Type the correct answer in the box. Use numerals instead of words.
For this item, a non-integer answer should be entered as a fraction using / as the fraction bar.

Simplify the numerical expression.


2
3

÷

2
4

+

(
3
4

+

1
6
)

÷

1
3

The expression has a value equal to

Answer:

Step-by-step explanation:

The statement that is correct according to the table is: Barrow has the coldest average temperature in January.

Answer:

Step-by-step explanation:

Given equation:

[tex]\csc^2 \theta - \cot^2\theta -\sin^2\theta =\cos^2\theta[/tex]

To verify the given trigonometric equation, we can use the following trigonometric identities:

[tex]\boxed{\begin{minipage}{5 cm}\underline{Trigonometric Identities}\\\\$\csc^2 \theta = 1 + \cot^2 \theta$\\\\$\cos^2 \theta + \sin^2 \theta = 1$\\\end{minipage}}[/tex]

Therefore:

[tex]\begin{aligned}\csc^2 \theta - \cot^2\theta -\sin^2\theta &=(1+\cot^2\theta) -\cot^2\theta -\sin^2\theta \\&=1-\sin^2\theta\\&=(\cos^2\theta +\sin^2\theta) -\sin^2\theta \\&=\cos^2\theta \end{aligned}[/tex]

The probability of pulling out a red pair of socks and sport shorts is 12/35.

We have,

10 pairs of socks, 6 are red, and 7 shorts, 4 of which are sport shorts.

So, The probability of pulling out a red pair of socks is given by:

= (number of red socks) / (total number of socks)

= 6 / 10

= 3 / 5

and, the probability of pulling out sport shorts is given by:

= (number of sport shorts) / (total number of shorts)

= 4 / 7

To find the probability of both events happening together

= P(red socks) x P(sport shorts)

= (3 / 5) x (4 / 7)

= 12 / 35

Therefore, the probability of pulling out a red pair of socks and sport shorts is 12/35.

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Answer:

70cm^2

Step-by-step explanation:

10×5=50cm^2 is the area of the rectangle

18-10=8 is the height of the triangle

8×2.5=20

20÷2=10 is area of half the triangle

10+10=20cm^2 is the area of the triangle

50cm^2+20cm^2=70cm^2

Answer:

Step-by-step explanation:

Answer:

Question 3:    5

Question 4:    91

Step-by-step explanation:

[tex](x+5)2-y[/tex]

[tex]x = -2[/tex]

[tex]y =1[/tex]

[tex](-2 + 5)2 - 1[/tex]

[tex](3)2-1[/tex]

[tex]6-1 = 5[/tex]

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

[tex]x = -3[/tex]

[tex]y=5[/tex]

[tex]3(-3)+4(5)^2[/tex]

[tex]-9 + 100[/tex]

[tex]=91[/tex]

Answer:

The Answer is 80√3 or 138.56 to 2d.p

Step-by-step explanation:

sin 60=L/8

L=sin60×8

L=4√3

Area of rectangle =L×W

A=20×4√3

A=80√3=138.56 to 2d.p

Hello !

A rectangle triangle ABC :

  A

  I\
  I  \
  I    \
  I      \  

  B       C

We first look for the ratio of the angle.

1.1.1 If the ratio = opposite ; hypotenuse

⇒ It's the sinus.

In the triangle ABC it's :

sin(A) = opposite/hypotenuse

1.1.2 If the ratio = adjacent ; hypotenuse

⇒ It's the cosinus.

In the triangle ABC it's :

cos(A) = adjacent/hypotenuse

1.1.3 If the ratio = opposite ; adjacent

⇒ It's the tangente.

tan(A) = opposite/adjacent

x has the ratio opposite ; adjacent

⇒ It's the tangente.

tan(x) = opposite/adjacent = 4/6

arctan(4/6) ≈ 33,69 ≈ 34°

y has the ratio opposite ; adjacent

⇒ It's the tangente.

tan(y) = opposite/adjacent = 6/4

arctan(6/4) ≈ 56,30 ≈ 56°

The angle x = 34°

The angle y = 56°

Have a good day!

The angle that has been formed and is shown as x is shown as 52.1°.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. The tangent function is denoted as tan.

We can see that we need to find the tangent of the angle;

Tan x = 36/28

x = Tan-1(36/28)

x = 52.1°

Thus it is clear from the calculation that we have done above that the angle that is marked x is 52.1°.

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Answer:

Part A: The data that Zoe would expect to collect from this question is the amount of time each student spends playing video games. She could collect this data by asking each student how many hours per week they spend playing video games.

Part B: This is not a statistical question because it is asking for a specific answer. A statistical question would be asking for a distribution of the data, such as the average amount of time students spend playing video games or the range of times students spend playing video games.

To make this question statistical, Zoe could ask the following question:

How much time do students in my class spend playing video games per week?

This question is statistical because it is asking for a distribution of the data. Zoe could then collect the data and use it to create a histogram or other graph to show the distribution of the data.

Answer:

Step-by-step explanation:

The mode of the data is 0

Central tendency is defined as the statistical measure identifying a single value as representative of an entire distribution.

It provides an accurate description of the entire data.

The three major measures of central tendency are given as;

The mode is defined as the measure of central tendency representing the most occurring number in a given data set

From the information given, we have;

0, 4 , 3, 4, 0, 9, 1

Then, the mode is 0

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Answer:

increases by 30

Step-by-step explanation: its right

Answer:

  (c)  0 < a < 1

Step-by-step explanation:

You want to know the value of 'a' in y = a·cot(x) that will cause a vertical compression without reflection.

When a function value is multiplied by a factor greater than 1, its graph is expanded vertically. When that factor is less than 1, the graph is compressed, as in the attachment.

If the scale factor is negative, the graph will be reflected across the x-axis.

Here, you want compression without reflection. That requires a positive scale factor less than 1.

  0 < a < 1

Answer:

IG: yiimbert

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

We are given that the center of the circle is (2, 3) and it contains the point (7, 15). To find the radius, we can use the distance formula between the center and the given point:

r = sqrt[(7 - 2)^2 + (15 - 3)^2]

r = sqrt[25 + 144]

r = sqrt(169)

r = 13

Substituting the given values into the equation of a circle, we get:

(x - 2)^2 + (y - 3)^2 = 13^2

Expanding the terms, we get:

x^2 - 4x + 4 + y^2 - 6y + 9 = 169

Simplifying and rearranging, we get:

x^2 - 4x + y^2 - 6y = 156

Therefore, the equation of the circle with center (2, 3) containing the point (7, 15) is:

x^2 - 4x + y^2 - 6y = 156

The solution is: 100! different ways can you draw all of the names from the hat.

Here, we have,

if we have n object, and as we know that arrangement given by = n!. (Permutation)

A permutation is a mathematical technique for determining the number of possible arrangements in a sentence where the order of arrangements is important. A common math problem involves choosing some items in a particular order from a set of items.

A permutation also called an "order number" or "sequence", is the rearrangement of the elements of an ordered list so that they correspond one-to-one with themselves. (Faculty; Ouspensky 1937, p. 18). Permutations are said to be ordered combinations. The number of permutations r of n objects acquired simultaneously is determined by the following formula: P(n,r)=n!(n-r)!

Hereafter taking each unique name, we will arrange it in raw, so we can say this problem is equivalently permutation problem, So we can say the way of drawing all names can be done in 100! Way.

So ANSWER IS 100!

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The surface area of the pyramid in this problem is given as follows:

96.4 ft².

To obtain the surface area of a figure, we must add the areas of all the parts that compose the figure.

From the net given by the image presented at the end of the answer, the pyramid is composed as follows:

Hence the surface area of the figure is given as follows:

S = 4 x 8 + 2 x 1/2 x 8 x 5 + 2 x 1/2 x 4 x 6.1

S = 96.4 ft².

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

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Answer:

The length of the second book is 10.5 inches, while the first book's thickness is in a ratio of 2:1.5, which simplifies to 4:3. Similarly, the length of the first book is also in a ratio of 4:3 with the second book. Hence, we can calculate the second book's length as 14 divided by 4, multiplied by 3, which equals 10.5 inches.

The total surface area of the cuboid in contact with the water is [tex]1300 cm^2.[/tex]

The volume of a cuboid formula, V = lwh, can be used to first determine the height of the water level in the tank.

Where

Converting the volume of the water to liters, we have:

[tex]4.8 L = 4800 cm^3[/tex]

Plugging in the values we have:

[tex]4800 cm^3 = 20 cm * 15 cm * h[/tex]

Simplifying this equation, we get:

h = 16 cm

Therefore, the height of the water level in the tank is approximately 16 cm.

The formula for the surface area of a cuboid can be used to determine the total surface area of the cuboid in contact with the water:

[tex]A = 2lw + 2lh + 2wh[/tex]

where A is the surface area of the cuboid in[tex]cm^2.[/tex]

Plugging in the values we have:

[tex]A = 2(20 cm * 15 cm) + 2(20 cm * 16 cm) + 2(15 cm * 16 cm)[/tex]

Simplifying this equation, we get:

[tex]A = 1300 cm^2[/tex]

So, the total surface area of the cuboid in contact with the water is[tex]1300 cm^2.[/tex]

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Answer:

Yes

Step-by-step explanation:

In terms of grade level because he can conduct through the age of the students in variation the interest of each student is different so we might say that lower students like from grade 1 might not be interested in the news that was forecast in the television but with higher leverage considering its maturity and experience will define much more appropriate in receiving news school.

The calculated value of the conditional probability P(Not A | Not B) is 0.8125

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

The table of values

The probability P(Not A | Not B ) is calculated as

P(Not A | Not B ) = (Not A and Not B)/(Not B)

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

(Not A and Not B) = 0.65

(Not B) = 0.80

Substitute the known values in the above equation, so, we have the following representation

P(Not A | Not B ) = 0.65/0.80

Evaluate

P(Not A | Not B) = 0.8125

Hence, the probability P(Not A | Not B) is 0.8125

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Answer:

The odd numbers between 1 and 7 are 1, 3, 5, and 7. There are four of them.

The total number of balls in the bag is 7.

Therefore, the probability of picking an odd number is:

number of odd numbers / total number of balls = 4/7

So the probability of picking an odd number is 4/7

Step-by-step explanation:

One rectangle  10 x 6 = 60 cm^2

Two sqaures     2 *    4x4 =  32 cm^2      Total = 92 cm^2

Answer:

The answer is number 2

The quotient of -4 1/6 and -3 1/3 is 5/4.

To find the quotient of -4 1/6 and -3 1/3, we need to divide the two mixed numbers. Here's how we can do it:

Step 1: Convert the mixed numbers to improper fractions.

-4 1/6 can be converted to an improper fraction as follows:

-4 1/6 = -25/6

Similarly, -3 1/3 can be converted to an improper fraction as:

-3 1/3 = -10/3

Step 2: Divide the two improper fractions.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

So, (-25/6) / (-10/3) becomes (-25/6) * (-3/10).

Step 3: Simplify the resulting fraction.

Multiply the numerators and denominators:

(-25 * -3) / (6 * 10) = 75/60

Step 4: Simplify the fraction, if possible.

The numerator and denominator have a common factor of 15:

75/60 = (5 * 15) / (4 * 15)

Simplifying, we get:

75/60 = 5/4

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Answer: 5

have a good day

The straight-line distance from your starting point at the end of driving is approximately 24.4 miles.

To find the straight-line distance from your starting point, we can use the Pythagorean states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance you drove west and turned left forms two sides of a right triangle, and the straight-line distance from the starting point will be the hypotenuse.

Given:

Distance driven west = 20 miles

Distance driven south = 14 miles

Using the Pythagorean:

Hypotenuse² = (Distance driven west)² + (Distance driven south)²

Hypotenuse² = 20² + 14²

Hypotenuse² = 400 + 196

Hypotenuse² = 596

To find the length of the hypotenuse (straight-line distance), we take the square root of both sides:

Hypotenuse = √596

Hypotenuse ≈ 24.4 miles (rounded to the nearest tenth)

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