amber and bethan tries a number of sweets and shares them in the ratio 2:1

The solution of given trigonometric Problem by using formula of sine , cosine , tangent is part A 1)cos-1(12/13) 2)∅=cos-1(2/3) 3)sin-1(4/13)

part B 1)13.75 unit 2) 8.112 unit 3) 5.5 unit

Trigonometry is a branch of mathematics that deals with the study of relationships between angles and sides of triangles. It primarily focuses on the properties and functions of angles, and how they can be used to calculate the measurements of sides and angles in a triangle.

Part A

1)In the given ΔACB  Right angle at ∠C

for find ∅ we use

          cos∅=B/H

          cos∅=AC/AB

          cos∅=12/13

           ∅=cos-1(12/13)

2)      cos∅= AC/AB

          ∅=cos-1(6/9)

           ∅=cos-1(2/3)

3)       sin∅=CB/AC

             ∅=sin-1(4/13)

Part-B

      1)   cos37°=11/x

              4/5=11/x

                x=55/4

                  x=13.75 unit

2)         tan32°=x/13

          0.624=x/13

          x= 8.112 unit

3)       cos 60°=x/11

         1/2= x/11

           x=11/2

            x=5.5 unit

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Answer:

If the common ratio is 0.6, then the percent change is a decrease of 40%.

If the common ratio is 0.6 then the percent change is 40%

percentage, a relative value indicating hundredth parts of any quantity.

The percent change for a geometric sequence with common ratio r is given by the formula:

percent change = (r - 1) × 100%

In this case, the common ratio is 0.6, so the percent change is:

percent change = (0.6 - 1) × 100% = -0.4 × 100% = -40%

The percent change is negative, which means the sequence is decreasing.

Hence, If the common ratio is 0.6 then the percent change is 40%

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Answer:

the answer is (HK) Because gj is the only other line that goes across the circle but it is not an option.

Part A: The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5

Part B: The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

Part C: the length of each of the five pieces of wood cut by Warren is 3.8 feet.

It is made up of two mathematical objects, with an equals sign (=) between them. Equations are used to represent relationships between unknown variables and can be solved to find their values.

Part A:

The equation that could be used to determine the length of each of the five pieces of wood cut by Warren is: x + 0.7 = 4.5, where x is the length of each piece of wood.

Part B:

The equation from Part A is correct because it takes into account the total length of the wood (4.5 feet), as well as the amount of wood that is left over (0.7 feet).

This equation can be used to calculate how much wood Warren has cut off from the original 4.5 feet of wood, which is the length of each of the five pieces of wood.

Part C:

Solving the equation from Part A:

x + 0.7 = 4.5

Subtract 0.7 from both sides:

x + 0.7 - 0.7 = 4.5 - 0.7

x = 3.8

Therefore, the length of each of the five pieces of wood cut by Warren is 3.8 feet.

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Answer:

Yes, the function f(x) = (x + 2)² is one-to-one.

Check the picture below.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{7})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - 2~~)^2 + (~~7 - 1~~)^2} \implies d=\sqrt{( 3 )^2 + ( 6 )^2} \\\\\\ d=\sqrt{ 9 + 36 } \implies d=\sqrt{ 45 }\implies d\approx 6.7[/tex]

Answer:

The constant of proportionality in the equation 2y = 2x is 1.

Note that this equation is actually the same as y = x, which is a linear equation with a slope of 1 and a y-intercept of 0. In this case, the coefficient of x (which is 2) is not the constant of proportionality because it does not represent a proportional relationship between x and y. Instead, the constant of proportionality is the ratio of the change in y to the change in x, which is 1.

The solution of compound interest problem using formula of amount  is

Anna have$2,734 more money than  Hudson.

Compound interest is a type of interest in which the interest gained is added to the principal sum before the interest for the subsequent period is calculated using the updated total sum. In other words, in addition to the initial principal, the accumulated interest from prior periods is also taken into account for calculating interest. As a result, as time passes, the interest earned increases, increasing the total amount earned or due. Savings accounts, loans, and investments frequently use compound interest.

For continuous compounding, the formula is:

A = Pe^(rt)

Where:

A = the amount after t years

P = the principal amount

r = the annual interest rate (as a decimal)

t = the time in years

For daily compounding, the formula is:

A = P(1 + r/n)^(nt)

Where:

A = the amount after t years

P = the principal amount

r = the annual interest rate (as a decimal)

n = the number of times compounded per year

t = the time in years

Using these formulas, we can calculate the amount that Anna and Hudson will have after 10 years, and then find the difference between them.

For Anna's investment:

r = 8.5% = 0.085 (as a decimal)

t = 10 years

P = $69,000

A = Pe^(rt) = 69000 * e^(0.085*10) = $156,794.63

For Hudson's investment:

r = 8 3/8% = 8.375% = 0.08375 (as a decimal)

n = 365 (daily compounding)

t = 10 years

P = $69,000

A = P(1 + r/n)^(nt) = 69000(1 + 0.08375/365)^(365*10) = $154,060.52

Therefore, the difference between the two amounts is:

$156,794.63 - $154,060.52 = $2,734.11

So Anna will have approximately $2,734 more in her account than Hudson after 10 years.

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Answer:

What is Saving?

Saving means to keep money aside, not using it for any purpose at all, until in reach of desired goal. While some save for emergencies, others save for family or materials.

Example: My father is saving for a really nice vacation trip to Canada. He needs enough money to pay for gas, the hotel rooms, food and other necessities.

What is Investing?

Investing is the practice of putting interest into something. Investing involves paying for something in increments while also having flowy income. You could invest in almost anything.

Example: My mother and I are investing into a large, family-sized, RV. We are making custom arrangements and changes while we are still living in, and keeping our tiny-home.

The value of x for which sin(x+16)°=cos(2x+14)° is 20

Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths

The given equation says:

sin(x+16)°=cos(2x+14)°

Remember that sin(90-x) = cos x

Applying this formula we have

So comparing we have,

sin(x+16)°=cos(2x+14)°

90 - (x + 16) = 2x +14

distributing - over the bracket

90 -x - 16 = 2x + 14

bringing like terms together,

90-16-14 = 2x +x

60 = 3x

Dividing both sides by 3,

x =20

Therefore the value of sin(x+16)°=cos(2x+14)° is 20⁰

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Answer:

sinA =9/41. CosA=40/41

Step-by-step explanation:

in right triangles, the sine, cosine and tangent represent ratios of the sides of a triangle. Sine of an angle is the ratio of the side opposite the angle divided by the hypotenuse and the cosine of the angle is side adjacent (touching) the angle divided by the hypotenuse.

The value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

here, we have,

The values of the angels will be calculated by using the trigonometry property.

Sin A = Perpendicular / Hypotenuse

Sin A = 9 /41

Cos A = Base / Hypotenuse

Cos A =  40 / 41

Therefore the value of Sin A = 9 / 41 and the value of Cos A = ( 40 / 41).

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The equation that represents the relationship between x and y, where y is the number of candy bars and x is the cost in dollars, is x = 0.75y.

An equation is a mathematical statement showing the equality or equivalence of two or more mathematical expressions.

Equations contain mathematical expressions with the equal symbol (=).

                                                     First Order    Second Order

The number of candy bars               36                  24

The total cost of order                   $27                 $18

The unit cost per candy bar =       $0.75           $0.75

                                                ($27 ÷ 36)       ($18 ÷ 24)

Let the number of candy bars bought = y

Let the cost of the candy bars = x

36x = $27

x = $0.75

Similarly, 24x = $18

x = $0.75

Therefore, the equation representing the relationship is:

x = 0.75y

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The solution to the inequality, 4 - 2x ≥ 10, is x ≤ -3.

The graph is shown below.

To graph the solution to the inequality given, we have to first of all solve for the possible values of x in the given inequality.

Given the inequality,  4 - 2x ≥ 10, we have:

4 - 2x ≥ 10

Subtract 4 from both sides:

4 - 4 - 2x ≥ 10 - 4

-2x ≥ 6

Divide both sides by -2:

-2x/-2 ≤ 6/-2

x ≤ -3

This means that the values of x are equal to -3 or less than -3.

The graph below shows the solution.

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Answer:

Step-by-step explanation:

Formula for trapezoid:

A=[tex]\frac{1}{2}[/tex](b1 + b2)h

1.  b1=5    b2=23  h=12

A=1/2(5+23)12

=168

The angle 9pi/4 is a positive coterminal angle of pi/4.

What is a coterminal angle?

Two angles are called coterminal if they have the same initial and terminal sides. In other words, two angles are coterminal if they differ by a multiple of 360 degrees or 2π radians. For example, 30 degrees and 390 degrees are coterminal angles, as are π/4 and 9π/4.

A coterminal angle of pi/4 can be found by adding or subtracting any multiple of 2pi until we get an angle between 0 and 2pi that is equivalent to pi/4.

One way to find a positive coterminal angle is to add 2pi:

pi/4 + 2pi = 9pi/4

So, The angle 9pi/4 is a positive coterminal angle of pi/4.

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Answer: I think the answer is $229.5, or $259.5 since it says he has to pay $30

Step-by-step explanation: Just multiply 270 by the percent as a decimal. 85% is equal to 0.85 and that multiplied by 270 is 229.5

Answer: x= 75.52 deg

Step-by-step explanation:

1) cos x = adjacent/hypotenuse

  cos x = 2 / 8

  x = cos^-1(2/8)

  x= 75.52 deg

y = x - 4 is  the equation of the line in slope-intercept form.

How do you interpret a slope-intercept form?

The data provided by that form can be used to graph a linear equation in slope-intercept form. As an illustration, the equation y=2x+3 indicates that the line's slope is 2 and that its y-intercept is located at (0,3). This reveals the single point at which the line passes as well as the direction in which we should draw the full line after that.

Point from graph = (2, -2 )

                slope (m) = y/x

                                = -2/2

                                = 1

slope-intercept form ⇒ y = mx + c    

                                        -2 = 1 * 2 + c

                                          - 2 = 2 + c

                                               c = -4

 slope-intercept form ⇒ y = x - 4

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The statement can be written as the inequality:

x ≥ 12

We know that x is at least 12, so x can be equal to 12, or larger. We want to write that as an inequality, and it can be written as:

x ≥ 12

The symbol:

"≥"

Means that the thing in the left is larger or equal than the thing in the right, so that inequlity represents the given statement.

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Answer:

x = -3

Step-by-step explanation:

We know that,

[tex]\sf a^x*a^y=a^{x+y}\\\\(a^x)^y=a^{xy}\\\\\frac{a^x}{a^y} =a^{(x-y)}[/tex]

Accordingly,

[tex]\sf \frac{(7^{10})^2}{7^4} =\frac{7^9*7^{10}}{7^x} \\\\\sf \frac{7^{10*2}}{7^4} =\frac{7^{9+10}}{7^x} \\\\\sf \frac{7^{20}}{7^4} =\frac{7^{19}}{7^x}\\\\7^{20-4}=7^{(19-x)}\\\\16=19-x\\\\16-19=x\\\\-3 =x[/tex]

Answer:

567

Step-by-step explanation:

n

The Ice Cream container will hold 1.2 liters of Ice Cream.

The Volume of Ice Cream can be calculated by Cubical Volume Equation V=l*b*h _______(1). We Have the data : Length = 0.2 meters, Width = 0.1 meters, Height = 0.06 meters

Now Having the Values of Length, Height & Width. Putting these Values in The Equation (1),

Volume = 0.2*0.1*0.06 m³

Volume = 0.0012 m³

We have got the Volume of Ice Cream that can be contained by the Container in m³. To Convert into Liters, we have equation 1 m³=1000 Liters. According to this, The Volume of Ice Cream Contained in The Container will be 1.2 Liters.

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The probability distribution for the number of spins that land on two is given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

Each spinner has a 3/4 probability of not landing on two, hence the probability of landing on two zero times is given as follows:

P(X = 0) = 3/4 x 3/4

P(X = 0) = 9/16

P(X = 0) = 0.5625.

For two times, the probability is given as follows:

P(X = 2) = 1/4 x 1/4

P(X = 2) = 1/16

P(X = 2) = 0.0625.

Hence the probability of one landing is given as follows:

P(X = 1) = 1 - (0.5625 + 0.0625)

P(X = 1) = 0.375.

(considering complementary events)

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The value of x is 31/64 or 0.484375 and the value of 61/64 is given by adding the value of 29/64 and 31/64 which is 0.9375.

To convert a fraction to a decimal, you need to divide the top number by the bottom number. Here are the steps to follow:

1. Fraction should be written as numerator (top) divided by denominator (bottom).

2. Divide the numerator by the denominator using long division or a calculator.

3. Keep dividing until you get a decimal that terminates or repeats.

a) The given equation is

       [tex]\frac{61}{64} = \frac{29}{64} + x[/tex]

       [tex]\frac{61}{64} - \frac{29}{64} = x[/tex]

       [tex]x = \frac{31}{64}[/tex]

b) Now 31/64 = 0.484375 and given that 29/64 = 0.453125

Hence from the equation 61/64 = 29/64 + 31/64 = 0.453125 + 0.484375

= 0.9375.

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The crucial t-value is determined to be 1.734 using a t-table with 19 degrees of freedom and a significance threshold of 0.05 for a one-tailed test.

A type of statistical hypothesis known as a null hypothesis claims that a certain collection of observations has no statistical significance. The viability of hypotheses is evaluated using sample data. known as "zero" at times and represented by the letter H0. The assumption made by researchers is that there is a relationship between the variables. The null hypothesis, on the other hand, asserts that such a connection does not exist. Although it might not seem significant, the null hypothesis is an important part of research.

We may run a one-tailed t-test for the standard deviation to test the hypothesis that the standard deviation of heights of major-league baseball players is less than 2.7 inches.

The following formula may be used to get the sample standard deviation of the players' heights among the 20 chosen at random:

where n is[tex]s = 1/(n-1) * \sum(x' - x)^2 = 1/(20-1) * (1.83-1.755)^2 + ... + (1.9-1.755)^2 = 0.0414[/tex] the sample size, xi is the player's height at position i, and x is the average player's height in the sample.

The test statistic may then be calculated as follows:

[tex]t = (n-1) * s^2 / \sigma ^2 = 19 * 0.0414^2 / 2.7^2 = 0.197[/tex]

The crucial t-value is determined to be 1.734 using a t-table with 19 degrees of freedom and a significance threshold of 0.05 for a one-tailed test.

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The amount of money in the account after 17 years, to the nearest dollar, would be $76,956.

What is the formula for the future value?

The formula for the future value of an investment with continuous compounding is [tex]A = Pe^{(rt)}[/tex] where A is the future value, P is the principal (initial investment), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the number of years.

Putting in the given values,

[tex]A = 52000 \times e^{(0.021 \times 17) }\\ A ≈ 76,956.18[/tex]

Therefore, the amount of money in the account after 17 years, to the nearest dollar, would be $76,956.

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Answer:

a₂₆ = 248

Step-by-step explanation:

to find the 26th term substitute n = 26 into the explicit formula

a₂₆ = 14 + 9(26) = 14 + 234 = 248

Answer:

To find the equation of the line containing the segment DE, we can use the coordinates of D and E to find the slope:

slope = (change in y) / (change in x) = (0 - 3) / (4 - 2) = -3/2

We can use the point-slope form of the equation of a line, using either D or E as the point:

y - 3 = (-3/2)(x - 2)

Simplifying this equation, we get:

y = (-3/2)x + 6

Similarly, to find the equation of the line containing the segment EF, we can find the slope using the coordinates of E and F:

slope = (change in y) / (change in x) = (-2 - 0) / (1 - 4) = 2/3

Using either E or F as the point, we can write the equation in point-slope form:

y - 0 = (2/3)(x - 4)

Simplifying, we get:

y = (2/3)x - (8/3)

To find the equation of the line containing the segment TV, we can find the slope using the coordinates of T and V:

slope = (change in y) / (change in x) = (0 - 3) / (-2 - 0) = 3/2

Using either T or V as the point, we can write the equation in point-slope form:

y - 3 = (3/2)(x - 0)

Simplifying, we get:

y = (3/2)x + 3

Finally, to find the equation of the line containing the segment VW, we can find the slope using the coordinates of V and W:

slope = (change in y) / (change in x) = (-2 - 0) / (1 - (-2)) = -2/3

Using either V or W as the point, we can write the equation in point-slope form:

y - 0 = (-2/3)(x - (-2))

Simplifying, we get:

y = (-2/3)x + (4/3)

Answer:

are reflection across the y-axis and translation 2 units right.

Step-by-step explanation:

The side length of the dilated side would be 3 cm.

The area of the original square is 16 cm ², so its side length is √ 16 = 4 cm.

When the square is dilated by a factor of 0. 75, its area will be reduced to ( 0. 75 ) ² times the original area , which would then be:

= ( 0.75 ) ² x 16 cm ² = 9 cm²

Therefore, the area of the scaled square is 9 cm². The area of a square equals to the size of its side duration, thus we can locate the side length of the magnified square by extracting the square root of its area:

√ 9 cm = 3 cm

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The answers are given below:

A conditional statement is a form of logical statement that consists of two parts: a conclusion and an antecedent (sometimes known as a "if-clause")  

If p, then q is a common way to represent the link between the hypothesis and the conclusion, where p stands for the hypothesis and q for the conclusion.

Therefore, the correct options are:

The statement can be written as a biconditional: Two angles are complementary if and only if the sum of their measures is 90.

The converse of the statement is false.

A counter-example to prove the converse is false is: a Linear pair of angles are not complementary, they add up to 180.

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