Kathy is adding a new slide to her swing set. The slide is 5 feet long, and the ladder is 4 feet high. How
many feet away is the base of the ladder from the end of the slide, g, as shown below?
5 ft
g
4ft

Answer:

10

Step-by-step explanation:

The mean of a set of numbers is the sum divided by the number of terms.

sin 135°=-√2/2, cos 135° = -√2/2, tan 135° = -1, csc 135°= -√2, sec 135°= -√2, cot 135° = -1; sin (-690°) = -1/2, cos (-690°) =√3/2, tan (-690°) = -√3/3, csc (-690°) = -2, sec (-690°) = 2/√3, cot (-690°) = -√3; sin 225° = -√2/2, cos 225° = -√2/2,  tan 225° = 1, csc 225° =-√2, sec 225° = -√2, cot 225° =-1; sin 1380° = -√3/2, cos 1380° = 1/2, tan 1380° = -√3, csc 1380° = -2/√3, sec 1380° = 2, cot 1380° =-1/√3.

Trigonometric ratios are mathematical functions used to relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.

To use these ratios, we typically label the sides of the right triangle relative to the angle we are interested in. The hypotenuse is always the side opposite the right angle and is labeled with the letter "c." The two other sides are labeled relative to the angle we are interested in: the side adjacent to the angle is labeled with the letter "a," and the side opposite the angle is labeled with the letter "b."

The sine of an angle is defined as the ratio of the length of the side opposite the angle (b) to the length of the hypotenuse (c): sin(angle) = b/c.

The cosine of an angle is defined as the ratio of the length of the side adjacent to the angle (a) to the length of the hypotenuse (c): cos(angle) = a/c.

The tangent of an angle is defined as the ratio of the length of the side opposite the angle (b) to the length of the side adjacent to the angle (a): tan(angle) = b/a.

To find the exact values of the six trigonometric functions for each angle, we need to first determine the reference angle, which is the acute angle formed between the terminal side of the angle and the x-axis. Then, we can use the properties of the trigonometric functions in each quadrant to determine the sign and value of each function.

135°

Reference angle = 45° (since 135° is in the second quadrant)

sin 135° = -sin 45° = -√2/2

cos 135° = -cos 45° = -√2/2

tan 135° = -tan 45° = -1

csc 135° = -csc 45° = -√2

sec 135° = -sec 45° = -√2

cot 135° = -cot 45° = -1

-690°

Reference angle = 30° (since -690° is in the fourth quadrant)

sin (-690°) = -sin 30° = -1/2

cos (-690°) = cos 30° = √3/2

tan (-690°) = -tan 30° = -√3/3

csc (-690°) = -csc 30° = -2

sec (-690°) = sec 30° = 2/√3

cot (-690°) = -cot 30° = -√3

225°

Reference angle = 45° (since 225° is in the third quadrant)

sin 225° = -sin 45° = -√2/2

cos 225° = -cos 45° = -√2/2

tan 225° = -tan 45° = 1

csc 225° = -csc 45° = -√2

sec 225° = -sec 45° = -√2

cot 225° = -cot 45° = -1

1380°

Reference angle = 60° (since 1380° is in the second quadrant)

sin 1380° = -sin 60° = -√3/2

cos 1380° = cos 60° = 1/2

tan 1380° = -tan 60° = -√3

csc 1380° = -csc 60° = -2/√3

sec 1380° = sec 60° = 2

cot 1380° = -cot 60° = -1/√3

Note: In the calculations above, we rationalized denominators whenever applicable to obtain exact values.

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Answer: 4

Step-by-step explanation:

z^2 = 16

Since z is squared and we know that it equals 16. Take the square root of 16 which is 4.

4 x 4 = 16

Answer:

Step-by-step explanation:

16

Answer:

True.

explanation:

The data from the Florida Crash Reports and annual registrations and licensure numbers indicate that in 2004, 416 motorcyclists  died in Florida while in 2008 the number reached 532.In 2008, 55 % of the fatalities were wearing helmets, while 35% were with no helmet. The Florida Rider Training Program (FRTP) is an effort established to educate the public on fatalities in motor cycle fatalities.

The recursive formula that represents the given sequence is:

(B) an = -44aₙ₋₁ - 2

Any term of a series can be defined by its preceding term in a recursive formula (s).

For instance: An arithmetic series has the recursive formula a = an-1 + d.

An = An-1r is the recursive formula for a geometric sequence.

Because each phrase, an, goes back to the preceding term, an1, the formula an=2an1+3 is recursive.

According to this equation, any term we want is equal to two times the previous term plus three.

This sequence's first three terms are 4, 11, and 25.

So, we have the sequence:

-44, -46,-48, ...

Now, we have d that is:

= -48 - (-46)

= -48 + 46

= -2

The 1st term would be: a1 = -44

Then, the correct formula would be: an = -44aₙ₋₁ - 2

Therefore, the recursive formula that represents the given sequence is:

(B) an = -44aₙ₋₁ - 2

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The percentage of the area under the density curve where x is less than 2 is 50%.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

To find the percentage of the area under the density curve where x is less than 2, we need to find the area under the curve to the left of x = 2 and divide it by the total area under the curve.

To calculate the area under the curve to the left of x = 2, we can break it up into two parts: the rectangular area to the left of x = 2 and the triangular area above it.

The rectangular area has a width of 2 and a height of 0.2, so its area is 2 × 0.2 = 0.4.

The triangular area has a base of 2 and a height of 0.2 - 0 = 0.2, so its area is (1/2) × 2 × 0.2 = 0.2.

Therefore, the total area under the curve to the left of x = 2 is 0.4 + 0.2 = 0.6.

To find the total area under the curve, we can calculate the area of the rectangle with width 6 and height 0.2, which is 6 × 0.2 = 1.2.

So the percent of the area under the density curve where x is less than 2 is -

(0.6 / 1.2) × 100% = 50%

Therefore, the area under curve is obtained as 50%.

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Yes

The logarithm function is continuous for all x>0. Its derivative is 1/x and r12 ln x dx = x ln x - x + c.

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Answer:

27.43% of the students scored 83 or more in the exam.

Step-by-step explanation:

We can use the Z-score formula to find the percentage of students scoring 83 or more:

Z = (X - μ) / σ

where X is the test score, μ is the mean test score, and σ is the standard deviation.

Substituting the given values, we get:

Z = (83 - 80) / 5 = 0.6

Using a Z-score table or calculator, we can find the percentage of students scoring 83 or more:

P(Z > 0.6) = 1 - P(Z < 0.6) = 1 - 0.7257 ≈ 0.274

27.43% of the students scored 83 or more in the exam.

OR. USING PROPERTIES OF NORMAL DISTRIBUTION

convert the raw score of 83 into a standardized score, also known as a z-score.

The formula for calculating the z-score is:

z = (x - μ) / σ

Where:

x = raw score

μ = mean

σ = standard deviation

Substituting the values given in the question, we get:

z = (83 - 80) / 5

z = 0.6

This means that a student who scored 83 on the exam has a z-score of 0.6.

Next, we need to find the area under the normal distribution curve to the right of this z-score. We can use a standard normal distribution table or calculator for this purpose.

Using a standard normal distribution table, we find that the area to the right of z = 0.6 is approximately 0.2743.

Therefore, the percentage of students scoring 83 or more in the exam is approximately:

0.2743 x 100% = 27.43%

So, about 27.43% of students scored 83 or higher on the exam.

Answer:

20.65

Step-by-step explanation:

The quantity (in pounds) of gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q(p) = 1000 - 40p.

In science and engineering, a quantity is something that has a magnitude or size that may be expressed in numerical terms and that is associated with a unit of measurement. For example, a distance is a quantity with a size expressed in units of length.

A physical quantity that has a directional aspect is referred to as a vector. A quantity is any measurable amount or property of something, typically consisting of a value and a unit of measurement, such as length, weight, volume, or time.

it's also used to refer to a particular sum or amount of something that is counted or measured, such as a number of things or the total amount of a substance.

Therefore, The formula for finding the quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a price of p dollars per pound is Q(p) = 1000 - 40p.

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The best measure of center for the data is Option D: The median, and it equals 8.

What is median?

In mathematics, the middle number in a sorted list of numbers is referred to as the median. By arranging the numbers, the middle number can be discovered. Ascending order is used to arrange the numbers. The middle number in the ordered set of numbers is referred to as the data set's median.

The best measure of center for this data is the median because the data is skewed and has outliers.

The median is the middle value when the data is arranged in order, which is less sensitive to outliers than the mean.

To find the median, we need to count the number of data points and find the middle value -

1, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9

We have 11 data points, so the median is the 6th value -

Median = 8

Therefore, the best measure of center for the data is the median, and its value is 8.

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Answer:

-9, -6, -4, -2, 2, 3

Step-by-step explanation:

the higher the negative the lower it is

The probability of at least one card being green is 0.807. Here's how to calculate it: Let's define the event G as getting a green card and the event Y as getting a yellow card.

The probability of getting a green card on the first draw is: P(G1) = 9/14
The probability of getting a yellow card on the first draw is: P(Y1) = 5/14
The probability of getting a green card on the second draw, given that the first card was yellow, is: P(G2 | Y1) = 9/13
The probability of getting a green card on the second draw, given that the first card was green, is: P(G2 | G1) = 8/13
The probability of getting a yellow card on the second draw, given that the first card was green, is: P(Y2 | G1) = 5/13
The probability of getting a yellow card on the second draw, given that the first card was yellow, is: P(Y2 | Y1) = 4/13
To calculate the probability of at least one card being green, we need to add up the probabilities of getting a green card on the first draw and a yellow card on the second draw, and the probabilities of getting a green card on the second draw given that the first card was yellow, and getting a green card on the second draw given that the first card was green:
P(at least one green card) = P(G1 and Y2) + P(G2 | Y1)
P(Y1 and G2 | G1) + P(G1 and G2) = 9/14 * 5/13 + 5/14 * 9/13 + 8/14 * 5/13 + 9/14 * 8/13 = 45/182 + 45/182 + 40/182 + 72/182 = 0.807

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⇒First take out the highest common factor 2 form the quadratic equation and divide each and every term of that equation by that common factor.

⇒Factorise the equation and equate the factors of the equation to 0 and solve for the unknown variable x.

⇒Below are the steps on solving for the unknown variable.

[tex]2(x^{2} -14x+49)=0 \\\frac{2(x^{2} -14x+49)}{2} =\frac{0}{2} \\x^{2} -14x+49=0\\(x-7)(x-7)=0\\x-7=0\\x=7[/tex]

There are 6720 8-letter words that can be formed from the letters of the word "wasteful" if repetition is not allowed.

To form an 8-letter word from the letters of the word "wasteful" without repetition, we must choose 8 letters from the 7 distinct letters "w", "a", "s", "t", "e", "f", "u" available.

Let's use the permutation formula to find the number of ways we can do this.

Permutation = (Number of objects)! / ((Number of objects) - r)!Permutation = 7! / (7 - 8)!Permutation = 7! / (-1)!But (-1)! is undefined, so there are no 8-letter words that can be formed from the letters of the word "wasteful" without repetition.

If repetition was allowed, then the number of 8-letter words that could be formed = 7^8 = 5764801.

Hence, the number of 8-letter words that can be formed from the letters of the word "wasteful" if repetition is not allowed is 6720.

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A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.

A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.

The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.

On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.

This approach can help to improve the accuracy of forecasts and predictions based on the time series data.

In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.

Therefore, Option C is correct answer.

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If a research company claims that more than 55% of americans regularly watch public access television, the test statistic for the population proportion is 1.61.

To calculate the test statistic for the population proportion, we first need to set up the null and alternative hypotheses. Let p be the true proportion of Americans who regularly watch public access television.

H0: p ≤ 0.55 (null hypothesis)

Ha: p > 0.55 (alternative hypothesis)

We use a one-tailed test with α = 0.05 level of significance.

Next, we calculate the sample proportion:

p' = 255/425 = 0.60

Then, we calculate the standard error of the proportion:

SE = √(p'(1-p')/n) = √(0.60*0.40/425) ≈ 0.031

Finally, we calculate the test statistic:

z = (p' - p0)/SE = (0.60 - 0.55)/0.031 ≈ 1.61

where p0 is the value of the proportion under the null hypothesis.

The test statistic is approximately 1.61. To determine whether this value provides evidence to reject the null hypothesis, we compare it to the critical value of the z-distribution at α = 0.05 level of significance.

For a one-tailed test with a significance level of 0.05, the critical value is 1.645. Since our test statistic is less than the critical value, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to support the claim that more than 55% of Americans regularly watch public access television.

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Dhruv will most probably admit precisely 1 chocolate if the probability is0.2181 or (21.81%).

Probability refers to eventuality. This area of mathematics examines how arbitrary events be.

First, the total number of ways

= C( 11, 3)

= 11!/ 8! 31

= 11 x 10 x 9/ 3x 2

= 165

Now, If Dhruv gets exactly 1 chocolate there are now 7 chocolate and

3- 1 = 2 bars

So, the number of ways for 1 exactly one chocolate

= C( 9, 2)

= 9!/ 7! 21

= 9 x 8/ 2

= 36 ways

The liability that Dhruv receives exactly one chocolate is now.

= 36/ 165

= 12/ 55

Thus, the probability that Dhruv gets exactly 1 chocolate is 12/55 ≈0.2181 or 21.81%.

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An exponential model for the worth of the savings account is [tex]W = 1250(1.045)^t[/tex]

The worth predicted by the exponential model is greater than predicted by the linear model at the end of 2020 by $131.2.

In Mathematics, an exponential function can be modeled by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

Based on the information provided about the savings account, we would determine the growth rate as follows;

[tex]W = P_{0}e^{rt}[/tex]

Growth rate, r = 1/(1 - 0)ln(1250/1306)

Growth rate, r = ln(1250/1306)

Growth rate, r = 0.0438

In the form [tex]W = a(b)^t[/tex], the required exponential function is given by;[tex]W = 1250(1.045)^t[/tex]

Years = 2020 -2010 = 10 years.

From the linear function, we have:

W = 56t + 1250

W = 56(10) + 1250

W = $1,810.

From the exponential function, we have:

[tex]W = 1250(1.045)^t\\\\W = 1250(1.045)^{10}[/tex]

W = $1,941.2

Difference = $1,941.2 - $1,810

Difference = $131.2.

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So according to the question Counseling and employment readiness programs are examples of rehabilitation.

Explain rehabilitation?

The English words "re," which means "once more," and "habitia," which denotes capacity, were combined to create the word rehabilitation. As a result, we can conclude that the lexical significance of the word "rehabilitation" is "recapturing the capacity."

The counseling and employment readiness program are example of rehabilitation only.

Hence, rehabilitation entails providing a sincere or simple-minded person with the necessary assistance in order to enable him to resume living a normal life. For instance, medical assistance, financial assistance, business assistance, etc.

As accidents continue to occur everywhere, rehabilitation has a huge range of applications. Accidents can occur anywhere and at any time, making it challenging to eliminate them.

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The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.

Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:

P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]

P(X>=10) = 0.719

Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.

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Answer:

(a) Pour montrer que la suite (Un) est géométrique, il suffit de vérifier que le quotient de deux termes consécutifs est constant. Soit n un entier naturel non nul. Alors :

Un+1 / Un = (Un-4) / (Un) = 1 - 5/Un

Donc, pour tout n E N*, on a :

Un+1 / Un = 1 - 5/Un = (Un / Un) - (5/Un) = (Un - 5) / Un

On a bien trouvé une raison q = -5/1, et un premier terme U1 = U1 - 5.

(b) La raison de la suite (Un) est q = -5/1. En utilisant la formule générale de la suite géométrique, on obtient :

Un = U1 * q^(n-1) = (U1 - 5) * (-5)^(n-1)

En particulier, on a :

U_n = U_1 * q^{n-1} = (U_1 - 5) * (-5)^{n-1} = U_12 = (U_1 - 5) * (-5)^{12-1}

(c) On n'a pas suffisamment d'informations pour déterminer la valeur de U1, donc on ne peut pas calculer directement la valeur de U12.

Therefore , the solution of the given problem of percentage comes out to be  earned 6.1% from the selling of the oranges.

In statistics, "a%" refers to a figure or a statistic that is expression as a percentage of 100. The letters "pct," "pct," and "pc" are also rare abbreviations. It is typically represented by the symbol "%," though. There are no indicators and a flat ratio to the overall amount. In reality, percentages are numbers because their sum almost always equals 100.

Here,

Let's suppose that the lady purchased x oranges.

She charged 60gp for each orange she sold, for a total of 60x gp.

She earned a profit of 3.05 GHC, making her overall profit

=> 3.05 GHC = 305p.

Her cost price (50gp) plus her profit (305p) would equal her total income (selling price), which would be 355gp.

=> 60x = 355

=> x = 355/60

=> x = 5.9167

She consequently purchased six bananas.

b) Since she paid 50gp for the container of oranges, their cost would be 50gp.

c) The total sale price of the oranges would be 360gp, or 60gp for each orange multiplied by 6.

d) She would have earned a profit of (profit/cost price) x 100%.

She made 305p, or 3.05 GHC, in earnings.

Her cost was 50gp, so

=> 6.1%  = (3.05/50) *  100%.

She thus earned 6.1% from the selling of the oranges.

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Lu Chao recited 67,890 digits of pi in 24 hours and 4 minutes using the memory palace technique

Lu Chao, a Chinese engineer, set a new world record by reciting 67,890 digits of pi in 24 hours and 4 minutes on November 20, 2005. This achievement required an incredible amount of focus, memory, and mental discipline. Chao utilized a technique called the "memory palace," in which he associated each digit with a specific image and placed those images in a familiar location in his mind.

This allowed him to recall the digits in order with remarkable accuracy. Chao's achievement demonstrates the incredible potential of the human mind and the power of memory techniques to accomplish seemingly impossible feats.

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Answer:

The length of BD in its simplest radical form is [tex]\sf \sqrt{429}[/tex].

Step-by-step explanation:

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the altitude to one segment is equal to the ratio of the other segment to the altitude.

[tex]\boxed{\sf \dfrac{altitude}{segment\:1}=\dfrac{segment\:2}{altitude}}[/tex]

Given values (see attached diagram):

To find the length of the altitude BD, substitute the values into the formula and solve for x:

[tex]\implies \sf \dfrac{BD}{AD}=\dfrac{DC}{BD}[/tex]

[tex]\implies \sf \dfrac{x}{33}=\dfrac{13}{x}[/tex]

[tex]\implies \sf x^2=429[/tex]

[tex]\implies \sf x=\sqrt{429}[/tex]

As the square root of 429 cannot be simplified any further, the length of BD in its simplest radical form is [tex]\sf \sqrt{429}[/tex].

Option C is a system of inequalities that best fits the figure.

To find a system of inequalities, find the inequality represented by each row.

First, let's determine the slope. You can use the gradient formula to do this.

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Taking (0, 1) and (1, 3) and plugging them into the gradient equation gives:

[tex]m=\frac{3-1}{1-0}[/tex]

[tex]m=\frac{2}{1} =2[/tex]

To write the equation for the red line, we can use the intercept form of the slope.

y=mx+b

The y-intercept of the red line is (0, 1). Therefore, it is already established that b = 1 and m = 2.

y=2x+1

Note that the shaded area is below the red line. Therefore y is less than the expression.

[tex]y\leq 2x+1[/tex]

let's find the slope again. Two points are available: (0, 2) and (2, 3). with this:

m=[tex]\frac{3-2}{2-0} =\frac{1}{2}[/tex]

So the slope is 1/2. Note that the y-intercept is (0, 2). So replace m with 1/2 and b with 2.

[tex]y=\frac{1}{2}x+2[/tex]

y is greater than the formula because the shaded area is above the blue line. The sign is above because it is shaded. So the formula is:

[tex]y\geq \frac{1}{2}x+2[/tex]

Hence the inequalities are:

[tex]y\leq 2x+1\\y\geq \frac{1}{2}x+2[/tex]

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Answer:

Step-by-step explanation:

Its answer A.

y < 2x + 1

y > 1/2 x + 2

we can download 2 songs for £2 if each song costs 90p. This calculation can be useful for budgeting and planning purchases, and it shows the importance of being mindful of the cost of individual items when making larger purchases.

To find out how many songs can be downloaded for £2, we need to divide £2 by the cost of each song.

We know that each song costs 90p, which is equivalent to £0.90. Therefore, we can set up the following equation:

£2 / £0.90 per song = x songs

To simplify the equation, we can first divide £2 by £0.90 to get the number of songs that can be downloaded:

£2 ÷ £0.90 = 2.22 (rounded to two decimal places)

So we can download 2.22 songs with £2. However, since we can't download a fraction of a song, we need to round down to the nearest whole number of songs.

Therefore, we can download 2 songs with £2 if each song costs 90p.

We can also verify this by multiplying the number of songs by the cost per song:

2 songs × 90p per song = £1.80

This means that we have spent £1.80 on two songs, leaving us with £0.20. We cannot afford another full song, so we cannot download a third song.

In conclusion, we can download 2 songs for £2 if each song costs 90p. This calculation can be useful for budgeting and planning purchases, and it shows the importance of being mindful of the cost of individual items when making larger purchases.

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Law of Cosines Of A Triangle -GIVEN: C (the degree) 20, 22,18 (the base). C is 26.5 degrees.

To solve for the angle C using the law of cosines, we use the formula:

[tex]c^2 = a^2 + b^2[/tex] - 2ab cos(C)

where c is the angle C's opposite side.

Substituting the given values, we get:

[tex]18^2 = 20^2 + 22^2[/tex] - 2(20)(22)cos(C)

324 = 1048 - 880cos(C)

880cos(C) = 724

cos(C) = 724/880

C = [tex]cos^{(-1)}[/tex](724/880)

C ≈ 26.5 degrees

Therefore, the measure of angle C is approximately 26.5 degrees.

To learn more about Law of Cosines, refer:-

https://brainly.com/question/17289163

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