(3x-1)(x-2)=5x+2 ecuación cuadrática incompleta

Answer:

We start with 17 marbles, 4 of which are red. So P(first marble is red) = 4/17. Since the red marble is not replaced, there are now 16 marbles, 3 of which are red. So P(second marble is red) = 3/16.

The correct calculation is

P(red, then red) = 4/17 × 3/16

Answer:

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

Angles ABD and DBC form a linear pair, hence their sum is 180°.

Set up an equation and solve for x:

Substitute 40.5 for x and find the measure of ∠DBC:

The correct representation for the joint probability of two dependent events Y and Z is P(Y) * P(Z|Y). Option E

The joint probability of two dependent events Y and Z can be written as the probability of Y occurring multiplied by the conditional probability of Z given Y. This can be represented as P(Y) * P(Z|Y).

Here's the justification:

P(Y) represents the probability of event Y occurring independently.

P(Z|Y) represents the conditional probability of event Z occurring given that event Y has already occurred.

When Y and Z are dependent events, the occurrence of Y affects the probability of Z happening. Therefore, we need to consider the probability of Y occurring first (P(Y)) and then the probability of Z occurring given that Y has already occurred (P(Z|Y)).

Multiplying these two probabilities together gives us the joint probability of both Y and Z occurring simultaneously, which is denoted as P(Y and Z).

Hence, the correct representation for the joint probability of two dependent events Y and Z is P(Y) * P(Z|Y). Option E.

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Angle C can be found by subtracting the sum of angles A and B from 180 degrees:

b. A = 34.1°; B = 44.4°; C = 101.5°

To solve a triangle with side lengths a = 4, b = 5, and c = 7, we can use the law of cosines and the law of sines.

First, let's find angle A using the law of cosines:

[tex]cos(A) = (b^2 + c^2 - a^2) / (2\times b \times c)[/tex]

[tex]cos(A) = (5^2 + 7^2 - 4^2) / (2 \times 5 \times 7)[/tex]

cos(A) = (25 + 49 - 16) / 70

cos(A) = 58 / 70

cos(A) ≈ 0.829

A ≈ arccos(0.829)

A ≈ 34.1°

Next, let's find angle B using the law of sines:

sin(B) / b = sin(A) / a

sin(B) = (sin(A) [tex]\times[/tex] b) / a

sin(B) = (sin(34.1°) [tex]\times[/tex] 5) / 4

sin(B) ≈ 0.822

B ≈ arcsin(0.822)

B ≈ 53.4°

Finally, angle C can be found by subtracting the sum of angles A and B from 180 degrees:

C = 180° - A - B

C = 180° - 34.1° - 53.4°

C ≈ 92.5°.

b. A = 34.1°; B = 44.4°; C = 101.5°

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Domain: (-∞, ∞) - all real numbers Range: (-∞, 2] - all real numbers less than or equal to 2.

To find the domain and range of the function 2 - |x - 5|, we need to consider the possible values for the input variable (x) and the corresponding output values.

Domain:

The domain of a function represents the set of all possible input values for which the function is defined. In this case, the function 2 - |x - 5| is defined for all real numbers. There are no restrictions or limitations on the values that x can take. Therefore, the domain is (-∞, ∞), which means that the function is defined for all real numbers.

Range:

The range of a function represents the set of all possible output values that the function can produce. To determine the range, we consider the possible values of the function for different input values.

The expression |x - 5| represents the absolute value of the quantity (x - 5). The absolute value function always produces non-negative values. So, |x - 5| will always be non-negative or zero.

When we subtract |x - 5| from 2, we have 2 - |x - 5|. The resulting values will range from 2 to negative infinity (2, -∞).

Therefore, the range of the function 2 - |x - 5| is (-∞, 2].

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Note the complete questions is

Find the domain and range of function 2 - |x - 5| ?

Answer:

Step-by-step explanation:

To simplify the expression, we can combine the square roots and simplify the exponents.

Starting with the expression:

3√(16x^7) * 3√(12x^9)

Let's simplify each term separately:

Simplifying 3√(16x^7):

The index of the radical is 3, so we need to group the terms in sets of three. For the variable x, we have x^7, which can be grouped as x^6 * x.

Now, let's simplify the number inside the radical:

16 = 2^4, and we can rewrite it as (2^3) * 2 = 8 * 2.

So, 3√(16x^7) becomes:

3√(8 * 2 * x^6 * x) = 2 * x^2 * 3√(2x)

Simplifying 3√(12x^9):

Again, the index of the radical is 3, and we group the terms in sets of three. For the variable x, we have x^9, which can be grouped as x^6 * x^3.

Now, let's simplify the number inside the radical:

12 = 2^2 * 3.

So, 3√(12x^9) becomes:

3√(2^2 * 3 * x^6 * x^3) = 2 * x^2 * 3√(3x^3)

Now we can multiply the simplified terms together:

(2 * x^2 * 3√(2x)) * (2 * x^2 * 3√(3x^3))

Multiplying the coefficients: 2 * 2 * 3 = 12.

Multiplying the variables: x^2 * x^2 = x^4.

Now, let's combine the square roots:

3√(2x) * 3√(3x^3) = 3√(2x * 3x^3) = 3√(6x^4).

Therefore, the simplified expression is:

12x^4 * 3√(6x^4)

The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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The probability that less than 10 out of 15 cash register receipts will show the three food items ordered is approximately 0.166.

To calculate the probability that less than 10 out of 15 cash register receipts show that the hamburger, french fries, and a drink were ordered, we can use the binomial probability formula. The formula for the probability of obtaining exactly k successes in n trials is:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of obtaining k successes,

n is the number of trials,

p is the probability of success in a single trial, and

(nCk) is the binomial coefficient, which represents the number of ways to choose k successes out of n trials.

In this case, we want to find the probability of less than 10 out of 15 receipts showing the three food items ordered. We need to calculate the probabilities for k = 0, 1, 2, ..., 9, and sum them up.

Let's calculate the probabilities using the formula:

P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 9)

where:

n = 15 (number of trials),

p = 0.60 (probability of success, i.e., ordering hamburger, french fries, and a drink).

Using a binomial calculator or a statistical software, we can calculate each individual probability and then sum them up.  The result will be the probability that less than 10 out of 15 receipts show the three food items ordered.

The probability that less than 10 out of 15 cash register receipts will show the three food items ordered is approximately 0.166.

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Answer:

B

Step-by-step explanation:

[tex]\frac{x^6-4x^4+3x^2}{5x^2}[/tex]

factor out the common factor of x² from each term on the numerator

= [tex]\frac{x^2(x^4-4x^2+3)}{5x^2}[/tex] ( cancel x² on numerator/ denominator )

= [tex]\frac{x^4-4x^2+3}{5}[/tex]

Answer:

Step-by-step explanation:

Anna ran the fastest with a speed of approximately 4.67 miles per hour.

To find the speed at which each person ran, we can use the formula: Speed = Distance / Time.

Let's calculate the speed for each person:

Noah:

Distance = 2 1/2 miles

Time = 3/5 hour

Speed = (2 1/2) / (3/5)

= (5/2) / (3/5)

= (5/2) [tex]\times[/tex] (5/3)

= 25/6 ≈ 4.17 miles per hour

Emily:

Distance = 3 3/4 miles

Time = 5/6 hour

Speed = (3 3/4) / (5/6)

= (15/4) / (5/6)

= (15/4) [tex]\times[/tex] (6/5)

= 9/2 = 4.5 miles per hour

Anna:

Distance = 3 1/2 miles

Time = 3/4 hour

Speed = (3 1/2) / (3/4)

= (7/2) / (3/4)

= (7/2) [tex]\times[/tex] (4/3)

= 14/3 ≈ 4.67 miles per hour

Based on the calculations, Noah ran at a speed of approximately 4.17 miles per hour, Emily ran at a speed of 4.5 miles per hour, and Anna ran at a speed of approximately 4.67 miles per hour.

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Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

Answer:

math = 227.98

programming = 42.55

Step-by-step explanation:

We have
3m + 4p = 854.14 -eq(1)

8m + 1p = 1866.39 -eq(2)

rq(2) x 4: 32m + 4p = 7465.56 -eq(3)

eq(3)-eq(1):

32m + 4p = 7465.56

- ( 3m + 4p = 854.14)

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

29m = 6611.42

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

⇒ m = 6611.42/29

m = 227.98

sub in eq(1)

3(227.98) + 4p = 854.14

4p = 854.14 - 683.94

4p = 170.2

p = 170.2/4

p = 42.55

Answer:

I have not comed across this question before

Answer:

Step-by-step explanation:

all circles have same round shape with no edges and corners so they all are similar in terms of their shape and appearance but not all the circles are congruent.

two circles are congruent if they have the same measurements of radius, circumference, diameter as well as the surface area. So, to determine whether the two circles are congruent or not we have to perform the calculations.

a. For a score of X = 70, a standard deviation of σ = 4 would give a better grade.

b. For a score of X = 80, both standard deviations would give the same grade.

a. To determine which standard deviation would give a better grade for a score of X = 70, we can compare the z-scores associated with each standard deviation.

The z-score measures the number of standard deviations a given value is from the mean.

For σ = 4:

Z = (X - μ) / σ

Z = (70 - 78) / 4

Z = -2  

For σ = 8:

Z = (X - μ) / σ

Z = (70 - 78) / 8

Z = -1

The z-score for σ = 4 is -2, while the z-score for σ = 8 is -1. A higher z-score indicates a better grade since it represents a score that is further above the mean.

Therefore, in this case, a standard deviation of σ = 4 would give a better grade.

b. Similarly, for a score of X = 80:

For σ = 4:

Z = (X - μ) / σ

Z = (80 - 78) / 4

Z = 0.5

For σ = 8:

Z = (X - μ) / σ

Z = (80 - 78) / 8

Z = 0.25.

The z-score for σ = 4 is 0.5, while the z-score for σ = 8 is 0.25.

Again, a higher z-score indicates a better grade.

Therefore, in this case, a standard deviation of σ = 4 would give a better grade.

In both scenarios, a standard deviation of σ = 4 would result in a better grade compared to σ = 8.

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Answer:

let, perimeter of square = 4a

where a = side of square

let, perimeter of the equilateral triangle = 3b

where b= side of triangle

therfore, 4a=3b

a/b = 3/4

area of the square = [tex]a^{2}[/tex]

are of the triangle = [tex]\frac{\sqrt{3} }{4} b^{2}[/tex]

dividing both the areas we get,

[tex]\frac{a^{2} }{\frac{\sqrt{3} }{4}b^{2} }[/tex]

[tex]a^{2}*\frac{4}{\sqrt{3} b^{2}}[/tex]

[tex]\frac{a^{2} }{b^{2} } * \frac{4}{\sqrt{3} }[/tex]

[tex]\frac{3^{2} }{4^{2} } * \frac{4}{\sqrt{3} }[/tex]

[tex]\frac{3\sqrt{3} }{4}[/tex]

hope you understand

Step-by-step explanation:

El supplemento y el complemento de cada ángulo son, respectivamente:

Caso A: m ∠ A' = 43°

Caso B: m ∠ A' = 31°

De acuerdo con la geometría, la suma de un ángulo y su complemento es igual a 90° and la suma de un ángulo y su suplemento es igual a 180°. Matemáticamente hablando, cada situación es descrita por las siguientes formulas:

Ángulo y su complemento

m ∠ A + m ∠ A' = 90°

Ángulo y su suplemento

m ∠ A + m ∠ A' = 90°

Donde:

Ahora procedemos a determinar cada ángulo faltante:

Caso A: Complemento

47° + m ∠ A' = 90°

m ∠ A' = 43°

Caso B: Suplemento

149° + m ∠ A' = 180°

m ∠ A' = 31°

El enunciado se encuentra escrito en español y la respuesta está escrita en el mismo idioma.

The statement is written in Spanish and its answer is written in the same language.

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Answer:

D

Step-by-step explanation:

to find the coterminal angles add/ subtract 360° to the given angle

- 255° + 360° = 105°

- 255° - 360° = - 615°

Answer:

Step-by-step explanation:

Let the centre be C.

Since TR is a straight line,  

∠SCT + ∠SCR = 180

∠SCT = 180 - 53

∠SCT = 127

The angle of a semicircle is 180°. Minor arcs are arcs less than a semicircle i.e. less than 180° and major arcs are arcs greator than a semicircle i.e. greater than 180°.

a) arc(SPT) has measure of 90 + 65 + 25 + 53 = 233° > 180° and hence a major arc

Also 1° = π/180 radians

233° = 233 * π/180 = 1.29π radians

b) arc(ST) has measure of 127° < 180° and hence a minor arc

127° = 127 * π/180 = 0.71π radians

c) arc(RST) has a measure of  53 + 127 = 180° which is a semicircle

180° = 180* π/180 = π radians

d) arc(SP) has a measure of 53 + 25 + 65 = 143° < 180° and hence a minor arc

143° = 143* π/180 = 0.79π radians

e) arc(QST) has a measure of 25 + 53 + 127 = 205° > 180° and hence a major arc

205° = 205 * π/180 = 1.14π radians

f) arc(TQ) has a measure of 90 + 65 = 155° < 180° and hence a minor arc

155° = 155 * π/180 = 0.86π radians

Answer:

[tex]\text{a.} \quad \text{Major arc}:\;\;\overset{\frown}{SPT}=233^{\circ}[/tex]

[tex]\text{b.} \quad \text{Minor arc}:\;\;\overset{\frown}{ST}=127^{\circ}[/tex]

[tex]\text{c.} \quad \text{Semicircle}:\;\;\overset{\frown}{RST}=180^{\circ}[/tex]

[tex]\text{d.} \quad \text{Minor arc}:\;\;\overset{\frown}{SP}=143^{\circ}[/tex]

[tex]\text{e.} \quad \text{Major arc}:\;\;\overset{\frown}{QST}=205^{\circ}[/tex]

[tex]\text{F.} \quad \text{Minor arc}:\;\;\overset{\frown}{TQ}=155^{\circ}[/tex]

Step-by-step explanation:

A major arc is an arc in a circle that measures more than 180°.

It is named with three letters: two endpoints and a third point on the arc.

A minor arc is an arc in a circle that measures less than 180°.

It is named with two letters: its two endpoints.

A semicircle is a special case of an arc that measures exactly 180°.  

The endpoints of the semicircle are located on the diameter, and the semicircle divides the circle into two equal parts.

The measure of an arc of a circle is equal to the measure of its corresponding central angle.

[tex]\hrulefill[/tex]

a)  Arc SPT is a major arc since it is named with three letters.

It begins at point S, passes through point P, and ends at point T.

    [tex]\begin{aligned}\overset{\frown}{SPT}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}+\overset{\frown}{PT}\\&=53^{\circ}+25^{\circ}+65^{\circ}+90^{\circ}\\&=233^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

b)  Arc ST is a minor arc since it is named with two letters.

It is measured in a counterclockwise direction from point S to point T.

    [tex]\begin{aligned}\overset{\frown}{ST}&=360^{\circ}-\overset{\frown}{SPT}\\&=360^{\circ}-233^{\circ}\\&=127^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

c)  Arc RST is a semicircle.

Arc RST is a semicircle since its endpoints are located on the diameter of the circle, RT.

    [tex]\overset{\frown}{RST}=180^{\circ}[/tex]

[tex]\hrulefill[/tex]

d)  Arc SP is a minor arc since it is named with two letters.

It is measured in a clockwise direction from point S to point P.

(If it was measured in a counterclockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).

    [tex]\begin{aligned}\overset{\frown}{SP}&=\overset{\frown}{SR}+\overset{\frown}{RQ}+\overset{\frown}{QP}\\&=53^{\circ}+25^{\circ}+65^{\circ}\\&=143^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

e)  Arc QST is a major arc since it is named with three letters.

It begins at point Q, passes through point S, and ends at point T.

    [tex]\begin{aligned}\overset{\frown}{QST}&=\overset{\frown}{QR}+\overset{\frown}{RS}+\overset{\frown}{ST}\\&=25^{\circ}+53^{\circ}+127^{\circ}\\&=205^{\circ}\end{aligned}[/tex]

[tex]\hrulefill[/tex]

f)  Arc TQ is a minor arc since it is named with two letters.

It is measured in a counterclockwise direction from point T to point Q.

(If it was measured in a clockwise direction, it would be a major arc, as it would be more than 180°, and therefore would be named using three letters).

    [tex]\begin{aligned}\overset{\frown}{TQ}&=\overset{\frown}{TP}+\overset{\frown}{PQ}\\&=90^{\circ}+65^{\circ}\\&=155^{\circ}\end{aligned}[/tex]

Answer:

Step-by-step explanation:

There is a 53.33% chance of drawing a piece of paper with a number less than 9 from the jar.

To calculate the probability of drawing a piece of paper with a number less than 9 written on it, we need to determine the number of favorable outcomes (pieces of paper with a number less than 9) and divide it by the total number of possible outcomes (all 15 pieces of paper).

In this case, the favorable outcomes are the numbers 1 through 8, as they are less than 9. There are 8 favorable outcomes.

The total number of possible outcomes is 15 since there are 15 pieces of paper in the jar.

Therefore, the probability of drawing a piece of paper with a number less than 9 is:

Probability = Number of favorable outcomes / Total number of possible outcomes

= 8 / 15

Simplifying the fraction, we find that the probability is approximately:

Probability ≈ 0.5333 or 53.33%

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The correct answer is A- A model with 12 squares labeled exact value and 3 squares labeled error.

To determine which model represents a percent error of 25%, we need to compare the number of squares labeled "exact value" and "error" in each model and calculate the ratio between them.

Let's calculate the ratio for each model:

Model A: 3 squares labeled error / 12 squares labeled exact value = 0.25 or 25%.

Model B: 5 squares labeled error / 10 squares labeled exact value = 0.5 or 50%.

Model C: 3 squares labeled error / 9 squares labeled exact value ≈ 0.3333 or 33.33%.

Model D: 4 squares labeled error / 8 squares labeled exact value = 0.5 or 50%.

From the calculations, we can see that only Model A represents a percent error of 25%. The other models have ratios of 50% and 33.33%, which do not match the desired 25% error.

Consequently, the appropriate response is A- A model with 12 squares labeled exact value and 3 squares labeled error.

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The result of the row operation on the matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The matrix in this problem is defined as follows:

[tex]\left[\begin{array}{cccc}2&0&0&16\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

The row operation is given as follows:

[tex]R_1 \rightarrow \frac{1}{2}R_1[/tex]

The meaning of the operation is that every element of the first row of the matrix is divided by two.

Hence the resulting matrix is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&8\\0&8&0&3\\0&0&5&6\end{array}\right][/tex]

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There are no valid values of 'a' and 'b' that satisfy the given equation.

a/(2x - 3) + b/(3x + 4) = (x + 7)/(6x^2 - x - 12)

We need to find the values of 'a' and 'b' that satisfy the equation.

First, let's find the common denominator of the fractions on the left-hand side of the equation, which is (2x - 3)(3x + 4):

[(a)(3x + 4) + (b)(2x - 3)] / [(2x - 3)(3x + 4)] = (x + 7)/(6x^2 - x - 12)

Expanding the numerator on the left-hand side, we get:

(3ax + 4a + 2bx - 3b) / [(2x - 3)(3x + 4)] = (x + 7)/(6x^2 - x - 12)

Combining like terms in the numerator:

(5ax + 2bx + 4a - 3b) / [(2x - 3)(3x + 4)] = (x + 7)/(6x^2 - x - 12)

Now, we can equate the numerators on both sides of the equation:

5ax + 2bx + 4a - 3b = x + 7

To solve for 'a' and 'b', we need to match the coefficients of 'x' and the constant terms on both sides of the equation.

Matching the coefficients of 'x':

5a = 1 (coefficient of 'x' on the right-hand side is 1)

2b = 1 (coefficient of 'x' on the left-hand side is 1)

Matching the constant terms:

4a - 3b = 7

We have a system of equations:

5a = 1

2b = 1

4a - 3b = 7

Solving the first equation for 'a':

a = 1/5

Solving the second equation for 'b':

b = 1/2

Substituting the values of 'a' and 'b' into the third equation:

4(1/5) - 3(1/2) = 7

4/5 - 3/2 = 7

(8 - 15)/10 = 7

-7/10 = 7

The equation is inconsistent, and there is no solution that satisfies all the conditions.

As a result, the preceding equation cannot be satisfied by any real values for 'a' and 'b'.

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The volume of the square based pyramid would be =60cm³.

To calculate the volume of a square based pyramid, the formula that should be used would be given below as follows;

Volume = 1/3× base²× height

where base length = 6cm

height = 5cm

Volume = 1/3× 6×6×5

= 60cm³

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The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

[tex]y = 20000(0.95)^5[/tex]

Calculating the expression, we find:

[tex]y ≈ 20000(0.774)[/tex]

Simplifying further, we get:

[tex]y ≈ 15480[/tex]

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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The graph that displays the line of best fit for the data is the one where the line with the best fit goes through the points.

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