5(2x - 1) + 3(x - 3) = -(4x - 6) + 2(13 - 3x)

The measure of angle A and B is 29° and 61° respectively

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.

sin(tetha) = opp/hyp

tan(tetha) = opp/adj

cos(tetha) = adj/hyp

The opposite is 6 and the adjascent = 11

Therefore tan (tetha) = 11/6 = 1.833

tetha = tan^-1( 1.833)

= 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore,

angle A = 180-( 61+90)

= 180-151

= 29°

therefore the measure of angle A and B is 29° and 61° respectively.

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Answer:

x = 4√5 ≈ 8.94 (2 d.p.)

y = 8√5 ≈ 17.89 (2 d.p.)

Step-by-step explanation:

To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.

[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]

From inspection of the given right triangle RST:

Substitute the values into the formulas:

[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]

Solve the equation for x:

[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]

[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]

[tex]\implies 80=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]

[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]

[tex]\implies x=4\sqrt{5}[/tex]

Solve the equation for y:

[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]

[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]

[tex]\implies 320=y^2[/tex]

[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]

[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]

[tex]\implies y=8\sqrt{5}[/tex]

The standard deviation of the ACT scores is approximately 4.2.

Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.

According to the given information:

To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.

Given:

Mean (μ) = 21.4

Percentage of scores above 26 = 15%

Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.

Z-score formula:

Z = (X - μ) / σ

Where:

Z = Z-score

X = Value (in this case, 26)

μ = Mean (21.4)

σ = Standard deviation (to be found)

We can rearrange the formula to solve for σ:

σ = (X - μ) / Z

Substituting the given values:

X = 26

μ = 21.4

Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)

Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:

σ = (26 - 21.4) / 1.04

σ = 4.4 / 1.04

σ ≈ 4.2 (rounded to the nearest tenth)

So, the standard deviation of the ACT scores is approximately 4.2.

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The 21st term of the sequence 3, 8, 13, 18, .. is 103

To find the indicated term in the sequence, we first need to identify the pattern followed by the sequence. It appears that each term is obtained by adding 5 to the previous term. So, we can write the general formula for the nth term of the arithmetic sequence as

a(n) = a(1) + (n-1)d

where a(1) is the first term of the sequence, d is the common difference, and n is the term number.

In this case, we have:

a(1) = 3 (the first term)

d = 5 (the common difference)

To find the 21st term, we substitute n = 21 in the formula:

a(21) = a(1) + (21-1)d

a(21) = 3 + 20(5)

a(21) = 103

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Answer:

≈ $26

Step-by-step explanation:

13% = 0.13

199.99 x 0.13 = $25.9987

So, 13% markup is ≈ $26

Answer:

2.36 miles

Step-by-step explanation:

radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles

When x is 2, the value of the expression is 9.

An algebraic expression is a mathematical phrase that contains one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It can also contain exponents, roots, and trigonometric functions.

Algebraic expressions are used to represent mathematical relationships and solve problems in a wide range of fields, including physics, engineering, finance, and statistics. They can be used to model real-world phenomena and to make predictions based on data.

Algebraic expressions can be simplified by combining like terms and using mathematical rules and properties. They can also be evaluated by substituting values for the variables and simplifying the expression. Solving equations involving algebraic expressions often involves manipulating the expression to isolate a variable and find its value.

When x is 2, the value of the expression 12/4+3(8−x)-12 can be found by substituting 2 for x and simplifying the expression:

12/4 + 3(8 - 2) - 12

= 3 + 3(6) - 12

= 3 + 18 - 12

= 9

Therefore, when x is 2, the value of the expression is 9.

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The complete question is :

When x is 2, what is the value of the expression 12/4+3(8−x)-12?

Answer:

Same equation just using the assocaitive property

Step-by-step explanation:

For example, 8 + (2 + 3) = (8 + 2) + 3 = 13

Hope this helps! =D

fraction wise, a whole is always simplified to 1, so

[tex]\cfrac{4}{4}\implies \cfrac{1000}{1000}\implies \cfrac{9999}{9999}\implies \cfrac{17}{17}\implies \text{\LARGE 1} ~~ whole[/tex]

so, we can say the whole of the players, namely all of them, expressed in fourth is well, 4/4, that's the whole lot,  and we also know that 3/4 of that is 12, the guys who chose the bottle of water

[tex]\begin{array}{ccll} fraction&value\\ \cline{1-2} \frac{4}{4}&p\\[1em] \frac{3}{4}&12 \end{array}\implies \cfrac{~~ \frac{4 }{4 } ~~}{\frac{3}{4}}~~ = ~~\cfrac{p}{12}\implies \cfrac{~~ 1 ~~}{\frac{3}{4}} = \cfrac{p}{12}\implies \cfrac{4}{3}=\cfrac{p}{12} \\\\\\ (4)(12)=3p\implies \cfrac{(4)(12)}{3}=p\implies 16=p[/tex]

Answer: If you want me to evaluate its 18x - 2

Hope it helped :D

Answer:

The answer is 3

Step-by-step explanation:

x×108=y

x×2²×3³=y

3×108=324

The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.

Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.

So, we can write this as a fraction:

$18.00 / $30.00

To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

$18.00 / $30.00 = 0.6

Another way to say this is that Maggie spent 60% of the money she had in her wallet.

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The distance between A and B is approximately 8.06 units.

In order to find the distance, d, of AB, we need to use the distance formula. The distance formula gives us the distance between two points in a coordinate plane. It is given as:$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ where (x1, y1) and (x2, y2) are the coordinates of the two points in question.

In this case, A and B are the two points for which we need to find the distance. Let's assume that the coordinates of A are (x1, y1) and the coordinates of B are (x2, y2).

Then the distance formula becomes:

$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$

$$d = \sqrt{((8 + 4) - 2)^2 + ((5 - 1) - 3)^2}$$

$$d = \sqrt{(10 - 2)^2 + (4 - 3)^2}$$

$$d = \sqrt{(8)^2 + (1)^2}$$

$$d = \sqrt{64 + 1}$$

$$d \approx \sqrt{65}$$

$$d \approx 8.06$$

Therefore, the distance between A and B is approximately 8.06 units.

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Step-by-step explanation:

x = -4     ( the value of the x-coordinate of the vertex is the axis of symmetry for normal up or down opening parabolas)

The means of two or more populations being equal is determined by a statistical approach for the ANOVA procedure. Option B is correct.

The ANOVA (Analysis of Variance) procedure is a statistical method used to determine whether there is a significant difference between the means of two or more groups. To statistically test the equality of means ANOVA uses F-tests.

The repeated-measures ANOVA is a two-stage process that is described as an analysis of dependencies. This test is used to prove an assumed cause-effect relationship between variables. The conditions that must be met for the results of an ANOVA are Independence, Random Sampling, Large Sample Size, and Normality.

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Answer:

Step-by-step explanation:

Let A be the area of the surface of the cube.

When the side length changes from s to 4s, the new area A' can be calculated as:

A' = 6(4s)^2 = 96s^2

The change in area is then:

ΔA = A' - A = 96s^2 - 6s^2 = 90s^2

To find the integral that quantifies the change in area, we can integrate the expression for ΔA with respect to s, from s to 4s:

∫(90s^2)ds from s to 4s

= [30s^3] from s to 4s

= 30(4s)^3 - 30s^3

= 1920s^3 - 30s^3

= 1890s^3

Therefore, the integral that quantifies the change in area of the surface of a cube when its side length quadruples from s units to 4s units is:

∫(90s^2)ds from s to 4s

= 1890s^3 from s to 4s

= 1890(4s)^3 - 1890s^3

= 477,840s^3 - 1890s^3

The sine function that describes the child's apparent distance from the center of the merry-go-round is d(t) = 5.3 sin(2π/15 * t)

To write a sine function that describes the child's apparent distance from the center of the merry-go-round as a function of time t, we can start by finding the amplitude, period, and phase shift of the motion.

Amplitude:

The amplitude of the motion is half the diameter of the merry-go-round, which is 10.6/2 = 5.3 feet. This is because the child moves back and forth across the diameter of the merry-go-round.

Period:

The period of the motion is the time it takes for the child to complete one full cycle of back-and-forth motion, which is equal to the time it takes for the merry-go-round to complete one full rotation.

From the given information, the child completes 8 rotations in 120 seconds, so the period is T = 120/8 = 15 seconds.

Phase shift:

The phase shift of the motion is the amount of time by which the sine function is shifted horizontally (to the right or left).

In this case, the child starts at one end of the diameter and moves to the other end, so the sine function starts at its maximum value when t = 0. Thus, the phase shift is 0.

With these values, we can write the sine function that describes the child's apparent distance from the center of the merry-go-round as:

d(t) = 5.3 sin(2π/15 * t)

where d is the child's distance from the center of the merry-go-round in feet, and t is the time in seconds. The factor 2π/15 is the angular frequency of the motion, which is equal to 2π/T.

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Answer: The answer is A.

Step-by-step explanation: Because I am smart don't underestimate me.

Answer:

C

Step-by-step explanation: (look at attachment)

3x + 4 = -2x -2

By looking at the y-intercepts, you automatically know the answer is C.

The y-intercept of the pink line is 4 because of 3x + 4.

The y-intercept of the blue line is -2, because of -2x - 2.

Answer:

£12063.57

Step-by-step explanation:

The value of Alfred’s car after 12 years can be calculated using the formula for exponential decay: Final Value = Initial Value * (1 - rate of depreciation)^(number of years). Plugging in the values we get: Final Value = 13960 * (1 - 0.0075)^12. Therefore, after 12 years, Alfred’s car will be worth approximately £12063.57.

Answer:

d. 1 7/30...............

Answer:

D

Step-by-step explanation:

2/5 + 5/6

Make the denominator same

(2×6)/30 + (5×5)/30

12+25/30

37/30

1 7/30

The balloon payment at the end of 7 years would be $173,819.97, which is option A.

A 7/23 balloon mortgage means that April will make payments on the loan as if it were a 23-year mortgage, but the remaining balance of the loan will be due in full after 7 years.

To find the balloon payment at the end of 7 years, we can first calculate the monthly payment using the loan amount, interest rate, and loan term:

n = 23 * 12 = 276 (total number of payments)

r = 4.15% / 12 = 0.003458 (monthly interest rate)

P = (r * PV) / (1 - (1 + r)^(-n))

where

PV = $197,000

P = (0.003458 * $197,000) / (1 - (1 + 0.003458)^(-276)) = $1,007.14 (monthly payment)

Now we can calculate the remaining balance on the loan after 7 years. Since April is making payments as if it were a 23-year mortgage, she will have made 7 * 12 = 84 payments by the end of the 7th year.

Using the formula for the remaining balance of a loan after t payments:

B = PV * (1 + r)^t - (P / r) * ((1 + r)^t - 1)

Where

t = 84 (number of payments made)

B = $197,000 * (1 + 0.003458)^84 - ($1,007.14 / 0.003458) * ((1 + 0.003458)^84 - 1)

B = $173,819.97

Therefore, the balloon payment at the end of 7 years would be $173,819.97, which is option A.

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Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.

For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.

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Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.

The starting point is truly random, and that the interval selected does not create any bias in the sample.

Systematic sampling is a method of selecting a sample from a population using a system or a pattern.

It involves selecting every nth item or person from the population after a random starting point has been determined.

To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.

Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.

The interval is calculated by dividing the population size by the desired sample size.

A researcher wants to select a sample of 100 from a population of 1000, the interval would be. [tex]1000/100 = 10.[/tex]

The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.

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Answer:

-2

Step-by-step explanation:

The explanation is in the picture

The means of a stock that has a beta measure of 2.5 is 2.5%.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

The beta measure is a measure of the volatility of a stock relative to the market.

If the market goes down by 1%, the stock is expected to go down by 2.5%.

Therefore,

The stock is considered to be more risky than the average stock in the market.

A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.

This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.

Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.

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Answer:

[tex]f(x) = 500( {.89}^{x} )[/tex]

The value of x is approximately 10.57 and the value of y is approximately 15.25.

In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.

The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.

In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:

105 + (7y + 1) + (7x + 1) + (4y + 14) = 180

Simplifying and solving for x and y, we get:

7x + 4y + 122 = 180

7x + 4y = 58 ......(1)

Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:

105 + (4y + 14) = 180 ......(2)

(7y + 1) + (7x + 1) = 180 ......(3)

Simplifying and solving for y in equation (2), we get:

4y + 119 = 180

4y = 61

y = 15.25

Substituting this value of y in equation (3) and solving for x, we get:

(7x + 1) + (7*15.25 + 1) = 180

7x + 106 = 180

7x = 74

x = 10.57

Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.

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Answer:

Yo, when you adding or subtracting mixed numbers with the same denominators, the numerators stay chill, they don't change, bro.

But the denominators, they also stay the same, man. It's like keeping things consistent, ya feel me? So the answer is A, dude. Numerators stay put, denominators stay put. It's all good vibes, bro! ✌️

Answer:

Your answer should be A