The function h is defined by h (x) = x² + 3. Find h (3x) A (3x) = []​

The frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

It is defined as the frequency that can be evaluated by the two-way frequency table. Usually, we can obtain this frequency by dividing the frequency that is not in the total frequency cell to total frequency.

It is given that:

24 children were asked which is their favourite colour from a choice of red, blue

green or yellow

From the data given in the question.

Red : 6

Blue: 4

Green: 8

Yellow : 1 (half of 2)

Pink: 1 (half of 2)

Thus, the frequencies will be Red : 6, Blue: 4, Green: 8, Yellow : 1 (half of 2), Pink: 1 (half of 2).

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Answer:

232

Step-by-step explanation:

[8*10*2]+[10*3]+[6*3]+[8*3] = 232

Answer:

What you are trying to do here is prove that the two triangles are congruent.

You want to do this using geometric statements. What kind of proof are you supposed to do?

Step-by-step explanation:

Given statement solution is :-  The Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

To find the sum of 4 + 20, we simply add the two numbers together:

4 + 20 = 24

As for the given vectors, let's perform the requested calculations:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 4 + (-4), -2 + (-32) > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 7 - (-8), -3 - (-30) > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 5 + 2, -11 + 0, 0 + 0, 0 + 0 > = < 7, -11, 0, 0 >

Therefore, the Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

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The present age of the elder brother is in a ratio of 23 to the present age of the younger brother, which can be simplified to a ratio of 5 to 4.

Let's assume the present age of the elder brother is E years, and the present age of the younger brother is Y years. According to the given information, the difference in their ages is 5 years, which can be expressed as E - Y = 5.

Six years ago, the elder brother's age was E - 6, and the younger brother's age was Y - 6. According to the second given condition, the product of their ages at that time was 696, which can be expressed as (E - 6)(Y - 6) = 696.

To find the ratio of their present ages, we need to solve the two equations simultaneously. We can start by expanding the second equation:

(E - 6)(Y - 6) = 696

EY - 6E - 6Y + 36 = 696

EY - 6E - 6Y = 660

Now we can substitute the value of E - Y from the first equation into the second equation:

(E - Y) - 6E - 6Y = 660

5 - 6E - 6Y = 660

-6E - 6Y = 655

Simplifying the equation:

6E + 6Y = -655

Now we have a system of linear equations:

E - Y = 5

6E + 6Y = -655

Solving these equations, we find that the present age of the elder brother (E) is 23 years and the present age of the younger brother (Y) is 18 years.

Therefore, the ratio of the present age of the elder brother to the younger brother is 23:18, which can be simplified to 5:4.

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Answer:

To find the area of a rectangle, we multiply its length by its width.

Area = length x width

In this case, the length is 3 feet and the width is 13 feet.

Area = 3 ft x 13 ft

Area = 39 ft²

Therefore, the area of the rectangle is 39 square feet. None of the given options is correct.

Solution for the given System of linear equation is:

Simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods to solving systems of equations: graphing, substitution, elimination and matrices.

Given,  the system of linear equations on the left with its solution type on the right

For  Y=2x-1 and Y=2x+1

Adding both equation,  we will get y = 4x

Thus, these equations have infinite number of solution

For 2x - y = 7 and 3x + y = 3

Adding these equations

5x = 10

x= 2

Substitute the value in equation 1

y = -3

Thus, solution is (2, - 3)

therefore, the Solution for the given System of linear equation is:

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Complete question:

For example, 0.123 would be a legitimate entry. Lower limit (first blank) = 0.285, Upper limit (second blank) = 0.562.

The confidence interval for proportions is

p±z *√p(1-p)/n.

In this case, p = 36/85 = .4235, and z* = 2.575 (the value of the standard normal distribution corresponding to 99%).

so,

0.4235 ± 2.576 * √0.4235*0.5765/85

0.4235 ± 0.13804

= (0.285, 0.562)

Therefore, Lower limit is 0.285 and Upper limit 0562.

A confidence interval is the mean of your estimate plus and minus the variation in that estimate. This is the range of values you anticipate your estimate to fall between if you redo your test, within a certain position of confidence.

Confidence, in statistics, is another way to describe probability. For illustration, if you construct a confidence interval with a 95 confidence position, you're confident that 95 out of 100 times the estimate will fall between the upper and lower values specified by the confidence interval.

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ANSWER

T = 1.49x + 15.99

EXPLANATION

Let the number of games to be downloaded be x.

The website charges a membership fee of $15.99 and a fee of $1.49 to download a game.

This means that if you want to download x games, the download fee will be:

1.49 * x = $1.49x

The total cost (in dollars) to download any number (x) of games will therefore be:

T = 1.49x + 15.99

Answer:

1/2 ÷ 1/8 =b

Step-by-step explanation:

The perimeter of the trapezoid is given as follows:

44 cm.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The missing side is a side of a right triangle, in which the other side is of 18 - 10 = 8 cm, while the hypotenuse is of 10 cm, hence:

8² + h² = 10²

64 + h² = 100

h² = 36

h = 6.

Hence the perimeter is given as follows:

P = 18 + 10 + 10 + 6 = 44 cm.

The trapezoid is given by the image presented at the end of the answer.

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Answer:

1/3

Step-by-step explanation:

3x + y = -6

y = -3x - 6

The slopes of two perpendicular lines are negative reciprocals of each other

so negative reciprocal of -3 is 1/3

\( \large{ \boxed{ \tt{Answer : - 3}}}\)

Please see the attached picture for full solution!

-------- HappY LearninG <3 --------

La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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Answer:

Step-by-step explanation:

You want to show that the point (4, -4) is on the graph of x² +y² = 32, and you want the tangent and normal lines at that point.

The point is on the curve because when x = 4 and y = -4 the resulting statement is 16 +16 = 32, which is a true statement.

The tangent to a circle is most easily found by first considering the normal. The normal line will be the line through the point on the circle and the center of the circle. Here, the center is (0, 0). The slope of the normal line is ...

  m = y/x = -4/4 = -1

The tangent line's slope is the opposite reciprocal of this:

  m = -1/(-1) = 1

The point-slope form of the equation for the tangent line is ...

  y -k = m(x -h) . . . . . equation for line with slope m through point (h, k)

  y -(-4) = 1(x -4) . . . . . equation for line with slope 1 through point (4, -4)

  x -y = 8 . . . . . . . . . . add 4-y to put in standard form

The equation of the tangent line is x - y = 8.

In the section above, we found the slope of the normal line is -1. We also noted that the normal line goes through the point (0, 0). Then the point-slope form of the normal line is ...

  y -0 = -1(x -0)

  y = -x

The equation of the normal line is y = -x.

__

Additional comment

The normal line can also be written as x + y = 0.

The tangent line can also be written as y = x -8.

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The standard deviation for the given data, can be found to be 3. 97

To find the standard deviation, you first need to find the mean of the data as:

= Sum of the numbers / Sample number

= ( 16 + 10 + 5 + 7 + 13 ) / 5

= 51 / 5

= 10. 2

The variance can then be found from this data, the mean, and a variance calculator to be 15.76.

The standard deviation is:

= √ 15.76

= 3. 97

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The result of 1/11 in the base 10 system is given as is 0.09.

To visualize the long division of 1 ÷ 11 in a base ten system:

Set up the long division: 11 outside and 1.00 inside the division bracket.

Place the decimal point in the quotient above the dividend's decimal point.

Bring down the first digit (0) and divide 11 into 10; it goes 0 times.

Subtract the product (0) from 10, leaving 10.

Bring down the next digit (0) and divide 11 into 100; it goes 9 times.

Subtract 99 from 100, leaving a remainder of 1.

The result is 0.09.

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Answer:

Suppose X ~ N(12,2) represents a normal distribution with mean 12 and standard deviation 2. According to the empirical rule, about 68% of the x values lie within one standard deviation of the mean .

We can calculate the endpoints of the interval that represents one standard deviation from the mean as follows:

Lower endpoint: 12 - 2 = 10

Upper endpoint: 12 + 2 = 14

Therefore, about 68% of the x values lie between 10 and 14 1.

Step-by-step explanation:

The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Answer:

Step-by-step explanation:

Answer:

1i.) x = 18

1ii.) x = 40

2.) x = 155

3i.) ABD = 115° (actually this is wrong, idk how to calculate this ;-;

3ii.) BEF = 135°

Step-by-step explanation:

*All triangles add up to 180° in total of all angles added together*

i.) Find x

4x + 3x + 3x = 180°

10x = 180°

10x/10 = 180/10

x = 18

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

ii.) Find x

180 - 115 = 65

65° + 75° + x° = 180°

140° + x° = 180°

x° = 180° - 140°

x = 40°

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

2.) Find x

180 - 145 = 35

45° + 35° + n° = 180°

80° + n° = 180°

n° = 180° - 80°

n° = 100°

*Vertical Angles of n and m (variables I randomly made so I can solve this), so they are both the same*

100 + 55 + m = 180

155 + m = 180

m = 180 - 155

m = 25

25 + x = 180

x = 180 - 25

x = 155

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

3.) Find Angles

i.) ABD

180° - 65° = 115°

Angle ABD = 115°

ii.) BEF

180° - 110° = 70°

70° + 65° + x° = 180

135° + x° = 180°

x° = 180° - 135°

x = 45°

180° - 45° = 135°

Angle BEF = 135°

Answer:

5.6 × 10⁻⁵ mol/L

Step-by-step explanation:

The probability of selecting a junior who takes the bus is P (Junior who takes the bus) = 12/200 = 0.06Hence, the probability that a randomly selected student is a junior who takes the bus is 0.06 or 6/100.

The given frequency table on how students get to school among the high school students is represented in the below table:Transportation Walk Bike BusDriveTotalGrade 9 11 10 14 15 50Grade 10 10 7 13 20 50Grade 11 8 6 12 24 50Grade 12 5 8 8 29 50 Total 34 31 47 88 200Given data from the above frequency table, we are interested in finding the probability of a randomly selected student being a junior who takes the bus.SolutionWe know that the total number of students is 200, and the total number of junior students is 50. Hence the probability of selecting a junior is P (Junior) = 50/200 = 0.25Similarly, the number of students who take the bus is 47 and the number of junior students who take the bus is 12.

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Answer:

676 square inches

a = L²

It has been established in the question that the length and the width of the chessboard has 8 rows an 8 columns respectively

length = with

rows = columns

8 × 3.25 = 26inches

AREA = L²

A = 26²

A = 676 square inches

The area in square inches of the chessboard given the side length of a square space is 676 inches².

A square is a quadrilateral with four equal sides.

The first step is to determine the area of a square space.

Area = length²

3.25² = 10.56 in²

The second step is to multiply the area of the square space by the number of squares.

8x 8 x 10.56 = 676 inches².

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The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Therefore, the 95% confidence interval for the difference in scores is (9.936, 11.864).

In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence, based on a sample of data.

Here,

To find the confidence interval for the difference in scores, we can use the formula:

CI = (x1 - x2) ± t(α/2, df) * SE

where x1 and x2 are the sample means for groups 1 and 2, t(α/2, df) is the critical t-value based on the level of significance α and the degrees of freedom df, and SE is the standard error of the difference between the means, given by:

SE = √((s₁²/n₁) + (s₂²/n₂))

where s₁ and s₂ are the sample standard deviations for groups 1 and 2, and n₁ and n₂ are the sample sizes.

Given:

x1 = 26.4, s₁ = 4.4, n₁ = 200

x2 = 15.5, s₂ = 2.4, n₂ = 200

α = 0.05

df = n₁ + n₂ - 2 = 398 (assuming equal variances)

First, we need to calculate the standard error:

SE = √((4.4²/200) + (2.4²/200))

= 0.492

Next, we need to find the critical t-value:

t(α/2, df) = t(0.025, 398)

= 1.964

Finally, we can calculate the confidence interval:

CI = (26.4 - 15.5) ± 1.964 * 0.492

= 10.9 ± 0.964

= (9.936, 11.864)

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Recurrence functions are used to preedict the subsequent value in a sequence. The fourth term of the sequence based on the recurrence relation is 25

Given the recurrence relations according to the question

s(1) = 2 and

s(2)=3

s(k) =s(k-1)+2s(k-2)+6

If s(1) = 2, hence;

s(3) =s(3-1)+2s(3-2)+6

s(3) = s2 + 2s1 + 6
s(3) = 3 + 2(2) + 6
s(3) = 13

Determine the fourth term:

s(4) =s(4-1)+2s(4-2)+6

s(4) = s3 + 2s2 + 6
s(4) = 13 + 2(3) + 6
s(4) = 25

Hence the fourth term of the sequence based on the recurrence relation is 25

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Answer:9

Step-by-step explanation:

Answer:

Width = x² + 5x - 4

Step-by-step explanation:

By the definition of an area model,

Area = Width × greatest common factor

Since, Area = 4x² + 20x - 16

And greatest common factor = 4

4x² + 20x - 16 = 4(Width)

By dividing both the sides of the equation by 4,

\(\frac{4x^2+20x-16}{4}=\frac{4(\text{Width})}{4}\)

x² + 5x - 4 = Width

Therefore, width = (x² + 5x - 4) will be he answer.

Find the third angle of a triangle with 126° and 41° as two of it's angles.

\( \star \: \small{ \rm{ In \: this \: question \: we \: are \: provided \: with }}\\ \small{\rm{ the \: two \: angles \: of \: the \: triangle}} \\ \small{\rm \: {and \: asked \: to \: calculate \: the \: third \: angle.}}\)

Let us assume the third angle as x

We know,

Sum of all angles of the triangle = 180°

According To Question

\( \small\bf \blue{ 126° + 41° + x° = 180°}\)

→ 167° + x° = 180°

→ x = 180° - 167° = 13°

\( \small\boxed{ \pink{ \frak{ x = 13°}}}\)

Hence, the third angle is 13°.