader. The z-score calculation used allows for comparative analysis across different groups.

To determine which leader is older relative to their group, we need to compute their z-scores. A z-score defines the number of standard deviations a given data point is from the mean. A higher z-score means an above-average age relative to their group, and a lower z-score implies below-average age relative to the group.

For Senate Minority Leader, z-score = (66 - 62) / 10 which equals to 0.4.

For House Minority Leader, z-score = (76 - 58) / 11 which equals to approximately 1.64.

Given that the House Minority Leader has higher z-score, they are older relative to their group compared to the Senate Minority Leader.

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The factor of the given expression 2x²+13x+15 will be (2x+3)(x+5).

To express equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need to factor the expression into an equivalent form 2x²+13x+15

This expression could also be given by;

2x²+13x+15

We know that if D≥0, then trinomial 'ax²+bx+c' can be written in form a(x-x1)(x-x2),

where x1 and x2 - roots of ax²+bx+c=0.

Then D=b²-4ac=13²-15*2*4=49,

2x²+13x+15

Factor =2(x+5)(x+1.5)

The answer is: (2x+3)(x+5).

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The expression is represented as 5x - 44

Algebraic expressions are simply described as expressions that are composed of terms, coefficients, constants, factors, and variables.

Algebraic expressions are also known to be composed of mathematical operations.

These operations are given thus;

From the information given, we have that;

difference when (2x-6) is subtracted from (7x-50

This is represented as;

7x - 50 - (2x - 6)

expand the bracket

7x - 50 - 2x + 6

collect the like terms

5x - 44

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Solving:

The equation for a graph is in the format: y = mx + b, so let's get this equation in that format, by solving for y.

4x - 2y = 24

-4x          -4x

-2y = -4x + 24

/-2     /-2    /-2

y = 2x - 12

Answer:

Therefore, the slope is 2, or 2/1, and the y-intercept is -12.

If I helped, pls make this answer brainliest, it helps a lot! ;)

a. The sample proportion will be approximately equal to the proportion of boys born in the population, which is 0.512.
b. The shape of the distribution will also become more symmetrical as the sample size increases.


a. The mean of the sample proportion can be found using the population proportion. In this case, the population proportion (p) is 0.512. Since we are randomly selecting 100 births each day, our sample size (n) is 100. The mean of the sample proportion (µ) is equal to the population proportion (p), so µ = p = 0.512.

b. The distribution of the sample proportion will have a bell shape if it follows the Central Limit Theorem. For this to be true, the sample size (n) should be large enough (typically n > 30). In this case, n = 100, which satisfies this condition. Therefore, the distribution of the sample proportion will be approximately bell-shaped, with a mean of 0.512 and a standard deviation equal to sqrt[(p * (1-p))/n], which is sqrt[(0.512 * (1-0.512))/100].

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The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

We have Equation: 2x²+ 12x - 3= 0

Now, simplifying the equation as

2x² + 12x - 3 = 0

2x² + 12x = 3

divide both side by 2

x² + 6x = ³/₂

Now, take half of coefficient of x and add the square of it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

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