Which expression is equivalent to the expression quantity negative 6 over 5 times t plus 3 over 16 end quantity minus expression quantity negative 7 over 10 times t plus 9 over 8 end quantity

The area of the smaller triangle is 12 square units

If the scale factor between two similar triangles is 2/3

It means that every length of the smaller triangle is 2/3 the length of the corresponding side of the larger triangle.

So, the ratio of their areas is the square of the scale factor

This is represented as

(area of smaller triangle) / (area of larger triangle) = (2/3)^2 = 4/9

We are given that the area of the larger triangle is 27

So, we have

Area of smaller triangle/27 = 4/9

Multiplying both sides by 27, we get:

Area of smaller triangle = (4/9) * 27

Evaluate

Area of smaller triangle = 12

Hence, the area of the smaller triangle is 12.

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Answer:

Graph A

Step-by-step explanation:

As can be seen, the trend in graph A is increasing with each month but not seemingly by as much as graph B;

This is because the scale of the y-axis in graph B has smaller increments;

This creates the impression of a slow increase in sales even though the data in both graphs is actually the same.

Answer: graph A.

appear to increase less.

Step-by-step explanation:

The values of x and y such that the table represents a function are given as follows:

x = 8, y = 7.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

The input-output pairs for the function in this problem are given as follows:

Hence the x-value can only by 8 or 12, and we choose y = 8, while the y-value is free, hence we choose y = 7.

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Answer:

61,770

Step-by-step explanation:

6.177 x [tex]10^{4}[/tex]

[tex]10^{4}[/tex] = 10,000

6.177 x 10,000 = 61,770

So, the answer is 61,770

The answer is (B) 1.5 percent.

You can find the growth accounting equation by using:

Growth rate of output equals Technology growth rate plus a* Capital growth rate plus (1-a*Labor growth rate)

Inputting the values provided yields:

5% equals 3% plus (0.8 * Capital Growth Rate) plus (0.2 * 4%).

When we simplify the equation, we obtain:

Capital growth rate equals (5% - 3% - 0.2%) / 0.8, or 1.5%

As a result, the capital growth rate is predicted to be 1.5%.

(B) 1.5 percent is the right answer.

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Answer:

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

Step-by-step explanation:

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity. As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits. As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)

x→∞ x→∞

= 4√(lim(x-6))

x→∞

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞

x→∞

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.

Answer:

Step-by-step explanation:

The end behavior of the given radical function f(x) = 4√(x-6) as x approaches positive infinity is option A: As x approaches positive infinity, f(x) approaches positive infinity.

This is because as x approaches positive infinity, the value inside the square root (x-6) also approaches positive infinity.
As the square root of a positive number is also positive, f(x) approaches positive infinity.

We can also see this by using the concept of limits.
As x approaches positive infinity, the limit of f(x) can be evaluated as:

lim f(x) = lim 4√(x-6)x→∞ x→∞= 4√(lim(x-6))x→∞.

Since the limit of (x-6) as x approaches positive infinity is positive infinity, we have:

lim f(x) = 4√(∞) = ∞x→∞.

Therefore, as x approaches positive infinity, f(x) approaches positive infinity.

The interquartile range for the amounts of money spent by some male students on their holidays is £ 160.

To find the interquartile range (IQR) on a box plot, the IQR is the difference between the upper and lower quartiles. The upper quartile (Q3) is the median of the upper half of the data, and the lower quartile (Q1) is the median of the lower half of the data.

The interquartile range for the amount spent by male students on their holidays is :

= Q3 - Q 1

= 800 - 640

= £ 160

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Therefore , the solution of the given problem of data plot comes out to be value (r) is roughly 0.975.

The most typical way to display data in a graph is to demonstrate how two additional factors relate to one another. Digital and hand-drawn sketches are both acceptable. From the beginning position, move two or more pieces to the correct and three pieces up. The reference system must display the numerals for positions 2, 3, and 4. In your points, be very clear. The pinkish haze with the letter P stands in for the number 2.3.

Here,

We must compute several numbers in order to determine the Pearson correlation coefficient r for the information provided in the table.

Before anything else, we figure out the average and standard deviation of the amount of TV airings (x) and car sales (y):

mean(x) = (40 + 30 + 20 + 50 + 10) / 5 = 30

mean(y) = (30 + 20 + 10 + 40 + 20) / 5 = 24

These mean numbers allow us to determine the standard deviation:

=> SX = √ (( (40-30)² + (30-30)² + (20-30)² + (50-30)² + (10-30)²) / 4)

≈> 15.81

=> SY = √(( (30-24)²+ (20-24)² + (10-24)² + (40-24)² + (20-24)²) / 4)

≈> 8.16

Next, we determine x and y's covariance:

=> cov(x,y) =

=> [(40-30)(30-24) + (30-30)(20-24) + (20-30)(10-24) + (50-30)(40-24) + (10-30)(20-24)] / 4

≈>  125

Last but not least, we can figure out the Pearson association coefficient:

0.975 r = cov(x,y) / (s x * s y)

As a result, the table's data's Pearson correlation value (r) is roughly 0.975. This shows a significant positive correlation between the volume of car purchases and the frequency of the TV ad.

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We can cοnclude that the expοnential functiοn represented by the given table is [tex]y = 3(0.5)^x[/tex]

An expοnential functiοn is a mathematical functiοn οf the fοrm [tex]f(x) = ab^x[/tex], where a and b are cοnstants and b is greater than 0 and nοt equal tο 1. It is a type οf mathematical mοdel that describes a prοcess where a quantity grοws οr decays at a rate prοpοrtiοnal tο its current value οver time οr space.

An expοnential functiοn has the fοrm:

[tex]\mathrm y = ab^x[/tex]

where "a" is the initial value οf the functiοn, and "b" is the grοwth factοr οr base οf the functiοn.

Tο find the equatiοn οf the expοnential functiοn represented by the given table, we can use the first twο data pοints tο determine the values οf "a" and "b", and then check if the remaining data pοints fit the functiοn.

Using the first data pοint (0, 3), we get:

[tex]3 = ab^0[/tex]

3 = a

Using the secοnd data pοint (1, 1.5), we get:

[tex]1.5 = ab^1[/tex]

1.5 = 3b

b = 0.5

Therefοre, the equatiοn οf the expοnential functiοn represented by the given table is:

[tex]y = 3(0.5)^x[/tex]

We can check the remaining data pοints tο see if they fit the functiοn:

Fοr [tex]x = 2, y = 3(0.5)^2 = 0.75[/tex]

Fοr[tex]x = 3, y = 3(0.5)^3 = 0.375[/tex]

Since all the data pοints fit the equatiοn, we can cοnclude that the expοnential functiοn represented by the given table is:

[tex]y = 3(0.5)^x[/tex]

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Si 25 dólares representan el 15% de una cuenta, podemos usar una regla de tres simple para determinar cuánto hay en total en la cuenta:

15% -----> $25

100% ----> ($25 x 100)/15

100% ----> $166.67

Por lo tanto, hay $166.67 en total en la cuenta.

After making the minimum payment of $125, the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

If the minimum monthly payment of $125 is made, we can calculate the new balance, unpaid balance, and interest charge as follows:

The interest rate per month is (18% per year) / 12 = 1.5% per month.

First, we calculate the interest charge for the month on the unpaid balance:

Interest charge = (1.5% per month) x ($5000 unpaid balance)

Interest charge = $75

Next, we subtract the minimum payment from the unpaid balance to get the new unpaid balance:

Unpaid balance = $5000 - $125

Unpaid balance= $4875

Then, we add the interest charge to the new unpaid balance to get the new balance:

New balance = $4875 + $75

New balance = $4950

Finally, we can calculate the purchasing power as the credit limit minus the new balance:

Purchasing power = $5000 - $4950

Purchasing power = $50

Therefore the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.

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Using Pythagoras theorem, we can find the length of the missing side to be 10 units.

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, also referred to as the Pythagorean theorem.

The Pythagorean Theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of its other two sides.

In the given triangle, the base is given as:

b = 6 units.

height, h = 8 units.

Let the missing side be = x.

Now as per the Pythagoras theorem,

x² = 8² + 6²

⇒ x² = 64 + 36

⇒ x² = 100

⇒ x = 10.

Therefore, the length of the missing side of the triangle here is 10 units.

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Answer:

4Step-by-step explanation:

The price οf the jacket was $115.

Let's start by defining sοme variables tο represent the unknοwn quantities:

Let x be the price οf the shirt

Let y be the price οf the jacket

Frοm the prοblem statement, we knοw that:

y = 2x + 17 (the cοst οf the jacket was $17 mοre than twice the price οf the shirt)

x + y = 164 (the tοtal cοst οf the shirt and jacket was $164)

We can use these twο equatiοns tο sοlve fοr the values οf x and y. One way tο dο this is tο substitute the expressiοn fοr y frοm the first equatiοn intο the secοnd equatiοn, and then sοlve fοr x:

x + (2x + 17) = 164

3x + 17 = 164

3x = 147

x = 49

Nοw that we knοw the price οf the shirt is $49, we can use the first equatiοn tο sοlve fοr the price οf the jacket:

y = 2x + 17

y = 2(49) + 17

y = 115

Therefοre, the price οf the jacket was $115.

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Answer:

the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).

Step-by-step explanation:

We can use the standard normal distribution to solve this problem. We first need to standardize the height requirements using the population mean and standard deviation.

a) To find the probability that a child can go on all rides, we need to find the probability of getting a height of at least 54 inches.

z-score = (54 - 53) / 4 = 0.25

Using a standard normal table or calculator, we find that the probability of getting a z-score of 0.25 or greater is 0.4013.

Therefore, the probability that a child can go on all rides is 0.4013 (rounded to three decimal places).

b) To find the probability that a child can participate in only mild and moderate rides, we need to find the probability of getting a height between 42 inches and 48 inches.

First, we find the z-scores for each height requirement:

z-score for 42 inches = (42 - 53) / 4 = -2.75

z-score for 48 inches = (48 - 53) / 4 = -1.25

Using a standard normal table or calculator, we find that the probability of getting a z-score between -2.75 and -1.25 is 0.2375.

Therefore, the probability that a child can participate in only mild and moderate rides is 0.2375 (rounded to three decimal places).

c) To find the probability that a child can only go on mild rides, we need to find the probability of getting a height of less than 42 inches.

z-score = (42 - 53) / 4 = -2.75

Using a standard normal table or calculator, we find that the probability of getting a z-score of -2.75 or less is 0.0030.

Therefore, the probability that a child can only go on mild rides is 0.0030 (rounded to three decimal places).

d) To find the probability that a child is excluded from all rides, we need to find the probability of getting a height less than 42 inches or greater than 54 inches.

First, we find the z-scores for each height requirement:

z-score for 42 inches = (42 - 53) / 4 = -2.75

z-score for 54 inches = (54 - 53) / 4 = 0.25

Using a standard normal table or calculator, we find that the probability of getting a z-score of less than -2.75 or greater than 0.25 is 0.0987 + 0.4013 = 0.5000.

Therefore, the probability that a child is excluded from all rides is 0.5000 (rounded to three decimal places).

Answer:

8

Step-by-step explanation:

line WL is a straight line intersecting line GZ at J so angles LJW is 180o

therefore

LJG + GJH + HJW = 180

9x + 90 + 18 = 180

9x = 180 - 90 - 18

9x = 72

x = 72/9 = 8

The probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu is: 0.087.

This is a binomial distribution problem, where n = 55 and the probability of success (i.e. a person subscribing to Hulu) is p = 0.41.

The probability mass function of a binomial distribution is:

P(X = x) = (nCx) * p^x * (1-p)^(n-x)

where nCx is the binomial coefficient (i.e. the number of ways to choose x items from n items).

So, in this case, we want to find P(X = 20):

P(X = 20) = (55C20) * 0.41^20 * (1-0.41)^(55-20)

P(X = 20) ≈ 0.087

Therefore, the probability that in a random sample of 55 18 to 29-year-olds, 20 will say they currently have a subscription to Hulu is approximately 0.087or 8.7%.

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To calculate the standard error σM for a sample, we can use the formula [tex]σM = s / \sqrt{n}[/tex], where s: sample standard deviation and n: sample size.

The formula for calculating the standard error, M, which indicates the standard deviation of the sampling distribution of the mean, is as follows:

[tex]σM = σ / \sqrt{n}[/tex]

where σ: population standard deviation and n: sample size.

If we don't know the population standard deviation, we estimate it using the sample standard deviation s. We use formula:

[tex]σM = s / \sqrt{n}[/tex]

We can apply the method above with the sample size n and the sample standard deviation s if we are given a sample and asked to determine the standard error M for this sample.

By adding up each value in the sample and dividing by the sample size, we can determine the sample mean x, from which we may compute the sample standard deviation. The sample variance is then determined by adding up the squared deviations between each value and the sample mean, then dividing the result by the sample size less one. Lastly, we calculate the sample standard deviation by taking the square root of the sample variance.

Once we have calculated the sample standard deviation s and the sample size n, we can plug these values into the formula for σM:

[tex]σM = s / \sqrt{n}[/tex]

and calculate standard error.

In conclusion, the formula M = s / [tex]\sqrt{n}[/tex]n, where s: sample standard deviation and n: sample size, can be used to compute the standard error M for a sample.

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m = (-12 - 5) / (3 - (-5))

m = (-17) / (3 + 5)

m = (-17) / 8

Therefore, the slope between the points (-5, 5) and (3, -12) is -17/8.

Please mark this answer as brainliest if possible.

Answer:

82.28

this was really easy,

Answer:

Step-by-step explanation:

a. 25% of 5000 tickets = 0.25 x 5000 = 1250 tickets

Total sales of $45 tickets = 1250 x $45 = $56,250

b. 15% of 5000 tickets = 0.15 x 5000 = 750 tickets

Total sales of $35 tickets = 750 x $35 = $26,250

c. General admission tickets = Total tickets - Reserved tickets

= 5000 - 1250 - 750

= 3000 tickets

d. Total sales for general admission tickets = Number of general admission tickets x Price per ticket

= 3000 x $20

= $60,000

e. Total sales = Sales of $45 tickets + Sales of $35 tickets + Sales of general admission tickets

= $56,250 + $26,250 + $60,000

= $142,500

Answer:

3

Step-by-step explanation:

Amount used:

8 - 7.25 = 0.75

He used 0.75 cup

Each day he had 0.25 cup.

0.75/0.25 = 3

Answer: 3

Therefore , the solution of the given problem of equation comes out to be spot A's coordinates are (80,-20).

In mathematical formulas, it is common to use the same variable term to guarantee agreement between two claims. Mathematical assertions, also known as equations expression, are employed to convey the equality of numerous academic figures. In this case, the normalise method adds b + 6 using the data of y + 6 rather than splitting 12 into two parts.

Here,

Let (a,b) represent the location of point A. Consequently, the inclination of the line through (0,0) and (a,b) is

=> m = (b - 0) / (a - 0) Equals b / a

This line being parallel to the initial road gives us:

=>  m = -1/4

Therefore:

=>  b / a = -1/4

=>  b = -a/4

=>  √[(a - 0)² + (-a/4 - 0)²] = √(17a²/16)

From (a,-a/4) to (85,0), the distance is:

=>  √[(85 - a)² + (0 - (-a/4))²] = √[(85 - a)² + (a/4)²]

These two separations are equal, so we can put them at the same value and find a:

=>  √[(85 - a)² + (a/4)²] = √(17a²/16)

When we square both edges, we obtain:

=>  (85 - a)² + (a/4)² = 17a²/16

=>  16(85 - a)² + a² = 17a²

=>  16(7225 - 170a + a²) + a² = 17a²

=>  115600 - 2720a + 17a² + a² = 17a²

=>  18a² - 2720a + 115600 = 0

=> 9a² - 1360a + 57800 = 0

=>  a = (1360 ± √(1360² - 4957800)) / (2*9)

=>  a = (1360 ± √(307600)) / 18

=>  a = (1360 ± 560) / 18

=>  a = 80 or a = 40/9

Point A's y-coordinate is:

=> b = -a/4 = -80/4 = -20

Consequently, spot A's coordinates are (80,-20).

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On solving the provided question, we can say that Given that you have already waited for 10 minutes, the inequality that you will have to wait another six minutes or longer is around 0.0183.

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.  

Applying the exponential distribution's memoryless characteristic, we have:

P(Y ≥ 6 | Y > 10) = P(Y ≥ 16)

= 1 - P(Y < 16)

= 1 - F(16) (16)

where F(t) is the exponential distribution's cumulative distribution function (CDF) with a mean of 4 minutes.

F(t) = 1 - e(-t/) yields the CDF of an exponential distribution with mean, where t 0. As a result, we have:

[tex]P(Y \geq 6 | Y > 10) = 1 - F(16) (16)\\= 1 - (1 - e^(-16/4))\\= e^(-4) (-4)\\≈ 0.0183[/tex]

Given that you have already waited for 10 minutes, the likelihood that you will have to wait another six minutes or longer is around 0.0183.

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The volume and sum of the composite shape is 13L² and 13V³ respectively

A square is a closed two-dimensional shape (2D shape) with four sides that are equal and parallel to each other. Also, In Euclidean Euclidean geometry, a square is a regular quadrilateral which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles

The composite is made up of 13 squares in total

The area of 1 square is given as A = S²

The volume of the composite is 13L³ units

Hence there are 13 squares. the sum of the areas and volume of the square is 13 S²

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Answer:

[tex]A=\frac{4}{6} *600 = 400\\B=\frac{2}{6} *600 = 200[/tex]

Answer:

the scale factor = 3

Step-by-step explanation:

the question is basically saying: how did (12,-4) jump to (36,-12)

we can make d represent the scale factor used to get (12,-4) to (36,-12)

so,

12d = 36

-4d = -12

all there's left to do is to simply solve for d, which is 3

The mistake that Rafael made is interchanging the y-values with the x-values.

The real slope of the line is 25.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (100 - 50)/(4 - 2)

Slope, m = 50/2

Slope, m = 25.

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