Chose one of two tables below to create your own Question (with solution).

Answer:

θ = 78.69°

Step-by-step explanation:

As this is a right angle triangle we use trigonometric ratios/

The perpendicular i.e the height of the mast = 50 ft

The base i.e the shadow = 10 ft

tanθ = perpendicular / base

tanθ = 50/10

θ = [tex]tan^{-1}[/tex] (50/10)

θ = 78.69°

Jill played for 10 mins. 25+15=40 50-40=10

If more than 400 sheets are duplicated, this equation will provide us with the overall expense, t.

A method that describes how two lines along both side of a sign connect each other. It typically contains an equal symbol and one variable. Similarly, 2x - 4 = 2. The variable x is present in the particular circumstance.

The equation that could be used to calculate the total cost, t, to copy p pages when p is greater than 400 is:

t = $5,000 + ($0.01 × (p - 400))

The base cost for copying the first 400 pages is $5,000. For each additional page above 400, the customer is charged $0.01 per page. Therefore, to calculate the total cost for copying p pages, we need to subtract 400 from p to determine the number of pages that are being charged at the additional rate, and then multiply that by $0.01 to determine the additional cost. This gives us:

Additional cost = $0.01 × (p - 400)

The total cost is then the sum of the base cost and the additional cost:

t = $5,000 + ($0.01 × (p - 400))

This equation will give us the total cost, t, for any number of pages greater than 400 that are copied.

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In interval notation, the the solution set in interval notation. (5)/(y-4)<9 is   (41/9, ∞).

Inequality is a mathematical statement that two values or expressions are not equal. It is represented by symbols, like >, <, or ≠, and is used to compare quantities or values.

To solve the inequality (5)/(y-4)<9, we need to isolate the variable on one side of the inequality. We can do this by multiplying both sides of the inequality by (y-4) and then simplifying.

(5)/(y-4)<9

5 < 9(y-4)

5 < 9y - 36

41 < 9y

y > 41/9

This means that any value of y greater than 41/9 will satisfy the inequality.

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(a) For a line, the ratio of the change in y to the change in x is called the slope of the line.
(b) The point-slope form of the equation of a line with slope m passing through (x1, y1) is y - y1 = m(x - x1).

The slope of a line is a measure of its steepness and is calculated by finding the ratio of the change in y (the rise) to the change in x (the run) between two points on the line.

The point-slope form of the equation of a line is a way to write the equation of a line when you know its slope and one point on the line. It is written as y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is the point on the line.

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What is Trapezium ?

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other. The trapezium is a two-dimensional shape that appears as a table when drawn on a sheet of paper. In Euclidean Geometry, a quadrilateral is defined as a polygon with four sides and four vertices. Hence, a trapezium also has four sides, four angles and four vertices.

ABCD is a trapezium, AB || DC

The area of ABCD = 180 cm²

AB = 17 cm

CD = 13 cm

Formula Used:

Area of trapezium = 1/2 x height x (Sum of parallel sides)

Calculation:

Area of trapezium = 1/2 x height x (Sum of parallel sides)

⇒ 180 = 1/2 x height x (AB + CD)

⇒ 180 x 2 = Height x (17 +13)

Height=360/30

Height = 12

.:. The height of the trapezium is 12 cm.

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Answer: A: 20,40,120

Step-by-step explanation:

Angle A is smaller than Angle B as it is less than 1 time as big as it.

The list of angles from smallest to largest is C, A, and B.

120 x (1/3) = 40

20 < 40

Hope this helps!

No, (8, 2) is not a solution to the inequality y ≥ 3x + 4 because when we substitute x = 8 and y = 2 into the inequality, we get a false statement. In other words, the point (8, 2) does not satisfy the inequality y ≥ 3x + 4, which means it is not a valid solution to the inequality.

To determine whether (8, 2) is a solution to the inequality y ≥ 3x + 4, we need to substitute the values of x and y into the inequality and check if the inequality holds true.

y ≥ 3x + 4

Substituting x = 8 and y = 2:

2 ≥ 3(8) + 4

2 ≥ 24 + 4

2 ≥ 28

The inequality is not true since 2 is not greater than or equal to 28.

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The expression 3^(-3) can be rewritten without an exponent as 1/27.

To rewrite the expression 3^(-3) without an exponent, we can use the rule that any expression with a negative exponent can be rewritten as the reciprocal of the expression with a positive exponent. In other words, a^(-b) = 1/a^(b).

So in this case, we can rewrite 3^(-3) as 1/3^(3).

Now, we can simplify the expression by evaluating the exponent. 3^(3) = 3*3*3 = 27.

So our final answer is 1/27.

Therefore, the expression 3^(-3) can be rewritten without an exponent as 1/27.

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Answer:

Step-by-step explanation:

OK so im not that smart im only in 8th grade but i think the answers either A or B. hope i kind of helped you and good luck and have a nice day.

a) n = 650 and p = 0.03

b)0.954

c)0.802

d)0.0206 to 0.0594

e)The result in (d) would be more precise

(a) The sampling distribution of the sample proportion is a binomial distribution with parameters n = 650 and p = 0.03.
(b) The probability that the sample proportion of death claims is between 2% and 6% is 0.954.
(c) The probability that the sample proportion is within 0.02 of the population proportion of death claims caused by accidents is 0.802.
(d) The 95% confidence interval for the proportion of death claims caused by accidents is 0.0206 to 0.0594.
(e) If the sample size were 2000 instead of 650, the result in (d) would be more precise. This is because with a larger sample size, the confidence interval will become narrower, allowing for a more accurate estimate of the population proportion.

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The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0. The question is a bit unclear and has multiple parts, so I will answer each part separately.

Part 1: Find the exact value of each of the remaining trigonometric functions of e.

sin 0 = 3/5
cos 0 = 4/5
tan 0 = 3/4
csc 0 = 5/3
sec 0 = 5/4
cot 0 = 4/3

Part 2: Find the lengths and area A.

The length of the arc is 80 * (15/360) = 3.333 yards.
The area of the sector is (80^2 * (15/360))/2 = 266.667 square yards.

Part 3: Find the distance from A to C across the gorge illustrated in the figure.

The distance from A to C is sqrt(170^2 + 170^2) = 240.42 feet.

Part 4: Name the quadrant in which the angle o lies.

The angle o lies in quadrant IV because sin 0 < 0 and cot 0 > 0.

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The measurements are shown in the solution

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Given are right triangles, we need to find the value of x in each,

We will use Trigonometric ratios to find the same,

The sine is the ratio between the length of the opposite leg and the length of the hypotenuse.

The cosine is the ratio between the length of the adjacent leg and the length of the hypotenuse.

The tangent is the ratio between the length of the opposite leg divided by the length of the adjacent leg.

1) sin 21° = 11/x

x = 30.7

2) cos 34° = x/28

x = 23.21

3) tan 49° = 33/x

x = 28.68

4) T =  cos⁻¹ (11/23)

=  61.42°

5) T = sin⁻¹(21/44)

= 28.50°

6) T = tan⁻¹(8/12)

= 33.7°

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The difference in the amount of tax withheld based on his previous W-4 form and the new W-4 form is estimated to be $7 per week for federal income tax withholding, meaning $7 more will be deducted from his weekly check if he claims no allowances.

The amount of tax withheld from Jason's paycheck depends on his taxable income, which is his gross income minus any deductions and exemptions. The number of allowances claimed on his W-4 form affects the amount of his paycheck that is subject to tax withholding.

If Jason claimed 1 allowance last year, his employer withheld tax as if he had $4,300 less in taxable income than if he had claimed no allowances. For 2023, the value of each allowance is $4,350.

Therefore, if Jason claims no allowances on his W-4 form, his taxable income will be $4,350 more than if he claimed 1 allowance.

Jason's gross income is $232.50 per week, which translates to $12,090 per year. If he claimed 1 allowance last year, his taxable income was $12,090 - $4,300 = $7,790. If he claims no allowances this year, his taxable income will be $7,790 + $4,350 = $12,140.

To determine how much more tax will be withheld from his weekly paycheck, we need to calculate the difference in the amount of tax withheld based on his previous W-4 form and the amount of tax withheld based on the new W-4 form.

Assuming that Jason is paid weekly, we can use the IRS tax withholding tables to estimate the federal income tax withheld for each situation.

Based on the 2023 IRS tax withholding tables, if Jason is single and claims 1 allowance, his employer would withhold $32 per week from his paycheck for federal income tax.

If he claims no allowances, his employer would withhold $39 per week from his paycheck for federal income tax.

Therefore, if Jason claims no allowances, $39 - $32 = $7 more will be deducted from his weekly check for federal income tax withholding.

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There are three possible triangles that can be formed using the given measurements.

Measurement is the process of quantifying or comparing the amount, size, or extent of something. It is an important concept for scientists, engineers, and other professionals in order to compare and understand the world around them. Measurement involves the use of physical tools, such as rulers, scales, and protractors, and mathematical equations, such as formulas and equations.

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 43^2 + 15^2 - 2(43)(15)\cos(123^\circ)$\\$b^2 \approx 799.5$\\$b \approx 28.3$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.977$\\$A \approx 79.4^\circ$\\$B \approx 23.6^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=79.4^\circ$[/tex], [tex]$B=23.6^\circ$[/tex], [tex]$C=77^\circ$[/tex], [tex]$a=43$[/tex], [tex]$b\approx 28.3$[/tex] , and [tex]$c=15$[/tex].

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 36^2 + 47^2 - 2(36)(47)\cos(47^\circ)$\\$b^2 \approx 1666.5$\\$b \approx 40.8$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.647$\\$A \approx 40.9^\circ$\\$C \approx 92.1^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=40.9^\circ$[/tex], [tex]$B=47^\circ$[/tex], [tex]C\approx 92.1^\circ, a\ =36$[/tex], [tex]$b\approx 40.8$[/tex],

We can use the Law of Cosines to solve for the missing side:

[tex]h^2 = k^2 + p^2 - 2kp\cos(K)\\$h^2 = 47^2 + 10^2 - 2(47)(10)\cos(139^\circ)$\\$h^2 \approx 2363.7$\\$h \approx 48.6$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

So the triangle is [tex]$\triangle KHP$[/tex] were [tex]$K=139^\circ$[/tex], [tex]$H\approx 56.5^\circ$[/tex], [tex]$P\approx 124.5^\circ$[/tex], [tex]$k=47$[/tex], [tex]$h\approx 48.6$[/tex], and [tex]$p=10$[/tex].

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Answer:

The capacity of the big vase is half times bigger than the capacity of the middle sized vase, which means it is 1 + 1/2 times the capacity of the middle vase.

So, the capacity of the big vase in terms of x is:

1/2x + x = 3/2x

Therefore, the capacity of the big vase in x is 3/2x.

The capacity of the middle sized vase is four times bigger than the capacity of the small vase, which means it is 4 times the capacity of the small vase.

So, the capacity of the small vase in terms of x is:

x/4

Therefore, the capacity of the small vase in x is x/4.

The total capacity of the three vases is 5.5 liters. We can set up an equation based on this information:

x + 3/2x + x/4 = 5.5

Multiplying both sides by 4 to eliminate the fraction:

4x + 6x + x = 22

11x = 22

x = 2

Therefore, the capacity of the middle sized vase is 2 in terms of x. To find the capacity in liters, we can substitute x = 2 into any of the expressions we found earlier:

Capacity of the big vase: 3/2x = 3/2 * 2 = 3 liters

Capacity of the small vase: x/4 = 2/4 = 0.5 liters

So, the capacities of the three vases are 3 liters, 2 liters, and 0.5 liters, and their total capacity is 5.5 liters.

Answer:

x = 9

Step-by-step explanation:

given a line parallel to a side of the triangle and intersecting the other 2 sides, then it divides those sides proportionally.

[tex]\frac{x-1}{3x+1}[/tex] = [tex]\frac{6}{21}[/tex] = [tex]\frac{2}{7}[/tex] ( cross- multiply )

7(x - 1) = 2(3x + 1) ← distribute parenthesis on both sides

7x - 7 = 6x + 2 ( subtract 6x from both sides )

x - 7 = 2 ( add 7 to both sides )

x = 9

The value of x is

x=-5

Generally, An angle is a figure formed by two rays (or line segments) that share a common endpoint. Angles are usually measured in degrees, with a full angle measuring 360 degrees.

Considering that the angle on a point is 630 , we have that the missing angle is

y=360-(148+92)

y=120

Therefore

y=x+125

Hence

x=y-125

x=120-125

x=-5

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The simplified answer is 16y² - 25x².

When multiplying conjugate binomials,

We use the formula (a+b)(a-b) = a²-b².

In this case, a = 4y and b = 5x. So,

We can pluggin these values into the formula and simplify:

(4y+5x)(4y-5x) = (4y)² - (5x)²

= 16y² - 25x²

Therefore, the simplified answer is 16y² - 25x². This is the final answer, and there are no further steps to simplify.

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So it will take 20 years for High School R and High School T to have the same enrollment.

Enrollment is the process of registering for classes at a college or university. The process usually involves submitting an application and providing transcripts and other documents to the school.

The enrollment at High School R is increasing by 15 students per year while High School T is decreasing by 10 students per year. To figure out how many years it will take for both schools to have the same enrollment, we need to calculate the difference between the two schools.
High School R currently has 200 students and High School T has 400 students. The difference between the two schools is 200 students (400-200 = 200).
Since High School R is increasing by 15 students per year and High School T is decreasing by 10 students per year, it will take 20 years for the two schools to have the same enrollment.
To calculate this, we divide the difference between the two schools (200 students) by the difference between the two schools' enrollment growth (15 students - 10 students = 5 students). This gives us 200/5 = 40. Since 40 years is too long, we divide 40 by 2 and get 20, which is the answer. So it will take 20 years for High School R and High School T to have the same enrollment.

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\pi (3)^2(4)\implies \stackrel{ \pi =3.14 }{V=113.04}[/tex]

Answer:

Step-by-step explanation:

where is the image don't see

Answer:

6

Step-by-step explanation:

Step 1: How many males are there?

40% of 60 = 0.4 × 60 = 24

There are 24 males.

Step 2: Of the 24 males, how many wear a hat?

25% of 24 = 0.25 × 24 = 6

Answer: 6

Answer: choose Answer B

Step-by-step explanation:

because if you flip the triangle back to what it was previously A B lines up with answer B so it’s B

Answer:

2 and -2

Step-by-step explanation:

For the expression to be equal to 0, it means it has to be undefined, so all we need do, is equate the denominator to 0, since any number divided by 0 = 0

Therefore,

5x² - 20 = 0

5x² = 0 + 20

5x² = 20

Divide both sides by 5,

x² = 20/5

x² = 4

Square root both sides,

x² = √4

x = ±2

Please mark brainliest.

Thanks.

Answer:

Sin A = [tex]\frac{12}{13}[/tex] ; Cos A = [tex]\frac{5}{13}[/tex]

Step-by-step explanation:

The sine of a given angle is  [tex]\frac{opposite}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length opposite to angle A is 24, and the hypotenuse is 26. This gives  [tex]\frac{24}{26} = 12/13[/tex].

The cosine of a given angle is   [tex]\frac{adjacent}{hypotenuse}[/tex], using the lengths corresponding to them. In this case, the side length adjacent to angle A is 10, and the hypotenuse is 26. This gives  [tex]\frac{10}{26} = 5/13[/tex].

Answer:

8cfct on cypur574 6th 9

Step-by-step explanation:

f5g uh yo h tu g fn l dl uge ser k

Answer:

$4.8

Step-by-step explanation:

5 for $3

So $3 ÷ 5 to get the price of one

Answer is 60c or $0.6

Then you multiply $0.6 with 8 to get the price of 8 oranges

So $0.6 x 8 = $4.8

Answer:

the cost of 8 oranges is 4.8$

step by step explanation

using ratio amd proportion

let x be the unknown amount

[tex]5 = 3 \\ 8 = x \\ cross \: multiply \\ 5x = 24 \\ divide \: \: both \: sides \: by \: 5 \\ \frac{5x}{5} = \frac{24}{5} \\ x = \frac{24}{5} \\ x = 4.8[/tex]

therefore the answer is 4.8 dollars will buy 8 oranges

thank you

Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

sum the 3 angles and equate to 180

4x + 21 + x - 10 + 2x + 8 = 180

7x + 19 = 180 ( subtract 19 from both sides )

7x = 161 ( divide both sides by 7 )

x = 23

Then angles in triangle are

4x + 21 = 4(23) + 21 = 92 + 21 = 113°

x - 10 = 23 - 10 = 13°

7x + 8 = 7(23) + 8 = 161 + 8 = 169°

the only 2 possible angle measures are A and E

Jane can buy 20 melons for the price of 32 apples.

To find out how many melons Jane can buy for the price of 32 apples, we need to use the given ratios to find the equivalent value of melons in terms of apples.

First, we know that 6 apples are equivalent to 3 bananas. So, we can simplify this ratio to 2 apples per 1 banana.

Next, we know that 4 bananas are equivalent to 5 melons. So, we can simplify this ratio to 4/5 of a banana per 1 melon.

Now, we can use these ratios to find the equivalent value of melons in terms of apples. If 2 apples are equivalent to 1 banana, and 4/5 of a banana is equivalent to 1 melon, then we can multiply these ratios together to find the equivalent value of melons in terms of apples:

2 apples/1 banana × 4/5 banana/1 melon = 8/5 apples/1 melon

This means that 1 melon is equivalent to 8/5 apples, or 1.6 apples.

Finally, we can use this ratio to find out how many melons Jane can buy for the price of 32 apples:

32 apples × 1 melon/1.6 apples = 20 melons

Therefore, Jane can buy 20 melons for the price of 32 apples.

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