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The mapping diagram shows a functional relationship.
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Using Function Notation
cowo!
опто
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9
Complete the statement.
f(3) is

El peso de tres cuartas partes de la tableta es \(\frac{3}{7}\) onzas.

La onza es una unidad de masa. En esta pregunta el peso de la porción de la tableta (\(x\)), en onzas, es igual al peso de una tableta (\(w\)), en onzas, multiplicado por la proporción requerida (\(r\)), sin unidades:

\(x = r \times w\) (1)

Si sabemos que \(r = \frac{3}{4}\) y \(w = \frac{4}{7}\,oz\), entonces la proporción requerida de la tableta es:

\(x = \frac{3}{4}\times \frac{4}{7}\,oz\)

\(x = \frac{3}{7}\,oz\)

En consecuencia, el peso de tres cuartas partes de la tableta es \(\frac{3}{7}\) onzas.

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The verification of the identity indicates that the left-hand side of the identity is equal to the right-hand side of the identity:

(2 sin(x) + sin(2x))/4 + 3 cos(x) - cos(2x) = (2 sin(x))/5 - 2 cos(x)

We can start by simplifying the left-hand side of the identity using trigonometric identities:

(2 sin(x) + sin(2x))/4 + 3 cos(x) - cos(2x)

= (2 sin(x) + 2 sin(x) cos(x))/4 + 3 cos(x) - (1 - 2 sin^2(x))

= (sin(x) + sin(x) cos(x))/2 + 3 cos(x) - 1 + 2 sin^2(x)

= sin(x) (1 + cos(x))/2 + 3 cos(x) - 1 + 2 (1 - cos^2(x))

= sin(x)/2 + sin(x) cos(x)/2 + 3 cos(x) - 1 + 2 - 2 cos^2(x)

Next, we can simplify the right-hand side of the identity:

(2 sin(x))/5 - 2 cos(x)

= 2/5 (sin(x) - 5 cos(x)/2)

Now we can try to make the two sides of the identity look more similar by using some algebraic manipulation. First, we can factor out sin(x)/2 from the left-hand side:

sin(x)/2 + sin(x) cos(x)/2 + 3 cos(x) - 1 + 2 - 2 cos^2(x)

= sin(x)/2 (1 + cos(x)) + 3 cos(x) - 2 cos^2(x) + 1

Next, we can rearrange the terms to make it easier to see how we can simplify further:

sin(x)/2 (1 + cos(x)) + 3 cos(x) - 2 cos^2(x) + 1

= -2 cos^2(x) + sin(x)/2 (1 + cos(x)) + 3 cos(x) + 1

Now we can see that the right-hand side of the identity contains -2 cos^2(x) and 3 cos(x), which suggests that we might be able to use the identity cos(2x) = 2 cos^2(x) - 1 to simplify the left-hand side. Let's substitute that identity into the left-hand side and see what happens:

sin(x)/2 (1 + cos(x)) + 3 cos(x) - 2 cos^2(x) + 1

= sin(x)/2 (1 + cos(x)) + 3 cos(x) - cos(2x)

Now we can substitute the right-hand side of the identity into the left-hand side:

sin(x)/2 (1 + cos(x)) + 3 cos(x) - cos(2x)

= sin(x)/2 (1 + cos(x)) + 3 cos(x) - (2 sin(x))/5 + 5 cos(x)/2

Now we can combine like terms:

sin(x)/2 (1 + cos(x)) + 3 cos(x) - (2 sin(x))/5 + 5 cos(x)/2

= sin(x)/2 (1 + cos(x)) - (4 sin(x))/10 + 15 cos(x)/10

= sin(x)/2 (1 + cos(x)) - 2 sin(x)/5 + 3 cos(x)

Finally, we can see that the left-hand side of the identity is equal to the right-hand side of the identity, so we have verified the identity:

(2 sin(x) + sin(2x))/4 + 3 cos(x) - cos(2x) = (2 sin(x))/5 - 2 cos(x)

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Solution

Since the robots must be at least 37 inches tall to enter the competition.

Therefore, the height of any robot must be Any value greater than or equal to 37

Answer:

A.

Step-by-step explanation:

Give the data set: 2, 4, 6, 8, 10, 12.

Find the following:

Min, Q1, Median, Q3, and Max.

Min. = 2

Q1 = 4

Median = (6+8)/2 = 7

Q3 = 10

Max = 12

Check the box plot to see which one represents these values above.

Thus:

The correct box plot would have the whisker to your left at 2, representing the min value.

The Q1 would be at represented by the beginning box the edge of the rectangular box that starts at 4.

The median would be represented by the vertical line that divides the box which would be on 7.

The Q3 would be on the end of the box which is at 10.

The max would be represented by the other whisker that goes to our right, representing 12.

The box plot is that represents this data is the box plot given in option A.

Answer: 135

Step-by-step explanation:

remember PEMDAS

3^3=27

(27*10)/2=270/2=135

Therefore , the solution of the given problem of expressions comes out to be roughly 19.1%,  think bananas are their favourite smoothie ingredient.

Calculations like random division, joining, variable multiplying, and removal are necessary. They would result in the following if they were combined: An equation, some statistics, and a mathematical formula. Numbers, components, formulae, and mathematical processes like additions, deductions, errors, and segments make up a declaration of veracity. Words and phrases can be evaluated and analysed.

Here,

Based on the sample he polled, Brady can conclude that

45 out of 147 customers, or about 30.6%,

think bananas are their favourite smoothie ingredient.

Similarly, Gregory can conclude from the sample he polled that 17 out of 89 customers, or

roughly 19.1%,  think bananas are their favourite smoothie ingredient.

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Step-by-step explanation:

1. 0.07 is the lowest like 7 cents

2. 0.077 is the second one and closer to 8 cents

3. 0.7 the 3rd and like 70 cents

4. 7.0 the greatest like 7 dollars

Answer:

115.38 is what I got when I tryed to work it out

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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Answer:

Step-by-step explanation:

l║m and line t is the transversal line intersecting these parallel lines.

9). If m∠7 = 100°,

    m∠3 = m∠7 = 100° [Since, ∠3 and ∠7 are alternate interior angles]

10). m∠7 = 95°

   m∠6 + m∠7 = 180° [Consecutive interior angles]

   m∠6 = 180° - m∠7

   m∠6 = 180° - 95°

   m∠6 = 85°

11. m∠1 = 120°

   m∠1 = m∠5 = 120° [Alternate exterior angles]

12. m∠4 = 20°

   Since, m∠4 = m∠6 = 20° [Vertically opposite angles]

   And m∠6 + m∠7 = 180° [Consecutive interior angles]

   20° + m∠7 = 180°

   m∠7 = 160°

13. m∠3 = 140°

   m∠3 + m∠6 = 180° [Linear pair of angles]

   m∠6 = 180° - m∠3

            = 180° - 140°

            = 40°

    m∠6 = m∠8 = 40° [Corresponding angles]

14. m∠4 = 30°

    m∠4 + m∠1 = 180° [Consecutive exterior angles]

    m∠1 = 180° - 30°

    m∠1 = 150°

15. m∠4 = 40°

    m∠4 = m∠2 = 40° [Corresponding angles]

16. m∠7 = 125°

    m∠6 + m∠7 = 180° [Consecutive interior angles]

    m∠6 = 180° - 125°

             = 55°

    m∠6 = m∠4 = 55° [Vertically opposite angles]

17. m∠1 + m∠3 = 230°

    Since, m∠1 = m∠3 [Corresponding angles]

    m∠3 + m∠3 = 230°

    m∠3 = \(\frac{230}{2}\)

             = 115°

    m∠3 + m∠6 = 180° [Linear pair of angles]

    m∠6 = 180° - 115°

    m∠6 = 65°

Answer:

0.75 g ≤ 35

Step-by-step explanation:

if each games costs $0.75, then the answer of g will be given by 35/0.75.

he can go up to exactly $35 but not over

so, the inequality is given by 0.75 g ≤ 35

The number of fidgets and pop bought was 15 each

From the information given, we have that;

1 fidget costs $3

1 Pop cost $4

Let the number of Fidgets be x

Let the number of Pop be y

Then, we have that a total of 20 fidgets and Pop cots $75

We have that;

20x + y = 75

Now, substitute the value of x as 3, we get;

20(3) + y= 75

expand the bracket

y = 75 - 60

y = 15

The number of fidgets is expressed as;

20x/4 = 20(3) /4 = 15

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Answer:

(-6,4)

Step-by-step explanation:

Solve the following system:

{4 y + 5 x = -14 | (equation 1)

2 y + x = 2 | (equation 2)

Subtract 1/5 × (equation 1) from equation 2:

{5 x + 4 y = -14 | (equation 1)

0 x+(6 y)/5 = 24/5 | (equation 2)

Multiply equation 2 by 5/6:

{5 x + 4 y = -14 | (equation 1)

0 x+y = 4 | (equation 2)

Subtract 4 × (equation 2) from equation 1:

{5 x+0 y = -30 | (equation 1)

0 x+y = 4 | (equation 2)

Divide equation 1 by 5:

{x+0 y = -6 | (equation 1)

0 x+y = 4 | (equation 2)

Collect results:

Answer: {x = -6 , y = 4

Answer:

Step-by-step explanation:

5x + 4y = -14

-5x - 10y = - 10

-6y = -24

y=  4

x + 2(4) = 2

x + 8 = 2

x = -6

(-6, 4)

Option 3

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

Answer: 12340

Step-by-step explanation:

Di jsjsjs

Siendo nxnsnen

Ncnsnsns

Jim did not buy any tickets (n_Jim = 0).

Larry bought 7 more tickets than Jim.

To determine the number of tickets Larry bought more than Jim, we need to find the values of n for Larry and Jim's ticket purchases.

For Larry:

Let's substitute C = $170 into the equation C = 24n + 2 and solve for n:

$170 = 24n + 2

Subtracting 2 from both sides:

$168 = 24n

Dividing both sides by 24:

n = 7

For Jim:

We can calculate the number of tickets Jim bought by subtracting 12 from Larry's number of tickets:

n_Jim = n_Larry - 12

n_Jim = 7 - 12

n_Jim = -5

Since we cannot have a negative number of tickets, we can conclude that Jim did not buy any tickets (n_Jim = 0).

To find the difference in the number of tickets bought, we subtract the number of tickets Jim bought from the number of tickets Larry bought:

n_difference = n_Larry - n_Jim

n_difference = 7 - 0

n_difference = 7

Therefore, Larry bought 7 more tickets than Jim.

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Question

The equation C=24n+2 represents the cost, C, in dollars, of buying n tickets to a play. J $170. How many more tickets did Larry buy than Jim? 12

A congruence statement is a mathematical statement that expresses that two shapes or figures are congruent, meaning that they have the same size and shape.

When talking about polygons specifically, a congruence statement would involve two polygons being congruent if they have the same number of sides and all corresponding sides are congruent. This means that all sides of the polygons have the same length and all angles have the same measure. For example, if there are two polygons, P and Q, a congruence statement for them would be written as “P ≅ Q”. This means that P and Q are equal in size and shape, and all sides and angles are equal. Another way to express this is that “P is congruent to Q”. To prove that two polygons are congruent, a variety of methods can be used, such as the Side-Angle-Side (SAS), Angle-Side-Angle (ASA), or Side-Side-Side (SSS) theorem. These theorems use angles and side lengths to determine whether or not two polygons are congruent.

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Answer:

Step-by-step explanation:

Statement                     Reason

PR ≅ TR                        Given

<PQR≅<TSR                 Given

<PRQ≅<TRS                Vertical Angles Theorem

PQR=TSR                      SAS  Theorem   (Side-Angle-Side)

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

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

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

The value of x is -1/2 or 3/2

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

Given:

x² − x − 3/4 = 0

4x² - 4x -3=0

4x² -6 x + 2x -3 =0

2x( 2x -3 ) +1 ( 2x -3)= 0

(2x +1) (2x-3)=0

x= -1/2, 3/2

x= -0.5, 1.5

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A) The probability of choosing a tile at random from a bag containing 2 As, 3 Bs, and 4 Cs is 1/9. This is because there are a total of 9 tiles in the bag and each tile has an equal chance of being chosen.

Probability is a measure of the likelihood that a given event will occur, expressed as a number between 0 and 1. A probability of 1 indicates that the event is certain to occur, while a probability of 0 indicates that the event is impossible.

B) The probability of choosing the same tile again after replacing the first tile is still 1/9. This is because replacing the first tile does not change the probability of any of the tiles being chosen. Each tile still has an equal chance of being chosen.

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SOLUTION:

Step 1:

In this question, we are given the following:

What are the coordinates of the origin?

Cartesian coordinates

The coordinates of the origin are always all zero,

for example, (0,0) in two dimensions.

CONCLUSION:

The final answer = ( 0, 0 ) -- ( OPTION D)

Answer:

y = 14 and lh = 16

Step-by-step explanation:

i already answered this in ur other question

Answer:

3816547290

Step-by-step explanation:

this is from a puzzle called notable numbers

Answer:

Step-by-step explanation:

Given that :

the side of the square = 90ft

The speed of the runner = 31 ft/sec

By the time the runner is halfway to the first base;  the distance covered by the runner in time(t)  is (31 t) ft and the distance half the base = 90/2 = 45 ft

Thus; 31 t = 45

t = 45/31

From the second base ; the distance is given as:

P² = (90)² + (90 - 31t )²  

P = \(\sqrt{(90)^2 + (90 - 31t )^2}\)

By differentiation with time;

\(\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } *(0+ 2 (90-31t)(0-31))\)

\(\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +(90-31t)^2} } * 2 (-31)(90-31t)\)

At t = 45/31

\(\dfrac{dP}{dt} =\dfrac{1}{ 2 \sqrt{90^2 +45^2} } * 2 (-31)(45)\)

\(\dfrac{dP}{dt} =\dfrac{-35*45}{100.623}\)

= - 13.86 ft/sec

Hence, we can conclude that  as soon as the runner  is halfway to the first base, the distance to the second base is therefore decreasing by 13.86 ft/sec

b) The distance from third base can be expressed by the relation:

q² = (31t)² + (90)²

\(q = \sqrt{(31t)^2+(90)^2}\)

By differentiation with respect to time:

\(\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + (31)t^2} } *(0+31^2 + 2t)\)

At t = 45/31

\(\dfrac{dq}{dt} = \dfrac{1}{2\sqrt{90^2 + 45^2} } *(0+31^2 + \frac{45}{31})\)

\(= \dfrac{31*45}{100.623}\)

\(= 13.86 \ ft/sec\)

Thus, the rate at which the runner's distance is from the third base is increasing at the same moment of 13.86 ft/sec. So therefore; he is moving away from the third base at the same speed to the first base)

a) The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.

b) The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.

a) As the batter runs towards the first base, both the distance from second base and the length of the line segment PQ decrease in time. The distance from the second base is determined by Pythagorean theorem:

\(QS^{2} = QP^{2}+PS^{2}\) (1)

By differential calculus we derive an expression for the rate of change of the distance from second base (\(\dot QS\)), in feet per second:

\(2\cdot QS \cdot \dot{QS} = 2\cdot QP\cdot \dot{QP} + 2\cdot PS\cdot \dot {PS}\)

\(\dot{QS} = \frac{QP\cdot \dot QP + PS\cdot \dot{PS}}{QS}\)

\(\dot {QS} = \frac{QP\cdot \dot {QP}+PS\cdot \dot {PS}}{\sqrt{QP^{2}+PS^{2}}}\) (2)

If we know that \(QP = 0.5L\), \(PS = L\), \(L = 90\,ft\), \(\dot {QP} = -31\,\frac{ft}{s}\) and \(\dot {PS} = 0\,\frac{ft}{s}\), then the rate of change of the distance from second base is:

\(\dot {QS} = \frac{(45\,ft)\cdot \left(-31\,\frac{ft}{s} \right)}{\sqrt{(45\,ft)^{2}+(90\,ft)^{2}}}\)

\(\dot {QS} \approx -13.864\,\frac{ft}{s}\)

The distance from second base is decreasing when the batter is halfway to first base at a rate of 13.9 feet per second.

b) As the batter runs towards the first base, both the distance from third base increases and the distance from home increase in time. The distance from the third base is determined by Pythagorean theorem:

\(QT^{2} = HT^{2}+QH^{2}\) (3)

By differential calculus we derive an expression for the rate of change of the distance from third base (\(\dot QT\)), in feet per second:

\(2\cdot QT\cdot \dot{QT} = 2\cdot HT\cdot \dot {HT} + 2\cdot QH\cdot \dot {QH}\)

\(\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{QT}\)

\(\dot {QT} = \frac{HT\cdot \dot {HT}+QH\cdot \dot {QH}}{\sqrt{HT^{2}+QH^{2}}}\)

If we know that \(HT = 90\,ft\), \(QH = 45\,ft\), \(L = 90\,ft\), \(\dot{HT} = 0\,\frac{ft}{s}\) and \(\dot {QH} = 31\,\frac{ft}{s}\), then the rate of change of the distance from third base is:

\(\dot{QT} = \frac{(45\,ft)\cdot \left(31\,\frac{ft}{s} \right)}{\sqrt{(90\,ft)^{2}+(45\,ft)^{2}}}\)

\(\dot{QT} \approx 13.864\,\frac{ft}{s}\)

The distance from third base is increasing when the batter is halfway to first base at a rate of 13.9 feet per second.

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The value of Betty's earnings of $55,000 in 1992 dolars is $44,141.25.

The consumer price index measures the changes in price of a basket of good.

CPI = (cost of basket of goods in current period / cost of basket of goods in base period) x 100

Value of the current earnings in 1992 dollars = $55,000 / 1.246 = $44,141.25

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