a senior math contest began at 6:00 am on a Sunday and ended 1000 min later then did the contest get over

Answer:

30°

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

In a 30°-60°-90° right triangle, the sides are always in the ratio of 1: √3:2, where 1 is the length of the short leg opposite the 30° angle, √3 is the length of the long leg opposite the 60° angle, and 2 is the length of the hypotenuse opposite the 90° angle1234.

In this case, we are given that the long leg is 9√3, so we can use this value to find the other sides by setting up a proportion:

short leglong leg​=13​​

short leg93​​=13​​

Cross-multiplying and solving for the short leg, we get:

short leg=3​93​×1​=9

Similarly, we can use another proportion to find the hypotenuse:

long leghypotenuse​=3​2​

93​hypotenuse​=3​2​

Cross-multiplying and solving for the hypotenuse, we get:

hypotenuse=3​2×93​​=18

Therefore, the measure of the hypotenuse n is 18 and the measure of the short leg m is 9.

The calculated base area of the paperweight is 9.6 square cm.

To calculate the base area of the paperweight, we can use the formula for the volume of a three-dimensional object:

Volume = Base area x Height

In this case, we know that the height of the paperweight is 4cm and the volume is 38.4 cubic cm.

So we can rearrange the formula and solve for the base area:

Base area = Volume / Height

Substituting the values we have:

Base area = 38.4 cubic cm / 4cm

Base area = 9.6 square cm

Therefore, the base area of the paperweight is 9.6 square cm.

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The calculated measure of the arc XYZ is 83 degrees

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

The circle

The angles created by secants and tangents that intersect outside a circle, which states that

The size of the angle formed by these two lines is equivalent to half the numerical difference between the measures of the arcs that they cut out from the circle.

So, we have

XYY = 1/2 * (166 - 0)

Evaluate

XYY = 83

Hence, the measure of the angle is 83 degrees

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Therefore, P(z > 0.97) = 0.166 using standard normal distribution table.

A standard normal distribution table, also called a z-score table or a standard normal table, is a table that provides the area under the curve to the left of a specific z-score value in a standard normal distribution. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of one.

The table usually includes positive z-score values in the right-hand column and the second decimal place in the top row. The intersection of a specific z-score value and decimal place provides the area under the curve to the left of that z-score value.

For example, if we want to find the area under the curve to the left of a z-score value of 1.32, we would locate the row with 1.3 in the top row and the column with 0.02 in the right-hand column. The intersection of this row and column gives the area under the curve to the left of 1.32, which is 0.9066.

Using a standard normal distribution table or calculator, we can find the probability of z being greater than 0.97 is approximately 0.166. Therefore, P(z > 0.97) = 0.166.

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The attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

What is arithmetic?

Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Here, we have

Given:

Seating capacity = 257

Charges: Children = $5.00; Students = $7.00; Adults = $12.00

Total sales of ticket = $1870

A number of children, students, and adults were present in the theatre.

Let A, C, and S represent adults, children, and students respectively.

There are half as many adults as there are children; this means that

A = ½C

If the total seat capacity is 257, then

A + C + S = 257

Also, if the total sales of tickets are $1870, then

12A + 7S + 5C = 1870

So, we have two equations to be solved simultaneously.

A + C + S = 257 --- (1)

12A + 7S + 5C = 1860 --- (2)

Substitute ½C for A in (1) and (2)

½C + C + S = 257

Multiply both sides by 2

2(½C + C + S) = 2 * 257

C + 2C + 2S = 514

3C + 2S = 514 ----- (3)

12(½C) + 7S + 5C = 1870

6C + 7S + 5C ,= 1870

6C + 5C + 7S = 1870

11C + 7S = 1870 --- (4)

Make S the subject of the formula in (3)

2S = 514 - 3C

S = ½(514 - 3C)

S = 257 - 1.5C

Substituton 257 - 1.5C for S in (4)

11C + 7(257- 1.5C) = 1870

11C + 1799 - 10.5C = 1870

Collect like terms

11C - 10.5C = 1870 - 1799

0.5C = 71

Multiply both sides by 2

2 * 0.5C = 2 * 71

C = 142

Recall that

S = 257 - 1.5C

S = 257 - 1.5(142)

S = 257 - 213

S = 44

Also, recall that

A = ½C

A = ½ * 142

A = 71

Hence, the attendance at the movie theatre is;

Children = 142

Students = 44

Adults = 71

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Answer:

[tex]5 {a}^{2} b + 15a {b}^{2} = [/tex]

[tex]5ab(a + 3b)[/tex]

Answer:

$23.30

Step-by-step explanation:

We Know

You paid $6.99

The shirt was 70% off

$6.99 = 30%

What was the original price of the shirt?

We Take

(6.99 ÷ 30) x 100 = $23.30

So, the original price is $23.30

Answer:

a)

[tex]y = 7( {1.03}^{t} )[/tex]

[tex]y = 7( {1.03}^{5} ) = 8.11[/tex]

There were about 8.11 billion subscribers in 2019.

b)

[tex]7( {1.03}^{t}) = 7.5[/tex]

[tex]t = 2.33 \: years \: after \: 2014[/tex]

sometime in 2016

Step-by-step explanation:

Use a modified Pythagorean theorem for 3 -D

diagonal = sqrt ( 9^2 + 12^2 + 8^2 ) = sqrt(289) = 17  units

(7) The volume of the triangular based prism is 41.16 m³.

(8) The volume of the haxagonal based prism is 1793.4 cm³.

Volume is the space ocuppied by a solid shape.

(7) To calculate the volume of the triangular based prism, we use the formula below

Formula:

Where:

Substitute these values into equation 1

(8) Also, to calculate the volume of the hexagon based prism, use the formula below

Where:

SUbstitute these values into equation 2

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Asnwer: 30 minutes

Explanation:

10 laps in 20 minutes is 1 lap every 2 minutes.

So we get this:

1 lap = 2 minutes

But we want 15 laps, so multiply both sides by 15 to get:

15 laps = 30 minutes

It would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.

To solve this problem, we can use the formula for exponential growth:

[tex]A = P * (1 + r)^t[/tex]

where:

A = final amount (in this case, $1,540)

P = principal amount (initial investment, in this case, $840)

r = rate of growth (as a decimal, in this case, the rate at which the money doubles every 10 years, or 1/10 = 0.1)

t = time (in years, which we need to find)

Plugging in the values:

[tex]1,540 = 840 * (1 + 0.1)^t[/tex]

Dividing both sides of the equation by 840:

[tex]1.83333... = (1.1)^tTaking the natural logarithm of both sides:ln(1.83333...) = ln((1.1)^t)Using the property of logarithms that ln(a^b) = b * ln(a), we get:ln(1.83333...) = t * ln(1.1)Finally, dividing both sides by ln(1.1) to solve for t:t = ln(1.83333...) / ln(1.1)[/tex]

Using a calculator, we can find that t ≈ 7.5 (rounded to the nearest tenth of a year).

So, it would take approximately 7.5 years (or 7 years and 6 months) for the value of the account to reach $1,540, assuming the money grows at a rate allowing it to double every 10 years.

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The maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.

The Federal Unemployment Tax Act (FUTA) tax rate is 6% on the first $7,000 paid to each employee in a calendar year. Therefore, the maximum FUTA deduction for each employee is $420 ($7,000 x 0.06).

Person 1 earned $4700, so the FUTA deduction for Person 1 is $282 ($4700 x 0.06).

Person 2 earned $19,800, but only the first $7,000 is subject to FUTA. Therefore, the FUTA deduction for Person 2 is $420.

Person 3 earned $6500, so the FUTA deduction for Person 3 is $390 ($6500 x 0.06).

The total FUTA deduction for the first quarter is the sum of the FUTA deductions for each employee:

$282 + $420 + $390 = $1092

Therefore, the maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.

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Answer: B. 12

Step-by-step explanation:

1) Alan can make 2.5 cookies per min

2) Abi can make 8/3 which is 2.7.

3) overall, 5.2 cookies per minute can be made.

multiple 5.2 x 6 and you get around 31.5?

then subtract =1. you have 30.5, now add onto that number 31.5, which is another 6 minutes. since you're still only subtracting 1, the answer would be above 60, which is 5 dozen, and it only took 12 mins

Answer:

Step-by-step explanation:

The equation for the height h of the object after t seconds is given by:

h = -16t^2 + 145t + 2

To find when the height will be 230 feet, we can set h = 230 and solve for t:

230 = -16t^2 + 145t + 2

We can simplify this equation by moving all the terms to one side:

16t^2 - 145t + 228 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 16, b = -145, and c = 228. Plugging in these values, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(228))) / 2(16)

t = (145 ± sqrt(21025 - 14592)) / 32

t = (145 ± sqrt(6433)) / 32

t ≈ 0.56 seconds or t ≈ 9.17 seconds

Therefore, the height of the object will be 230 feet at approximately 0.56 seconds or 9.17 seconds after it is thrown.

To find when the object will reach the ground, we can set h = 0 and solve for t:

0 = -16t^2 + 145t + 2

Again, we can simplify this equation by moving all the terms to one side:

16t^2 - 145t - 2 = 0

Using the quadratic formula again, we get:

t = (-(-145) ± sqrt((-145)^2 - 4(16)(-2))) / 2(16)

t = (145 ± sqrt(21249)) / 32

t ≈ 9.51 seconds or t ≈ 0.15 seconds

Therefore, the object will reach the ground at approximately 0.15 seconds or 9.51 seconds after it is thrown. However, since the negative solution does not make physical sense in this context, the object will reach the ground after approximately 9.51 seconds.

~~~Harsha~~~

Answer:

To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.

8a^3b^2 can be written as:

8a^3b^2 = 2^3 * 2 * a * a * a * b * b

12ab^4 can be written as:

12ab^4 = 2^2 * 3 * a * b * b * b * b

The common factors are 2, a, and b^2.

Therefore, the GCF of 8a^3b^2 and 12ab^4 is:

2 * a * b^2 = 2ab^2

The value "Sin 100°" is greater than "sin 250°", that is, sin 100° > sin 250°

To compare the values of sin 100° and sin 250°, we need to understand the behavior of the sine function. The sine function oscillates between -1 and 1 over a period of 360°, with its maximum value of 1 at 90° and its minimum value of -1 at 270°.

Using the sine wave, we can see that sin 100° is located in the second quadrant, where the sine values are positive, while sin 250° is located in the third quadrant, where the sine values are negative. Therefore, sin 100° is greater than sin 250°, because sin 100° has a positive value closer to the maximum value of 1, while sin 250° has a negative value closer to the minimum value of -1.

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Answer:

350° 33' 10".

Step-by-step explanation:

To convert the decimal degree 350.5527° to degrees, minutes, and seconds, we can use the following steps:

Therefore, 350.5527° is equivalent to 350° 33' 10".

The answer of the given question based on the Rectangular prism is , the surface area of the given triangular prism is 3360 cm².

A rectangular prism is a three-dimensional geometric shape with six rectangular faces. It is also known as rectangular parallelepiped or cuboid. A rectangular prism has a length (l), width (w), and height (h) and the formula for the volume of a rectangular prism is given as V = l * w * h.

To find the surface area of a triangular prism, we need to add up the areas of all of its faces. A triangular prism has two identical triangular bases and three rectangular faces.

First, let's find the area of the triangular base. We know that it is an isosceles triangle with a perpendicular height of 35 cm and base of 24 cm, and the length of the two equal sides is 37 cm. We can use the formula for the area of a triangle:

Area of base = (1/2) * base * height

Area of base = (1/2) * 24 cm * 35 cm

Area of base = 420 cm²

Since there are two identical bases, we can multiply this by 2 to get the total area of the triangular bases:

Total area of bases = 2 * 420 cm²

Total area of bases = 840 cm²

Now, let's find the area of the three rectangular faces. We know that the height of the prism is 35 cm, and the length of each rectangular face is equal to the base of the triangular base, which is 24 cm. To find the width of each rectangular face, we need to use the Pythagorean theorem to find the length of the altitude of the triangular base:

a² + b² = c²

where a and b are the two equal sides of the triangular base, and c is the base.

Substituting the given values, we get:

a² + b² = c²

37² + 12² = c²

1369 + 144 = c²

c² = 1513

c = √1513

c = 38.95 cm

Therefore, the altitude of the triangular base is approximately 35 cm, and we can use this value as the width of each rectangular face. So, area of each rectangular face is given:

Area of each rectangular face = length*width

Area of each rectangular face = 24 cm * 35 cm

Area of each rectangular face = 840 cm²

Since there are three identical rectangular faces, we can multiply this by 3 to get the total area of the rectangular faces:

Total area of rectangular faces = 3 * 840 cm²

Total area of rectangular faces = 2520 cm²

Finally, we can find the total surface area of the prism by adding the areas of the two triangular bases and the three rectangular faces:

Total surface area = Total area of bases + Total area of rectangular faces

Total surface area = 840 cm² + 2520 cm²

Total surface area = 3360 cm²

Therefore, the surface area of the given triangular prism is 3360 cm².

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Answer:

y= -1/5x-5

Step-by-step explanation:

You can use the slope formula and the slope intercept form which is y=mx+b.

Answer:

7

Let's call the width = x

width : x

so (x + 2x-4)2 = 34 (perime formula of a rectangle) x+2x-4 = 7

3x = 21

x = 7

so x is 7

Answer:

The slope-intercept form of the equation of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

We are given that the y-intercept is (0,2), which means that the value of b is 2.

We are also given that the slope is -2, which means that the value of m is -2.

Substituting these values into the slope-intercept form, we get:

y = -2x + 2

Therefore, the slope-intercept form of the equation of the line is y = -2x + 2.

Step-by-step explanation:

Answer:

that is correct just to give you feedback on that

Answer:

7(-6) + 4(8) = -42 + 32 = -10, so (-6, 8) is the solution to this system of equations.

The answer is Yes.

Therefore , the solution of the given problem of probability comes out to be pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.

Any considerations technique's fundamental objective is to determine the likelihood that a claim is true or that a particular incident will take place. Any number range from one to one, when 0 traditionally signifies a percentage and 1 typically implies the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The total number of pizzas made yesterday can be determined using the information provided as follows:

2121 cheese pizzas total.

Pizzas with vegetables: 1414

2323 pepperoni pizzas total.

1414 sausage pizzas were consumed.

Total pizzas produced were

=>2121 + 1414 + 2323 + 1414 = 7272.

Therefore, there were 2121 cheese pizzas prepared yesterday out of a total of 7272 pizzas.

The likelihood that the following pizza will be a cheese pizza is calculated as follows:

=> 2121 / 7272

The likelihood that the next pizza prepared won't be a cheese pizza is thus:

=> 1 - (2121 / 7272) = 5151 / 7272

Therefore, a conservative estimate of the likelihood that the following pizza won't be a cheese pizza is roughly 0.7089, or 70.89%.

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Answer:

  11

Step-by-step explanation:

You want the degree of the monomial -3q⁴rs⁶.

The degree of a variable expression is its exponent. The degrees of the variables in the given expression are ...

  q: 4

  r: 1

  s: 6

The degree of their product is the sum of the exponents:

  monomial degree = 4 + 1 + 6 = 11

The degree is 11.

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Answer: The California state sales tax rate is 7.25%. This rate is made up of a base rate of 6%, plus California adds a mandatory local rate of 1.25% that goes directly to city and county tax officials.

Step-by-step explanation:

Hope this helped! :)

The area in square centimeters, of the trapezoid below is equal to 84.4 cm².

In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):

Area of trapezoid, A = ½ × (a + b) × h

Where:

a and b represent the base areas of a trapezoid.

h represent the height of a trapezoid.

By substituting the given side lengths into the formula for the area of a trapezoid, we have the following:

Area of trapezoid, A = ½ × (7.9 + 13.2) × 8

Area of trapezoid, A = 84.4 cm².

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.