How is 19-2 equal to 20

Step-by-step explanation:

10/1(-4)

10(-4)

=-2.5 or 5/-2

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

The measures of the angles and the lengths of the sides of the triangle can

be found using sine rule.

The correct responses are;

Reasons:

The given parameter are;

∠B = 65°20', b = 5.38 inches, c = 4.88 inches

∠C ≥ 90°

By sine rule, we have;

\(\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{4.88}{sin(\angle C)}}\)

\(sin(\angle C) = \mathbf{ \dfrac{sin(65^{\circ} 20') \times 4.88}{5.38}}\)

\(\angle C = arcsin \left(\dfrac{sin(65^{\circ} 20') \times 4.88}{5.38} \right) \approx \mathbf{ 55.517 ^{\circ}}\)

∠C = 55.517° < 90°, therefore, the correct response is; None

\(\dfrac{sin(65^{\circ} 20')}{5.38} = \dfrac{4.88}{sin(\angle C)}\)

∠A = 180° - 65°20' - 55.517° = 59.15° = 59°9'

∠A = 59°9'

Therefore;

\(\dfrac{5.38}{sin(65^{\circ} 20')} = \mathbf{ \dfrac{a}{sin(59.15^{})}}\)

\(a = \dfrac{5.38 \times sin(59.15^{\circ}) }{sin(65^{\circ} 20')} \approx \mathbf{ 5.083}\)

a ≈ 5.083 inches

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Answer:

tourist: 28%

non-tourist: 72%

Step-by-step explanation:

total: 50

tourists: 14

non-tourists:50 - 14 = 36

tourist percentage: 14/50 × 100% = 28%

non-tourist percentage: 36/50 × 100 = 72%

The price per cup when a 2-quart carton of yogurt costs $5.36 is $0.67.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

In this case, a 2-quart carton of yogurt costs $5.36. It should be noted that 1 quart = 4 cups.

Therefore, 2 quarts will be:

= 2 × 4.

= 8 cups

Therefore, the price per cup will be:

= $5.36 / 8

= $0.67

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Answer:

Step completed incorrectly:  2

Correct Answer: y = -4x + 22

Step-by-step explanation:

The graph is a straight line through points M(4, -1) and N(8, 0).  Point Q is located at (6, -2).

To calculate the slope of the line, substitute the points into the slope formula:

\(\textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-(-1)}{8-4}=\dfrac{1}{4}\)

Therefore, the slope of MN is 1/4, so step 1 of Francisco's calculations is correct.

If two lines are perpendicular to each other, the slopes of these lines are negative reciprocals. The negative reciprocal of a number is its negative inverse.

The negative reciprocal of 1/4 is -4.

Therefore, the slope of the perpendicular line is -4.

So Francisco has made an error in his calculation in step 2 by not making the perpendicular slope negative.

Corrected work

\(\textsf{Step 1:} \quad \sf slope\;of\;MN:\; \dfrac{1}{4}\)

\(\textsf{Step 2:} \quad \sf slope\;of\;the\;line\;perpendicular:\; -4\)

\(\begin{aligned}\textsf{Step 3:} \quad y-y_1&=m(x-x_1)\;\; \sf Q(6,-2)\\y-(-2)&=-4(x-6)\end{aligned}\)

\(\textsf{Step 4:} \quad y+2=-4x+24\)

\(\textsf{Step 5:} \quad y+2-2=-4x+24-2\)

\(\textsf{Step 6:} \quad y=-4x+22\)

Therefore, step 2 has been completed incorrectly.

The correct answer is y = -4x + 22.

Experimental and theoretical probabilities do not match; Field Trip B is the most popular with 32% relative frequency.

What is frequency?

Frequency refers to the number of times an event or observation occurs within a given period, sample size, or population. In the context of data analysis, frequency is often used to describe how often a particular value or category appears in a dataset or sample. It can be expressed as an absolute frequency (the actual number of times an event occurred) or a relative frequency (the proportion or percentage of times an event occurred compared to the total number of observations).

The experimental probability of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins. For example, the experimental probability of selecting Field Trip A is 8/50 = 0.16 or 16%, the experimental probability of selecting Field Trip B is 16/50 = 0.32 or 32%, and so on.

The theoretical probability of selecting each field trip is 1/5 or 0.2 or 20%. This is because the spinner has 5 equal sections, and each section represents a different trip.

The experimental and theoretical probabilities do not match exactly. For example, the experimental  of selecting Field Trip B is 0.32 or 32%, while the theoretical probability is only 0.2 or 20%. This could be due to chance or random variation, as the teacher only spun the spinner 50 times. With a larger sample size, the experimental and theoretical probabilities should converge closer to each other.

The relative frequency of selecting each field trip can be calculated by dividing the number of times each trip was selected by the total number of spins, and then multiplying by 100 to express it as a percentage. For example, the relative frequency of selecting Field Trip A is (8/50) x 100 = 16%, the relative frequency of selecting Field Trip B is (16/50) x 100 = 32%, and so on.

Based on the data, Field Trip B appears to be the most popular, as it was selected the most number of times (16 times out of 50 spins).

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Commplete Question:

A science teacher uses a fair spinner to simulate choosing one of five different field trips for her classes. The spinner has 5 equal sections, each representing a different trip. The teacher spins the spinner 50 times and records the results in the table below:

Field Trip Number of times selected

A                8

B                16

C               9

D                12

E                5

Apply math models to analyze the data and answer the following questions:

What is the experimental probability of selecting each field trip?

What is the theoretical probability of selecting each field trip?

Do the experimental and theoretical probabilities match? If not, what could be the reason for the difference?

What is the relative frequency of selecting each field trip?

Based on the data, which field trip appears to be the most popular?

Answer: 330 miles

Step-by-step explanation:

The distance provided for the question is:

Wrexham

18 Ruthin

21 12 Cornwen

15 33 23 Oswestry

What this means is that Ruthin and Oswestry are 33 miles apart.

Each day, Jane travels back and forth for a total of:

= 33 * 2

= 66 miles

In 5 days she would have travelled:

= 5 * 66

= 330 miles

Answer:

But where are the rectangles??

Answer:

Step-by-step explanation:

Answer:

0,2

1,-1

2,-4

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

  $625,000

Step-by-step explanation:

The maximum revenue will be found where the derivative of the revenue function is zero.

  r'(x) = 50 -2x = 0

  50 = 2x

  x = 25

When 2500 gallons are sold, the revenue is ...

  r(25) = 50(25) -25(25) = (50 -25)(25) = 25(25) = 625 . . . thousands

The maximum revenue is $625,000.

The polynomials completely factorized have the following expressions;

50). x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

51). x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

52). x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

53). x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

For the polynomial x³ - 3x² - 26x - 12 divisible by x - 6;

(x³ - 3x² - 26x - 12)/(x - 6) = x² + 3x + 2

x² + 3x + 2 = (x + 1)(x + 2)

so;

x³ - 3x² - 26x - 12 = (x - 6)(x + 1)(x + 2)

For the polynomial x³ - 12x² + 12x + 80 divisible by x - 10;

(x³ - 12x² + 12x + 80)/(x - 10) = x² - 2x - 8

x² - 2x - 8 = (x + 2)(x - 4)

so;

x³ - 12x² + 12x + 80 = (x - 10)(x + 2)(x - 4)

For the polynomial x³ - 18x² + 95x + 126 divisible by x - 9;

(x³ - 12x² + 12x + 80)/(x - 9) = x² - 9x + 14

x² - 9x + 14 = (x - 2)(x - 7)

so;

x³ - 18x² + 95x + 126 = (x - 9)(x - 2)(x - 7)

For the polynomial x³ - x² + 21x + 45 divisible by x + 5;

(x³ - x² + 21x + 45)/(x + 5) = x² - 6x + 9

x² - 6x + 9 = (x - 3)(x - 3)

so;

x³ - x² + 21x + 45 = (x + 5)(x - 3)(x - 3)

Therefore, by complete factorization the expressions (x - 6)(x + 1)(x + 2), (x - 10)(x + 2)(x - 4), (x - 9)(x - 2)(x - 7), and (x + 5)(x - 3)(x - 3) are the factors of their respective polynomial.

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Answer:

the base of a lateral pyramid is related to lateral faces because though it is not a lateral face itself is connected to the sides of the pyramid and the side of the pyramid is connected to the vertex of the shape

Step-by-step explanation:

the base of a lateral pyramid is related to lateral faces because though it is not a lateral face itself is connected to the sides of the pyramid and the side of the pyramid is connected to the vertex of the shape

Answer:

The net of a triangular pyramid with an equilateral triangle for the base consists of four triangles, and at least three are congruent.

Step-by-step explanation:

I just got born again I'm  a Christian

Answer:

Point G

Step-by-step explanation:

The mapping rule for a 90° counterclockwise rotation is:

Therefore, if A = (4, 1):

The point that represents A' after A(4, 1) is rotated 90° counterclockwise is:

The subsets of the set {e, n, t} are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:

\(2^n\)

The set for this problem is given as follows:

{e, n, t}

The cardinality is given as follows:

n = 3.

Hence the number of subsets is given as follows:

2³ = 8.

The subsets are given as follows:

{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.

In which {} is the empty set.

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Answer:

$2

Step-by-step explanation:

Because 3/12 is 0.25 and then you multiply it by 8 to get 2.

Answer:

12x + 6

Step-by-step explanation:

perimeter equals the sum of all sides

if each side is 4x+2 then 3(4x+2) = 12x+6

The number of outfits that the CEO can wear to his office would be = 1050

Combination can be defined as the number of possible arrangements that can be gotten from a number of a given value of item.

From the question,

The number of pairs of pants owned by the CEO = 10

The number of shirts owned by the CEO= 7

The number of ties owned by the CEO = 3

The number of jackets owned by CEO = 5

Therefore the different types of outfit that the CEO can wear to the office = 10×7×3×5 = 1050

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Answer:

x<-12 or x>16

Step-by-step explanation:

Answer:

|x - 2| + 3 > 17

|x - 2| > 14

x - 2 < -14 or x - 2 > 14

x < -12 or x > 16

The point (0, -5) lies on the graph of the quadratic equation y = x² - 5. The shape of the graph is a parabola.

An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.

The equation y = x² - 5 represents a quadratic equation. A quadratic equation have the shape of a parabola.

When x = 0;

y = 0² - 5

y = -5

The point (0, -5) lies on the graph of y = x² - 5

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Answer:

B

Step-by-step explanation:

The midpoint formula is \((\frac{x1+x2}{2} ,\frac{y1+y2}{2} )\)

Lets plug in our points:

\(\frac{(-6)+(-4)}{2}\)=-5 (the x value)

\(\frac{(-9)+(-9)}{2}\)=-9 (the y value)

- 8 + 2(- 5)

- 8 - 10

= - 18

The correct answer is the second option

Answer:

Question: What is thirty-five and seven thousandths in decimal?

Answer: is 35.007

Option A. c - 0 = b - a is the missing statement in Step 4 of the proof.

To determine the missing statement in Step 4 of the proof, let's examine the given table and image related to the relationship between the slopes of two parallel lines.

Step 1: Given the slopes of two parallel lines, m₁ and m₂.

Step 2: Assume two points on each line: (0, a) and (c, b).

Step 3: Calculate the slopes using the slope formula: m₁ = (b - a) / (c - 0) and m₂ = (d - a) / (0 - c).

Step 4: ??? (Missing Statement)

Step 5: Since the lines are parallel, the slopes are equal, so m₁ = m₂.

By analyzing the given information, we can identify the missing statement by comparing the calculated slopes:

From Step 3, we have:

m₁ = (b - a) / (c - 0)

m₂ = (d - a) / (0 - c)

Comparing the two slopes, we can see that (b - a) / (c - 0) = (d - a) / (0 - c).

To express this relationship, the missing statement in Step 4 should be:

A. c - 0 = b - a

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Answer:

1) B = 88°, a = 13.1, b = 26.9

2) C = 73°, a = 20.9, b = 12.6

Step-by-step explanation:

To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies B=180^{\circ}-A-C\)

\(\implies B=180^{\circ}-29^{\circ}-63^{\circ}\)

\(\implies B=88^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 29^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies a=\dfrac{24\sin 29^{\circ}}{\sin 63^{\circ}}\)

\(\implies a=13.0876493...\)

\(\implies a=13.1\)

Solve for b:

\(\implies \dfrac{b}{\sin 88^{\circ}}=\dfrac{24}{\sin 63^{\circ}}\)

\(\implies b=\dfrac{24\sin 88^{\circ}}{\sin 63^{\circ}}\)

\(\implies b=26.9194211...\)

\(\implies b=26.9\)

\(\hrulefill\)

Given values:

As the interior angles of a triangle sum to 180°:

\(\implies A+B+C=180^{\circ}\)

\(\implies C=180^{\circ}-A-B\)

\(\implies C=180^{\circ}-72^{\circ}-35^{\circ}\)

\(\implies C=73^{\circ}\)

Substitute the values of A, B, C and c into the Law of Sines formula and solve for sides a and b:

\(\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

Solve for a:

\(\implies \dfrac{a}{\sin 72^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies a=\dfrac{21\sin 72^{\circ}}{\sin 73^{\circ}}\)

\(\implies a=20.8847511...\)

\(\implies a=20.9\)

Solve for b:

\(\implies \dfrac{b}{\sin 35^{\circ}}=\dfrac{21}{\sin 73^{\circ}}\)

\(\implies b=\dfrac{21\sin 35^{\circ}}{\sin 73^{\circ}}\)

\(\implies b=12.5954671...\)

\(\implies b=12.6\)

we know A is 45% salt, so the amount of salt in A is (45/100)*A or 0.45A.

likewise we know that B is 95% salt, so the salt amount in it is (95/100)*B or 0.95B.

\(\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.45&0.45x\\ B&y&0.95&0.95y\\ \cline{2-4}&\\ mixture&60&0.85&51 \end{array}~\hfill \begin{cases} x+y=60\\ 0.45x+0.95y=51\\[-0.5em] \hrulefill\\ y = 60 -x \end{cases}\)

\(\stackrel{\textit{substituting on the 2nd equation}}{0.45x+0.95(60-x) = 51}\implies 0.45x+57-0.95x=51 \\\\\\ 0.45x-0.95x=-6\implies -0.5x=-6\implies x = \cfrac{-6}{-0.5} \\\\\\ \boxed{x = 12}~\hfill \stackrel{\textit{we know that}}{y = 60 -x}\implies \boxed{y=48}\)