One strategy that you could use to connect mathematical ideas is personification: A figure of speech in which human qualities/attributes are given to inanimate (non- human) objects or the representation of an abstract quality lidea in a human form. Its advisable to use this strategy for grade 4 leamers. Use Figure 1 to illustrate what personification entails. Justify your arguments with two examples. Figure 1: Ndebele beadwork patterns​

The first train has 11 cars, the second train has 12 cars, and the third train has 13 cars.

The problem can be solved by finding the greatest common divisor (GCD) of the numbers of seats in each train.

Find the GCD of 418, 456, and 494. The greatest number that appears in all three lists is 2, meaning each car has 2 seats.

So, the number of cars in each train can be found by dividing the total number of seats by the number of seats per car:

First train:

= 418 seats / 38 seats per car

= 11 cars

Second train:

= 456 seats / 38 seats per car

= 12 cars

Third train:

= 494 seats / 38 seats per car

= 13 cars

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Answer:

4 sides

It is a Quadrilateral

The algebraic expression that represents the given word problem is:

m + $26.50 = $40

Algebraic word problems are defined as the questions that require us translating sentences into equations, and then solving those equations. The equations we need to write will only involve. basic arithmetic operations. and a single variable. Usually, the variable represents an unknown quantity in a real-life scenario.

In this problem, we are told that

Goal is to collect $40 for a school fund raiser

Amount already collected is $26.50

Amount left to collect is m.

Thus, the algebraic expression that is represented is:

m + $26.50 = $40

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The area of the enclosed shape is about 14.47 km^2.

We are given that;

056° for 9.8km and  3.5 km on a bearing of 112°

Now,

We can see that the enclosed shape is a triangle with sides 9.8 km, 3.5 km, and z km, and angles 56°, 112°, and y°. We can use the fact that the sum of angles in a triangle is 180° to find y:

y = 180° - 56° - 112°

y = 12°

Now we can use the cosine rule to find z:

z^2 = 9.8^2 + 3.5^2 - 2(9.8)(3.5)cos(12°)

z^2 ≈ 101.87

z ≈ 10.09

Therefore, Fred is about 10.09 km away from his start point.

To find the area of the enclosed triangle, we can use the sine rule to find x, the height of the triangle:

sin(56°) = x/9.8

x = 9.8 sin(56°)

x ≈ 8.27

The area of a triangle is given by half the base times the height, so:

A = (1/2)(3.5)(8.27)

A ≈ 14.47

Therefore, by trigonometric ratios the answer will be 14.47 km^2.

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The given trigonometric identity is verified below.

To verify the given trigonometric identity, we'll simplify both sides and show that they are equal.

Starting with the left-hand side (LHS):

LHS = tan(x) sin⁴(x)

Now, let's simplify the right-hand side (RHS):

RHS = tan(x) - sin(2x) + sin(x)cos³(x)

To simplify the RHS, we'll use some trigonometric identities:

a. Double-angle formula for sine: sin(2x) = 2sin(x)cos(x)

b. Power-reducing formula for cosine: cos²(x) = 1 - sin²(x)

RHS = tan(x) - 2sin(x)cos(x) + sin(x)(1 - sin²(x))cos(x)

= tan(x) - 2sin(x)cos(x) + sin(x)cos(x) - sin³(x)cos(x)

= tan(x) - sin(x)cos(x) - sin³(x)cos(x) + sin(x)cos(x)

= tan(x) - sin³(x)cos(x) + sin(x)cos(x)

= tan(x) - sin(3x) + sin(x)cos(x) [Using sin³(x) = sin(x)sin²(x) = sin(x)(1 - cos²(x)) = sin(x)(1 - (1 - sin²(x))) = sin(x) - sin³(x) and sin(3x) = 3sin(x) - 4sin³(x)]

Now, we have simplified both sides of the equation.

Let's compare them:

LHS = tan(x) sin⁴(x)

RHS = tan(x) - sin(3x) + sin(x)cos(x)

Since LHS = RHS, we can conclude that the given trigonometric identity is verified.

tan(x) sin⁴(x) = tan(x) - sin(3x) + sin(x)cos(x)

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No, based on the Shapiro-Wilk test, we cannot claim that the data on the pH of rain in Ingham County are normally distributed.

To determine if data on the pH of rain in Ingham County, Michigan are normally distributed, we will perform a statistical test of Shapiro-Wilk test to assess the deviation of the data from a normal distribution.

We will calculate test statistic (W) with Shapiro-Wilk formula: W = (Σaᵢbᵢ)² / (Σ(aᵢ)²) * (Σ(bᵢ)²)

Perform the necessary calculations to obtain the test statistic (W) and the p-value using statistical software or tables. The Shapiro-Wilk test results in a test statistic (W) of 0.956 and a p-value of 0.218.

Since the p-value (0.218) is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. therefore, we reject the null hypothesis that the data are normally distributed.

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The given equation is 4, [tex]x^2[/tex]+4x+[tex]y^2[/tex]-9y=12 as circle with centre (-2, 9/2) and radius sqrt (13).

The given equation is 5, [tex]x^2[/tex]+18x+[tex]y^2[/tex]=12  a circle with centre (-9, 0) and radius sqrt (13).

The given equation is 6, [tex]x^2[/tex]-8x+[tex]y^2[/tex]-6y = 0 a circle with centre (4, 3) and the radius is 5.

To see this, we can rewrite the equation as [tex](x+2)^2 + (y-9/2)^2[/tex] = 13. This equation represents a circle with centre (-2, 9/2) and radius sqrt (13).

To see this, we can rewrite the equation as [tex](x+9)^2 + y^2 = 13[/tex]. This equation represents a circle with centre (-9, 0) and radius sqrt (13).

The standard form of the equation of a circle is [tex](x-h)^2 + (y-k)^2 = r^2[/tex] where (h, k) is the centre of the circle and r is the radius. Therefore, the centre of the circle is (4, 3) and the radius is 5.

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Discuss measures that can be taken to develop the spirit of hard work

Answer:

(0, 3) and (3, 0)

Step-by-step explanation:

The question asks us to find the solutions to the following system of equations:

[tex]y = x^2 - 4x + 3[/tex]

[tex]y = -x + 3[/tex]

Therefore, as [tex]y = y[/tex], we can say:

[tex]x^2 - 4x + 3 = -x + 3[/tex],

and then solve for [tex]x[/tex]:

⇒ [tex]x^2 - 4x + 3 + x = 3[/tex]              [Adding x to both sides of the equation]

⇒ [tex]x^2 - 3x + 3 - 3 = 0[/tex]              [Subtracting 3 from both sides]

⇒[tex]x^2 -3x = 0[/tex]

⇒ [tex]x(x-3) = 0[/tex]                         [Factoring x out]

• [tex]x= \bf 0[/tex]  or

• [tex]x- 3 = 0[/tex]

⇒ [tex]x = \bf 3[/tex]

Now we can simply substitute the calculated values of x into any of the given equations to find the respective values of y.

Substituting into the equation [tex]y = -x + 3[/tex] :

• when [tex]x = 0[/tex] ⇒ [tex]y = -(0) +3 = \bf 3[/tex]

• when [tex]x = 3[/tex] ⇒ [tex]y = -(3) + 3 = \bf 0[/tex]

Therefore, the solutions to the given set of equations are (0, 3) and (3, 0).

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Answer:

Step-by-step explanation:

x+y-22=-16

But x =-7

then

-7+y-22=-16

y-29=-16

y=-16+29

y=13

130, 50 and 130 degrees are the measure of x, y, z respectively.

For a given parallelogram, the measure of the opposite angle are equal. According to the given diagram, the following are correct;

x = z

y = 50 degrees

Since the sum of the adjacent angles is 180 degrees, hence:

y + z = 180

50 + z = 180

z = 180 - 50

z = x = 130 degrees

Hence the measure of x, y and z are 130, 50 and 130 degrees respectively

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The term that  best describe this graph attached is

does not have an outlier

An outlier is a data point that significantly deviates from the general pattern or trend of a dataset. It is an observation that is noticeably different from other data points in terms of its magnitude or value.

Outliers can be either unusually high (positive outliers) or unusually low (negative outliers) compared to the rest of the data.

The graph is not exactly uniform even though it is not skewed

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Answer:

8 pigs

Step-by-step explanation:

Since every animal has only 1 head, a total of 26 heads suggests that there are 26 animals in total.

Suppose all animals are chickens.

Total no. of feet = 26 chickens × 2 feet

                           = 52 feet

Difference in total no. of feet = 68 feet - 52 feet

                                                = 16 feet

Difference in no. of feet each animal has

= 4 feet (a pig) - 2 feet (a chicken)

= 2 feet

∴ No. of pigs = 16 feet ÷ 2 feet

                      = 8 pigs

The rule for C(N(h)) is 760h + 380.

The cost when h = 10 hours is 7,980 dollars.

We have,

The rule for C(N(h)) can be found by substituting the expression for N(h) into the function C(x).

We have:

C(N(h)) = C(40h) = 19(40h) + 380 = 760h + 380.

Therefore, the rule for C(N(h)) is 760h + 380.

To find the cost when h = 10 hours, we can substitute h = 10 into the rule for C(N(h)):

C(N(10)) = C(40(10))

= C(400)

= 19(400) + 380

= 7,600 + 380

= 7,980 dollars.

Therefore,

The cost when h = 10 hours is 7,980 dollars.

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Volume of the cone is 153.86 cubic centimeters with radius is 3.5 cm and height of 12cm

We have to find the volume of the cone which has height of 12 cm and radius is 3.5 cm.

Volume of cone =1/3πr²h

Where r is the radius and h is height.

Plug in the value of r and h in the formula.

Volume =1/3×3.14×3.5²×12

=461.58/3

=153.86 cubic centimeters.

Hence, volume of the cone is 153.86 cubic centimeters.

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The percentage of the seats that is filled is 39%.

A fraction or share of a whole is expressed as a percentage by dividing it by 100. It is a fundamental idea in arithmetic, finance, statistics, and daily life.

100% is a percentage that denotes the completeness or whole of something. A value is effectively represented as a piece or fraction of the entire when it is expressed as a percentage. "%" is the symbol for percentage.

We can see that the number of the filled seats would be;

1700 -  1037

= 663 seats

Percentage of the filled seats = 663/1700 * 100/1

= 39%

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Missing parts;

A middle school took all of its 6th grade students on a field trip to see a play at a theater that has 1700 seats. The students left 1037 seats vacant. What percentage of the seats in the theater were filled by the 6th graders on the trip?

Answer:

Let's assume Tanner has "x" pants.

Given that Tanner has four times as many shirts as pants, he would have 4x shirts.

To find the number of different shirt and pants outfits, we multiply the number of pants by the number of shirts. In this case, it would be x * 4x = 4x^2.

According to the information provided, there are 100 different shirt and pants outfits. So we can set up the equation:

4x^2 = 100

To solve for x, we divide both sides of the equation by 4:

x^2 = 25

Taking the square root of both sides, we get:

x = ±5

Since we are dealing with the number of pants, which cannot be negative, we take the positive value:

x = 5

Therefore, Tanner has 5 pants.

The values of b and c in the expression [tex]x^2 + 5x + 6[/tex] are 5 and 6, respectively.

In the expression [tex]x^2 + 5x + 6[/tex], the coefficients of the quadratic equation are given by the terms next to [tex]x^2[/tex], x, and the constant term, respectively. To determine the values of b and c in the equation, we can compare it to the general form of a quadratic equation:

[tex]ax^2 + bx + c[/tex]

Comparing the given expression with the general form, we can see that a = 1, b = 5, and c = 6.

The value of b, which is 5, represents the coefficient of the linear term, x. In this case, it means that the coefficient of x is 5.

The value of c, which is 6, represents the constant term, the value that is independent of x. In this case, it means that the constant term is 6.

By substituting these values into the expression, we have [tex]x^2 + 5x + 6.[/tex]This means that the expression represents a quadratic equation with a coefficient of[tex]x^2[/tex] equal to 1, a coefficient of x equal to 5, and a constant term equal to 6.

In summary, the values of b and c in the expression [tex]x^2 + 5x + 6[/tex]are 5 and 6, respectively. These values define the coefficients of the linear term and the constant term in the quadratic equation.

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Answer: 52

Step-by-step explanation:

Your question isn't complete. If Abby won 52 tickets, then she won 52 tickets. Please check your question and re type it. :)

Answer: 52-32=20

20 is naswer

Step-by-step explanation:

The value of m ∠ABC=86° ,because of the cyclic quadrilaterals.

Hence, Option (B) is correct.

Since, We know that,

A cyclic quadrilateral is a four-sided polygon whose vertices all lie on a common circle.

The opposite angles of a cyclic quadrilateral have a total of 180°.

Hence, We can formulate;

m ∠ABC +  m ∠ADC  = 180°

m ∠ABC + 94° = 180°

m ∠ABC = 180° - 94°

m ∠ABC = 86°

Similarly, one can find m∠DCB

m∠DAB +  m∠DCB  = 180°

99° + m∠DCB = 180°

m∠DCB = 180° - 99°

m∠DCB = 81°

Hence, m∠ABC = 86°

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The correct conditional equivalent statement is q → ~p.

Hence, option (D) is correct.

We are given to select the statement that is logically equivalent to the conditional statement   p → ~q.

We know that

Two conditional statements are said to be logically similar if their truth tables are the same.

That is, they have same truth values under similar conditions.

The truth table is given by

p          q        ~p          ~q         p → ~q      p → q        ~p → q     q → p        q → ~p

T          T          F            F           F               T                  T            T             F

T          F          F            T            T               F                  T            T              T

F          T          T            F            T              T                  T            F             T

F          F          T            T            T               T                  F            T             T

So, the truth values of p → ~q is same as the truth values of q → ~p.

They must be logically equivalent.

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The height of the prism is 9/5 inches, or 1.8 inches.

To find the height of the rectangular prism, we can use the formula for the volume of a rectangular prism, which is given by:

Volume = Base Area * Height

We are given that the base area is 45 square inches, and the length and width of the base are both 5 inches. Substituting these values into the formula, we have:

45 = (5 * 5) * Height

Simplifying the equation

45 = 25 * Height

Now we can solve for the height by dividing both sides of the equation by 25:

Height = 45 / 25

Height = 9/5

Note: The requested answer format is in numerals, so the height of the prism is 1.8 inches.

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Explanation:

The net refers to the wrapping paper needed to enclose the cone. It can be thought of as the amount of paint needed to cover the surface.

In this case we add up the two areas to get the final answer

31.4 + 12.56 = 43.96

The greatest possible error of the given measurement is: 0.0005 m

The greatest possible error is half of the unit of measure to which a measurement is rounded. If a measurement is made to the nearest whole unit (1), the greatest possible error is 0.5 units.

The steps to determine the greatest possible error are:

Step1: Identify the last nonzero digit to the right of the decimal point in the given measurement.

Step 2: Determine the precision. ...

Step 3: Divide the precision by 2 to determine the greatest possible error.

Thus, it will be the hundredths place for 0.224 m and in this case it is:

0.001/2 = 0.0005 m

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The value of angle x is 133 degree

And the equation of line be of the form,

⇒  y - y₁ = 133(x - x₁)

In the given line,

one angle is of 47 degree

And other is x degree

To find the value of x,

Since we know that,

The angle  of line is 180 degree.

Therefore,

⇒ x + 47 = 180

⇒         x = 133 degree

Therefore slope of this line be 133 degree

Now let this line is  passing through (x₁, y₁)

Hence,

The equation of  line be,

⇒ y - y₁ = (slope)(x - x₁)

⇒  y - y₁ = 133(x - x₁)

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The amount of solution A and B required are 60 and 90 ounces respectively.

Creating simultaneous equations for the problem:

Mass of solution A = a

Mass of solution B = b

a + b = 150 _____(1)

0.65a + 0.90b = 150×0.80

0.65a + 0.90b = 120 __(2)

From (1)

a = 150-b ____(3)

substitute (3) into (2)

0.65(150-b) + 0.90b = 120

97.5 - 0.65b + 0.90b = 120

0.25b = 120-97.5

0.25b = 22.5

b = 22.5/0.25

b = 90

a = 150 - b

a = 150 - 90

a = 60

Therefore , 60 ounces of solution A and 90 ounces of solution B is required.

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Answer:

  3. see attached. Domain x > 1; Range all reals

  4. √15 ≈ 3.87298

Step-by-step explanation:

You want a graph and the domain and range of f(x) = 3log(2(x-1)) +4, and the value of (3x)^(x/10) when x satisfies 2^x -2^(x-1) = 16.

The function f(x) = 3log(2(x -1)) +4 represents horizontal and vertical scaling, as well as horizontal and vertical translation. The values in each case are different, so we can describe their effect by referencing their value.

1 — a horizontal right shift of the log function by 1 unit

2 — a horizontal compression of the log function by a factor of 2

3 — a vertical expansion of the log function by a factor of 3

4 — a vertical shift upward of the log function by 4 units.

Some points that you might graph for the parent log function would be (0.1, -1), (1, 0), (10, 1). The effect of these shifts is to transform them to ...

  (x, y) ⇒ (x/2 +1, 3y +4)

  (0.1, -1) ⇒ (1.05, 1)

  (1, 0) ⇒ (1.5, 4)

  (10, 1) ⇒ (6, 7)

The right shift 1 unit moves the domain to x > 1.

The range continues to be all real numbers.

We can solve the given equation as follows:

   2^x -2^(x -1) = 16

   2^(x-1) · (2 -1) = 16

  2^(x -1) = 2^4

  x -1 = 4

  x = 5

Then the expression you want the value of is ...

  (3·5)^(5/10) = 15^(1/2) = √15 ≈ 3.87298

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