Find the missing angle

The calculated value of w from the similar triangles is 21/4

From the question, we have the following parameters that can be used in our computation:

Similar triangles A and B

Also from the similar triangles, we have the following proportional relation

4    7     12

3    W     9

Using the above as a guide, we have the following equation

4/3  =  7/W  =   12/9

So, we have

W * 12 = 7 * 9

Evaluate the products and divide both sides by 12

W = 21/4

Hence, the value of W is 21/4

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Answer:

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Given expression:

Group the expression as below and factorize:

Hence the factored form of the expression is (2x + 5)(x² + 3).

The factored form of the expression is,

⇒ (2x + 5)(x² + 3).

Given that;'

The expression is,

⇒ 2x³ + 5x² + 6x + 15

Now, Group the expression as below and factorize:

2x³ + 5x² + 6x + 15

(2x³ + 5x²) + (6x + 15)

x²(2x + 5) + 3(2x + 5)

(2x + 5)(x² + 3)

Hence, the factored form of the expression is (2x + 5)(x² + 3).

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Explanation for problem 14

There are 4 aces and 4 copies of "9".

4+4 = 8 cards we want to select out of 52 total

8/52 = (4*2)/(4*13) = 2/13  which points to choice D as the final answer

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Explanation for problem 15

4 kings gives a probability of 4/52 = 1/13.

After the king is chosen, there are 52-1 = 51 cards left since we aren't replacing it. The probability of getting a queen on the second selection is 4/51

(1/13)*(4/51) = 4/663 is the probability of a king, then a queen, with no replacement. We arrive at choice C as the final answer.

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Explanation for problem 16

face card = picture card

face card = Jack, Queen, King

aces are not considered a face card

3*4 = 12 face cards in total

A = 12/52 = (4*3)/(4*13) = 3/13 is the probability of selecting a face card.

That card is then put back (aka replacement) and we still have 52 cards in the deck. We don't drop down to 51.

13 hearts ---> B = 13/52 = 1/4 is the probability of getting a heart

A*B = (3/13)*(1/4) = 3/52 is the probability of getting a face card, then a heart, when replacement is done. The final answer is choice B

Answer:

4250 kilos

Step-by-step explanation:

(a) Sum of values = Mean × Number of values = 64 × 5 = 320

(b) Sum of values = Mean × Number of values = 8.2 × 5 = 41

Fifth value = Sum of values - sum of known values = 41 - (6 + 10 + 7 + 12) = 41 - 35 = 6

(c) The resulting middle number when computing 10, 20, 30, 40, 50;that is (10 + 20 + 30 + 40 + 50)/5, totals up to 150 and dividing that number by 5 reflects a mean of 30.

i) Forming an average of 20, 30, 40, 50, 60;that is (20 + 30 + 40 + 50 + 60)/5 provides an outcome of 200 and divided by 5 reveals a mean of 40.

ii) With 0, 10, 20, 30, 40 used, (0 + 10 + 20 + 30 + 40)/5 practices calculation yielding a total of 100 which, split into five parties, imparts a mean of 20.

iii) Taking into consideration the input of 100, 200, 300, 400, 500;whereby (100 + 200 + 300 + 400 + 500)/5 develops a collective of 1500, cut in half produces a mean of 300.

iv) Calculating 1, 2, 3, 4, 5's mean; namely (1 + 2 + 3 + 4 + 5)/5 ascertains a collective amount of 15, divide that figure by five culminates with a mean of 3.

v) Accordingly, the following general assumptions can be made:

i) Introducing a constant to each value augments the mean by that very same constant.

ii) Extracting a constant from all values decrements the mean by such said constant.

iii) Multiplying every value by one constant multiplies the mean by the same specific constant.

iv) Dividing all values by a particular constant divides the mean by that given constant.

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Answer: the tangent of the smaller acute angle in this right triangle is 8/15.

Step-by-step explanation:

Since the side lengths of the correct triangle are given as 8, 15, and 17, able to see that the sides with lengths 8 and 15 are the legs of the proper triangle, and the side with length 17 is the hypotenuse.

We know that the littler intense point θ is inverse the shorter leg of length 8. Hence, the digression of θ is:

tan(θ) = opposite/adjacent = 8/15

The value of x, given that when it divides a number, there is a quotient and a remainder, is 400

To find the value of divisor, we can use a variant of the division algorithm formula :

Divisor = ( Dividend - Remainder ) / Quotient

x is the divisor

Dividend = 19, 432

Remainder = 232

Quotient = 48

This means that the value of x is:

x = ( 19, 432 - 232 ) / 48

x = 19, 200 / 48

x = 400

In conclusion, x is 400.

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Volume of the prism given is 51 [tex]\frac{17}{40}[/tex].

The volume of the prism is given by the formula,

Volume of the prism = Base area × height

Base area = 2 3/4 × 5 1/2

                 = 11/4 × 11/2

                 = 121 / 8

Volume of the prism = 121 / 8 × 3 2/5

                                  = 121/8 × 17/5

                                  = 2057/40

                                  = 51 17/40

Hence the volume of the prism is 51 [tex]\frac{17}{40}[/tex].

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Answer:

2 boxes

Step-by-step explanation:

8 cupcakes in 1 box = 16 cupcake in x box

We Take

16 ÷ 8 = 2 boxes

So, the answer is 2 boxes.

According to the information, we can infer that the area of the triangle is: 19 1/4ft²

To calculate the area of the triangle, we need to use the formula for the area of a triangle:

where,

To find the height of the triangle, we need to use the Pythagorean theorem, which relates the slant height, height, and half the base:

Substituting the given values, we get:

Multiplying both sides by 36, we get:

So the height of the triangle is approximately 2.04 ft.

Now we can plug in the values for the base and height into the formula for the area:

Therefore, the area of the triangle is approximately 19.25 square feet.

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The number of friends that get 7 walnuts is 3 and there are 5 walnuts are left over

Here, we have

So, we have

Friends = 26/7 = 3 R 5

This means that 3 friends get 7 walnuts and there are 5 walnuts are left over

Here, we have

Oranges = 57

Oranges in each bags = 6

So, we have

Bags  57/6 = 9 R 3

This means that there are 9 full bags of oranges, 3 oranges are not in the bag and Juan needs 10 bags in total

Here, we have

Craft sticks = 85

Friends = 9

So, we have

Sticks left = 85\9

Evaluate

Sticks left = 4

Hence, there will be 4 sticks left

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The calculated radius of the cone is 5 inches

From the question, we have the following parameters that can be used in our computation:

Volume = 109.95 cubic inches

Height = 4.2 inches.

The volume is calculated as

V = 1/3 * 3.14 * r^2h

So, we have

1/3 * 3.14 * r^2 * 4.2 = 109.95

So, we have

r^2 = 3 * 109.95/(4.2 * 3.14)

So, we have

r^2 = 25.01

Take the square roots

r = 5

Hence, the radius is 5 inches

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The graph in this problem is not a function, as it contains vertically aligned points.

The domain and the range are given as follows:

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

When we trace a vertical line through the circle, it would cross the circle at two points, meaning that the graph contains vertically aligned points, and thus, is not a function.

The domain and the range are defined as follows:

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i) finite set, ii) infinite set, iii) infinite set, iv) infinite set, and v) finite set are the required solutions.

A Set is a collection of objects with similar properties. There are different types of set two of them are finite and infinite set.

Finite set- A set is called a finite set when the elements inside the set are countable or where we can know the starting and the ending of the elements. For example- A set of players in a cricket team.

Infinite set- A set is called an infinite set when the elements inside the set are uncountable or where the ending of the elements is not known. For Example- A set of positive numbers.

Here in the question the option (i) and (v) are finite sets because the no.of months in the year and no.of alphabets are countable or finite. Option (ii), (iii), and (iv) are infinite sets as no.of stars in the galaxy, even integers, and odd integers are uncountable.

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Answer:

the set of months in a year is finite

the set of star in the Galaxy is finite

the set of even integers is infinite

the set of odd integers is infinite

the set of alphabet is finite

Step-by-step explanation:

1) the set of month in a year is finite because they are limit and we can count them easily

2) the set of star in the galaxy is finite cause there are zillions of stars

3) the set of even integer is infinite because numbers are unlimit or infinite

4) the set of odd integers is infinite cause numbers are infinite ir they have not limit

5) the set of alphabet is finite because we can count them limitedly

Answer:

The measure of angle E is 56°.

The crocodile weighs 0.005 times as much as the hippopotamus.

To determine how many times as much as the hippopotamus a crocodile weighs, we need to compare the weights of both animals. However, they are currently in different units, so we need to convert them to a common unit.

We can convert the weight of the hippopotamus from tons to pounds by multiplying by 2,000, since there are 2,000 pounds in a ton. This gives us:

Hippopotamus weight = 2 tons × 2,000 pounds/ton = 4,000 pounds

Now that both weights are in pounds, we can compare them. To determine how many times as much as the hippopotamus the crocodile weighs, we can divide the weight of the crocodile by the weight of the hippopotamus. This gives us:

Crocodile weight / Hippopotamus weight = 20 pounds / 4,000 pounds = 0.005

Alternatively, we could say that the hippopotamus weighs 200 times as much as the crocodile.

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The labelled parts are described as follows

1. BC - Tangent

3. DH - Chord

4. EH - Diameter

5. G - center of the circle

6. GF Radius of the circle

7. B. a point of tangency

Tangent: Referenced as a point of tangency, a tangent to a circle is a line that meets the circumference at one solitary area while never penetrating inside its bounds. To explain further, this line is perpendicular to the radius of the circle right at the tip of contact.

Chord: Referring to such an element, a chord of a circle is a straight piece between two areas that lay along the circumference. Without having any relation to the middle of the target object, it has both of its extremities on the peripheral border.

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In the given image, H is a non-empty set of complex numbers, a and b are complex numbers, and x is a variable.

"The equation ax = b has a solution for every b ∈ H" means that for any complex number b in the set H, there exists a complex number x such that the product of a and x is equal to b.

In other words, for every numbers of b in H, there exists a solution for x that satisfies the equation ax = b.

This statement has important implications in linear algebra and functional analysis, where it is used to define the concept of a surjective linear transformation in numbers. It also has applications in many areas of mathematics and science, including engineering, physics, and computer science.

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The surface area of the box is 408 square inches whose dimensions of the box are 15 in. by 7 in. by [tex]4\frac{1}{2}[/tex] in.

The formula for the surface area of a rectangular box is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the box.

Given that the dimensions of the box are 15 in. by 7 in. by [tex]4\frac{1}{2}[/tex] in., we have:

l = 15 in.

w = 7 in.

h = [tex]4\frac{1}{2}[/tex] in. = 9/2 in.

Substituting these values into the formula, we get:

Surface Area = 2lw + 2lh + 2wh

Surface Area = 2(15)(7) + 2(15)(9/2) + 2(7)(9/2)

Surface Area = 210 + 135 + 63

Surface Area = 408

Therefore, the surface area of the box is 408 square inches.

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The matching table is given in the image below:

A scatter plot, an undeniably essential chart for visualizing the correlation between two variables, is constructed by putting one variable on the x-axis and another one alongside the y-axis, with each individual data point symbolizing both associated values.

Scatter plots are not only indispensable when inspecting trends and peculiarities in a given set of data but can likewise be applied to examine the relationship or link between the two components.

Essentially imperative to fields such as economics, engineering, and statistics, these diagrams are efficiently drawn up through popular software applications like Excel or Python.

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The probability of passing at least one will be 0.70.

We know that,

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

here, we have,

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

so, we get,

Probability of passing at least one will be

⇒ 0.59 + 0.60 – 0.49

⇒ 0.70

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complete question:

A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?

Answer:

(- 2, - 4 )

Step-by-step explanation:

4x - 3y = = 4 → (1)

3x + 3y = - 18 → (2)

adding the equations term by term will eliminate y

(4x + 3x) + (- 3y + 3y) = 4 - 18

7x + 0 = - 14

7x = - 14 ( divide both sides by 7 )

x = - 2

substitute x = - 2 into either of the 2 equations and solve for y

substituting into (2)

3(- 2) + 3y = - 18

- 6 + 3y = - 18 ( add 6 to both sides )

3y = - 12 ( divide both sides by 3 )

y = - 4

solution is (- 2, - 4 )

Answer: 67.65

Step-by-step explanation:

Multiply 3.0*4.1 and you get 12.3

Then take that sum and multiply it by the 5.5

So 12.3*5.5=67.65

The  area of the reduced rectangle is 1.8 unit²

The correct answer is an option (b)

Here the length of the rectangle is 15 units.

And the width of the rectangle is 12 units.

The rectangle has been reduced by a scale of 1/10

so, the new length of the rectangle is:

l = 1/10 × 15

  = 1.5 units

And the new width of the rectangle is:

w = 1/10 × 12

   = 1.2 units

We need to determine the area of the reduced rectangle.

Using the formula for area of rectagle, the area of the reduced rectangle would be:

A = l × w

A = 1.5 × 1.2

A = 1.8 unit²

Therefore, the correct answer is an option (b)

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The complete question is:

The rectangle below has been reduced by a scale of StartFraction 1 over 10 EndFraction. A rectangle has a length of 15 and width of 12. [Not drawn to scale] What is the area of the reduced rectangle?

a) 0.18 square units

b) 1.8 square units

c) 18 square units

d) 180 square units

The Probability of both balls being green is  0.36 or 36%

b) The Probability of neither ball being green is 0.16 or 16%

Based on question A,  To find the probability that both balls are green, we use the equation below:

P (both green) = P (first green) x P (second green)

= (6/10) x (6/10)

= 36/100

= 9/25

=0.36

b) To find the probability that neither ball is green,  we use the formula below:

P (neither green) = P (first not green) x P (second not green)

= (4/10) x (4/10)

= 16/100

= 4/25

=0.16.

Therefore, the statement will be:  The Probability of both balls being green: 0.36 and the probability of neither ball being green is 0.16

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Dingaka took out a loan of R12650 with a simple annual discount rate of 12.5%. He has to repay R11595.83 in eight months, after deducting the simple discount of R1054.17.

To find the amount that Dingaka has to repay, we can use the formula for simple discount

Simple Discount = Principal * Rate * Time

Where Principal is the original amount borrowed, Rate is the annual simple discount rate, and Time is the time period in years.

We know that Dingaka received R12650 as the principal amount and the annual simple discount rate is 12.5%, which is equivalent to 0.125 as a decimal. The time period is 8/12 = 2/3 years, since the loan has to be repaid in eight months' time.

Plugging these values into the formula, we get

Simple Discount = 12650 * 0.125 * 2/3

= 12650 * 0.08333333

= 1054.166625

Therefore, the amount that Dingaka has to repay is the principal minus the simple discount, which is

Amount to Repay = Principal - Simple Discount

= 12650 - 1054.166625

= 11595.833375

So, Dingaka has to repay R11595.83 after eight months.

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Answer:

I helped you last time so I'll help you again.

Step-by-step explanation:

We can find the average rate of change of f(x) over the interval [10, 20] using the formula:

average rate of change = (f(b) - f(a))/(b - a)

where a = 10 and b = 20.

So, we have:

f(a) = f(10) = 1.85(10)^2 = 185

f(b) = f(20) = 1.85(20)^2 = 740

average rate of change = (740 - 185)/(20 - 10) ≈ 55.5

Therefore, the average rate of change of f(x) over the interval [10, 20] is approximately 55.5.

Answer:

step 2 is wrong

Step-by-step explanation:

Here, The work of a student to solve the equation :

[tex]4(2x - 4) = 8 + 2x + 8[/tex]

The steps for calculating the value of x are :

Step 1: [tex]4(2x - 4) = 8 + 2x + 8[/tex]

Step 2: [tex]6x - 8 = 16 + 2x[/tex]

Step 3: [tex]6x - 2x = 16 + 8[/tex]

Step 4: [tex]4x = 24[/tex]

Step 5: [tex]x = 6[/tex]

Step 2 is incorrect, as the student instead of multiplying, adds the number as:

[tex]4(2x - 4) = 8 + 2x + 8[/tex]

Here, the correct step is:

[tex]\boxed{\bold{8x - 16 = 16 + 2x}}[/tex]

[tex]6 x = 32[/tex]

[tex]x = 5.33[/tex]

So, the error is in STEP 2 and the correct option is (B).