Find the gradient of the line passing through the points (– 2,– 4) and (3,5).

The following statements are considered to be propositions:

Deductive reasoning can be defined as a type of logical reasoning that typically involves drawing conclusions based on a given set of rules and conditions or from one or more premises (factual statements) that are assumed to be generally (universally) true.

A proposition can be defined as a type of statement (assertion) that is typically used to express an opinion or a judgement, with either a true or false answer.

This ultimately implies that, a proposition refers to a type of statement (assertion) that is either a true or false.

In this context, we can infer and logically deduce that the following statements are considered to be propositions:

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Answer:

x² + 6x + 9

Step-by-step explanation:

(x + 3)²

= (x + 3)(x + 3)

each term in the second factor is multiplied by each term in the first factor , that is

x(x + 3) + 3(x + 3) ← distribute parenthesis

= x² + 3x + 3x + 9 ← collect like terms

= x² + 6x + 9 ← in standard form

Answer:

5

Step-by-step explanation:

46/9.2 = 5

Answer:

it's simple, put the values in the equation.

5 + d( 3b-2d) = 5 + 4( 3×-3 - 2× 4)

= 5 + 4( -9-8)

= 5+ 4 × -17

= 5-68 = -63 ans.

Answer: 105 dollars

Step-by-step explanation:

Let's say that the original price x dollars, we can use the equation to find the original price.

80%x = 84

x = 105

Answer:

$105

Step-by-step explanation:

The multiplier is 0.8

To get the price after the discount,the original price was multiplied by 0.8(100 - 20 = 80% = 0.8

Therefore to obtain the original price from the price after the discount, we use reverse percentage:

$84 ÷ 0.8 = $105

The length of segment A.F in the circles given is: 62 units.

A radius of a circle is half the diameter of a circle, which is a point from the center to any point on the circumference of the circle. This implies that any segment that is drawn from the center of a circle to any point on the circumference of a circle is a radius. Also, all radii of a circle are always congruent to each other.

Radius of circle B = AB = BD = 24 units [all radii of a circle are congruent to each other].

Radius of circle E = CE = EF = 9 units [all radii of a circle are congruent to each other].

CD = 4

DE = x

CD + DE = CE

Plug in the values into the equation

4 + x = 9

x = 9 - 4

x = 5

DE = 5

The length of segment DE is 5 units

A.F = AB + BD + DE + EF

Plug in the values into the equation

A.F = 24 + 24 + 5 + 9

A.F = 62 units.

Therefore, the length of segment A.F in the given circle is determined as: 62 units.

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Answer:

13, 21, 29

Step-by-step explanation:

You are adding 8 to each term. -27 + 8 = -19 + 8 = -11 + 8 = -3, etc.

Answer:

there are 8 million different phone numbers whose phone numbers whose digits aren't 0 or 1

Answer:

(A)81/399

Step-by-step explanation:

The probability that the Principal selects a voyager on the first try is

82/400

Since another student is to be selected, the total population has reduced by 1 and the number of voyagers has been reduced by 1.

Probability that another voyager is selected on the second try is

81/399

The correct answer is A.

Answer:

1/4

Step-by-step explanation:

Rebecka already chose a retriever, so the puppies left for Aaron to pick are:

2 poodles

2 terriers

1 retriever

Total: 4

Number of retrievers left after Rebecka's pick: 1

p(Aaron picks retriever) = 1/4

Considering the given linear function, we have that:

A linear function is modeled by:

y = mx + b

In which:

His payment for x copies bought is:

y = 120x + 2400.

Hence:

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Using translation concepts, the set of transformations that was performed on the triangle are given as follows:

A) reflect horizontally and reflect vertically.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the orientations of the triangle changed both horizontally and vertically, with no change in the format, hence there were reflections, which means that the correct option is:

A) reflect horizontally and reflect vertically.

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The equation in the form of the given expression is (0)² + (1)² = 1

According to some of the trigonometry identity

sin 0 = 0

cos 0 1

Given the expression below

sin^2 0+cos^2 0=1

This can also be expressed as:

(sin0)² + (cos0)² = 1

Substitute

(0)² + (1)² = 1

Hence the equation in the form of the given expression is (0)² + (1)² = 1

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Applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

In geometry, a chord is defined as the line segment that joins two points on the circumference of a circle.

In a circle, if two chords are congruent, then they are equidistant from the center of a circle, according to the congruent chords theorem.

In the circle given, chords JK = LM = 12 units. This means both chords are congruent, therefore, they are equidistant from the center of the circle S.

According to the congruent chords theorem, NS = PS, thus:

8 = 2x - 6

8 + 6 = 2x

14 = 2x

Divide both sides by 2

14/2 = 2x/2

7 = x

x = 7

LP = 1/2(12)

LP = 6 units.

In summary, applying the congruent chords theorem, the value of x is: 7.

Length of segment LP is: 6 units.

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July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

This is further explained below.

Generally, The term "cumulative balance" refers to the total amount of money left over at the end of a fiscal year after all surplus amounts have been subtracted from deficit amounts. If there is a negative amount in the Cumulative Balance at the conclusion of a fiscal year, then that balance will be carried forward and used as the opening balance for the next fiscal year.

The term "cumulative account" refers to the total amount of an employee's account under a defined contribution plan (for an unaggregated plan) or the total amount of an employee's account under all defined contribution plans included in an Aggregation Group (for aggregated plans), both of which are determined as of the most recent plan valuation date within the most recent 12-month period that ends on the...

In conclusion, for the following data  July Aug. Sept. Oct. Nov. Dec. Receipts $500 $550 $700 $850 $795 $715 Expenses $490 $550 $600 $795 $ $650 Net Cash Flow $ $0 $ $55 $45 $ Cumulative Balance $10 $ $110 $ $210 $275 the missing values are 750, 10, 100, 65, 10, 165

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If the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.

The measures of central tendency include the mode, the median, and the mean.

Statistically, a central tendency is a typical value for a probability distribution.

The mode's value appears most often in a set of data values.  The median is the middle value of a dataset.  The mean represents the average.

To determine the possible values of A and B, we can start by finding the median value, which is the middle value in ascending order.

Median (Middle value) = 8

Mode = 8

Total value = 40 (8 x 5)

A = 8

B = 12.

Mean = 8 (40/5)

Thus, if the mean, median, and mode of the five numbers 5, 7, 8, A, and B are equal, the possible values of A+B are 20, where A is 8, and B is 12.

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The required rewritten equation in terms of variable 'r' is r = -u/s²t. By applying simple arithmetic operations, the required equation is obtained.

Consider an equation c = ax + by. Solving for variable 'a'.  

Step1: Write the required variable terms on one side

Step2: Add/Subtract like terms if any or take common if any

Step3: Divide/Multiply the coefficient of the required variable

Step4: simplify the obtained terms for the required variable

As follows:

c = ax + by

⇒ ax = by - c

⇒ ax/x = (by - c)/x

∴ a = (by - c)/x

The given equation is u = -s²rt

dividing by 't' on both sides:

⇒ u/t = -s²rt/t

⇒ u/t = -s²r

dividing by 's²' on both sides:

⇒ u/s²t = -s²r/s²

⇒ u/s²t = -r

∴ r = -u/s²t

Thus, the required equation for variable 'r' is r = -u/s²t.

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Answer: [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]

Step-by-step explanation:

Let the smallest angle be x.

Then, the middle angle is x+30.

The largest angle is 2x+30.

Angles in a triangle add to 180 degrees, so:

[tex]x+x+30+2x+30=180\\\\4x+60=180\\\\4x=120\\\\x=30[/tex]

So, the angles measure [tex]\boxed{30^{\circ}, 60^{\circ}, 90^{\circ}}[/tex]

The measures of all three angles are 30°,60°, and 90°.

A triangle is a 3-sided polygon occasionally (though not frequently) referred to as the trigon. Every triangle has three sides and three angles, some of which may be the same.

Find the measures of all three angles:

The three angles be a, b and c.

Angle “a" = x

Angle “b" = x + 30°

Angle “c" = “a" + “b"

                = x + x + 30°

                = 2x + 30°

Total angle in a triangle = 180°

Therefore;

“a" + “b" + “c" = 180°

Births; (x + (x + 30°) + (2x + 30°)) = 180°

So,

4x + 60° = 180°

x = (180° - 60°) ÷ 4

x = 30°

Plugging this value of x into the earlier equations for angles “a,” “b,” and “c."

“a" = x = 30°

“b" = x + 30° = 60°

“c" = 2x + 30° = 90°

The measures of all three angles are 30°,60°, and 90°.

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The measure of the longer diagonal is 24.31 units

The side lengths are given as;

a = 16

b = 10

The shorter diagonal is represented as d1, and it is given as

d1 = 11

The longer diagonal is represented as d2, and it is calculated using

d1^2 + d2^2 = 2 * (a^2 + b^2)

Substitute the known values in the above equation

11^2 + d2^2 = 2 * (16^2 + 10^2)

Evaluate the sum

121 + d2^2 =2 * 356

Evaluate the product

121 + d2^2 = 712

Subtract 121 from both sides

d2^2 = 591

Take the square root of both sides

d2 = 24.31

Hence, the measure of the longer diagonal is 24.31 units

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The two curves intersect when [tex]y=0[/tex] and [tex]y=1[/tex]. Over the range [tex]0\le y\le1[/tex], the curve [tex]x=12y^2[/tex] lies above [tex]x=12y^3[/tex]. Hence the area of the shaded region is

[tex]\displaystyle \int_0^1 (12y^2 - 12y^3) \, dy = 4y^3 - 3y^4\bigg|_0^1 = (4-3)-(0-0) = \boxed{1}[/tex]

Answer:

2/7 = 29% (nearest percent)

Step-by-step explanation:

Calculate the totals and add them to the table:

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} & \sf Freshman & \sf Sophmore & \sf Juniors & \sf Seniors & \sf Total \\\cline{1-6} \sf Male & 4 & 6 & 2 & 2 & 14\\\cline{1-6} \sf Female & 3 & 4 & 6 & 3 & 16\\\cline{1-6} \sf Total & 7 & 10 & 8 & 5 & 30\\\cline{1-6}\end{array}[/tex]

Probability Formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student is a freshman

Let P(B) = probability that the student is male

Use the given table to calculate the probability that the student is male:

[tex]\sf \implies P(B)=\dfrac{14}{30}[/tex]

And the probability that the student is a freshman and male:

[tex]\implies \sf P(A \cap B)=\dfrac{4}{30}[/tex]

To find the probability that the student owns a credit card given that the they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

[tex]\sf P(A|B)=\dfrac{P(A \cap B)}{P(B)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(Freshman|Male)=\dfrac{\dfrac{4}{30}}{\dfrac{14}{30}}=\dfrac{4}{14}=\dfrac{2}{7}=0.28571...=29\%[/tex]

Therefore, the probability that the student is a freshman given they are male is 29% (nearest percent).

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The glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y =  -29.202x + 293.5.

In the question, we are informed that the equation of the line of best fit, for the, scatter plot with x representing the number of ice cubes and y representing the milliliters of juice is given as y =  -29.202x + 293.5.

We are asked to tell how many milliliters of juice will be in a glass with 7 ice cubes based on the line of best fit.

To find the milliliters of juice in the glass with 7 ice cubes, we substitute x = 7, in the equation of the line of best fit, to get a value of y, representing the milliliters of juice in the glass.

Thus,

y =  -29.202x + 293.5,

or, y =  -29.202(7) + 293.5 {Substituting x = 7},

or, y = -204.414 + 293.5,

or, y = 89.086.

Thus, the glass will contain 89.086 milliliters of juice with 7 ice cubes, using the equation of the line of best fit, y =  -29.202x + 293.5.

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The area based on the information illustrated will be 825 unit².

Your information is incomplete. Therefore, an overview will be given. It should be noted that area simply means the quantity which expresses the extent of the region on a plane as well as a curved surface. Based on this information, it should be noted that the area of a rectangle is given as:

Area = Length × Width

Let's assume that the width is 25 units and the length is given as 33 units.

Then, the area will be:

= Length × Width

= 33 × 25

= 825 units²

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Step-by-step explanation:

there are

1 red marble

3 blue marbles

4 green marbles

in the box.

that means there are 8 marbles in the box. which gives us 8 different outcomes for pulling randomly 1 marbles.

the probability for each of these 8 outcomes is equal : 1/8.

remember, the probability is always the number of desired cases over the number of total possible cases.

so, the probability of pulling a red marble is :

1 desired case

8 total cases

->

1/8 or 0.125

the probability of pulling a blue marble is :

3 desired cases

8 total cases

->

3/8 or 0.375

the probability of pulling a green marble is :

4 desired cases

8 total cases

->

4/8 = 1/2 or 0.5

now the experiment is pulling 2 marbles in a row, but the first pulled marble is put back into the box again.

this makes this a combined event, where the first AND the second event must fulfill the desired over total cases.

if the 2 events are independent (not overlapping or influencing each other), then we can simply multiply the probabilities. which is the case here, because the first marble is put back.

why ?

because now we have 8 possible outcomes for the first ball, and again 8 possible outcomes for the second ball, and when we combine all possibilities from the first with all possibilities from the second pull, we get 8×8 = 64 possible outcomes :

red. red

red. blue1

red. blue2

red. blue3

red. green1

...

green4 green4

so, the probability to pull a blue ball first is

3/8

and the probability to pull a blue ball second is

3/8 too

the combined probability of the combined event is

3/8 × 3/8 = 9/64

we have 3×3 = 9 desired outcomes of combining 3 blue and 3 blue balls out of the total of 64 possible outcomes.

Answer:

angle G

Step-by-step explanation:

the quadrilateral did not change position or ration, it only shrank, so all the angles are in the same place and angle C = angle G

Answer:

2

Step-by-step explanation:

Answer:

550

Step-by-step explanation:

165 x 100= 16500/30=550

Using the normal distribution, the indicated probability is given as follows:

P(7 ≤ x ≤ 11) = 0.6247.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 8, \sigma = 2[/tex]

P(7 ≤ x ≤ 11) is the p-value of Z when X = 11 subtracted by the p-value of Z when X = 7, hence:

X = 11:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (11 - 8)/2

Z = 1.5

Z = 1.5 has a p-value of 0.9332.

X = 7:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (7- 8)/2

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

0.9332 - 0.3085 = 0.6247.

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