A lorry travels 320km and uses 40 litres of petrol, work out the average rate of petrol usage. Amswer in km. Litre

Result obtained is $460

Answer:Let X denote the number of tests that need to be performed until a satisfactory result is obtained. Then X has a geometric distribution with p = 0.25. Therefore,X ~ Geo(0.25) E[X] = 1/p = 1/0.25 = 4 tests.For the first 5 tests, the cost is $100 each. So the cost of running the first 5 tests is 5 × $100 = $500. Thereafter, the cost of each test is $40. The expected cost of running the tests until a satisfactory result is obtained is given by:E(Cost) = $500 + E(X – 5) × $40Expected Cost = $500 + (E(X) – 5) × $40= $500 + (4 – 5) × $40= $460Therefore, the expected cost of running the tests until a satisfactory result is obtained is $460.

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b.  [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.

d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value(s) fοr the variable(s).

Given expression y√x

a. Is not equivalent as power is rational and exponent are non equal,

b. [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex]

=  [tex]\dfrac{\sqrt{x} }{\frac{1}{y}}[/tex]

= y√x

Thus, b.  [tex]\dfrac{x^\frac{1}{2} }{y^{-1}}[/tex] is an equivalent expression of y√x.

c. Is not a n equivalent expression at has a different variable.

d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex]

[tex]\rm\sqrt{ (xy^2)} }[/tex]

[tex]\rm y \sqrt{ (x)} }[/tex]

Thus,  d. [tex]\rm (xy^2)^{\tfrac{1}{2} }[/tex] is an equivalent expression of y√x.

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a) The system of inequalities that can be used to represent the situation is x + y ≤ 15 and 4x + 8y ≥ 80

b) One combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours is 10 hours babysitting and 5 hours as a library assistant.

To start, we know that Edith can work no more than 15 hours per week. Therefore, we can write the following inequality:

x + y ≤ 15

Next, we know that Edith earns $4 per hour babysitting and $8 per hour as a library assistant. We want her to earn at least $80 per week, so we can write the following inequality:

4x + 8y ≥ 80

This inequality states that the total amount Edith earns from both jobs (4x + 8y) must be greater than or equal to $80.

Now that we have two inequalities, we have a system of inequalities that can be used to represent the situation:

x + y ≤ 15

4x + 8y ≥ 80

To determine one combination of hours that will allow Edith to earn at least $80 per week while working no more than 15 hours, we can solve this system of inequalities.

Let's solve the first inequality for y:

y ≤ 15 - x

Now we can substitute this expression for y into the second inequality:

4x + 8(15 - x) ≥ 80

Simplifying and solving for x, we get:

-4x + 120 ≥ 80

-4x ≥ -40

x ≤ 10

To find the number of hours she should work as a library assistant, we can substitute x = 10 into our expression for y:

y ≤ 15 - x

y ≤ 15 - 10

y ≤ 5

So Edith should work no more than 5 hours as a library assistant per week.

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The number of balls, given the ratio of white balls to yellow balls that could not be in the bag is C. 42 balls.

The number of balls that could not be in the bag, given the ratio of white balls to yellow balls, is the number that would not give a whole number when multiplied by the ratio of white balls to yellow balls.

26 balls :

= 3 / ( 10 + 3 white balls ) x 26

= 3 / 13 x 26

= 6 balls

39 balls :

= 3 / 13 x 39

= 9 balls

42 balls :

= 3 / 13 x 42

= 9.69 balls

There therefore cannot be 42 balls.

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Options for this question include:

The value of q is 6

The constant is k

The first step the to calculate the value of the constant which is k

k= qr

Write out the parameters given in the question

The value of q is 2.8

The value of r is 11.25

k= 2.8 × 11.25

= 31.5

The value of q can be calculated by the value of k which is 31.5 and r which is 5.25

k= qr

31.5= q × 5.25

31.5= 5.25q

q= 31.5/5.25

q= 6

Hence the value q is 6

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As a result, when x = -5a /, the subject of the formula a/b = 2x/(x + 5) is x. (a - 2b).

For instance, C is the subject of the formula C = 2r, which calculates the circumference of a circle. To modify the subject of a formula is to rewrite it such that the quantities are still related in the right way. M/2 equals D if M = 2D.

In order to eliminate the fraction and make x the subject of the formula a/b = 2x/(x + 5), we can cross-multiply:

a(x + 5) = 2bx

Next, we can distribute the a:

ax + 5a = 2bx

We can now separate the x terms from the constant terms on each side:

ax - 2bx = -5a

x(a - 2b) = -5a

Finally, we can solve for x by dividing both sides by (a - 2b):

x = -5a / (a - 2b).

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Answer:

5/2

Step-by-step explanation:

substitute the values into the cosine rule:

(2[tex]\sqrt{7}[/tex])² = ((2x - 1)² + (2x + 1)²) - 2(2x - 1)(2x + 1)cos(60))

work out each part separately:

(2[tex]\sqrt{7}[/tex])² = 28

(2x - 1)² = 4x² - 4x + 1

(2x + 1)² = 4x² + 4x + 1

(2x - 1)² + (2x + 1)² = (4x² - 4x + 1) + (4x² + 4x + 1) = 8x² + 2

2((2x - 1)(2x + 1)cos(60)):

(2x - 1)(2x + 1) = 4x² - 1

cos(60) = √1/2 = 1/2

2(4x² - 1)(1/2) = 4x² - 1

substitute back in:

28 = (8x² + 2) - (4x² - 1)

28 = 4x² + 3

25 = 4x²

25/4 = x²

x = √(25/4)

x = 5/2

The inverse of the function is t = (r - 1.13) / 0.83.

What is function ?

In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output. A function can be thought of as a rule or a machine that takes an input value and produces a corresponding output value.

The given equation is: r = 0.83t + 1.13

To find the inverse of the function, we need to solve the equation for t.

r = 0.83t + 1.13

Subtract 1.13 from both sides:

r - 1.13 = 0.83t

Divide both sides by 0.83:

(r - 1.13)/0.83 = t

So the inverse function is:

t = (r - 1.13)/0.83

Or we can write it as:

[tex]f^{(-1)(r)} = (r - 1.13)/0.83[/tex], where [tex]f^{(-1)}[/tex]  represents the inverse function.

Therefore, the inverse of the function is t = (r - 1.13) / 0.83.

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lim_{x\to{\frac{\pi}{2}}^-} \tan x is 0.

The given function can be rewritten as;$$\frac{\sin x}{\cos x}$$Let us calculate the left hand limit$$\lim_{x\to{\frac{\pi}{2}}^-} \frac{\sin x}{\cos x}=\lim_{x\to{\frac{\pi}{2}}^-} \frac{1}{\cos x}= \frac{1}{\cos \frac{\pi}{2}}=0$$Thus, the evaluation of  $$\lim_{x\to{\frac{\pi}{2}}^-} \tan x$$ is 0.

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Answer:f(1) = f(3) = f(9) = f(27) = f(81).

Step-by-step explanation:To show that f(1) = f(3) = f(9) = f(27) = f(81), we can use the given equation and substitute x with different values.

Let x = 1:

f(3x) = f(3) + f(x)

f(3(1)) = f(3) + f(1)

f(3) = f(3) + f(1) (since f(3x) = f(3) + f(x) when x = 1)

f(1) = 0

Now, let x = 3:

f(3x) = f(3) + f(x)

f(3(3)) = f(3) + f(3)

f(9) = 2f(3)

Since we already know that f(3) = f(3) + f(1), we can substitute it into the equation above:

f(9) = 2f(3) = 2(f(3) + f(1)) = 2f(3) + 2f(1)

f(9) - 2f(3) = 2f(1)

Now let x = 9:

f(3x) = f(3) + f(x)

f(3(9)) = f(3) + f(9)

f(27) = f(3) + f(9)

We can substitute the expression for f(9) we just derived:

f(27) = f(3) + (f(9) - 2f(3))

f(27) = f(9) - f(3)

f(27) = 2f(3) - f(3)

f(27) = f(3)

Finally, let x = 27:

f(3x) = f(3) + f(x)

f(3(27)) = f(3) + f(27)

f(81) = f(3) + f(27)

We can substitute the expression for f(27) we just derived:

f(81) = f(3) + f(27)

f(81) = f(3) + f(3)

f(81) = 2f(3)

Since we know that f(27) = f(3), we can substitute it into the equation above:

f(81) = 2f(3) = 2(f(27)) = 2(f(9) - f(3)) = 2f(9) - 4f(3)

We also know that f(9) = 2f(3) + 2f(1) from our earlier work, so we can substitute it into the equation above:

f(81) = 2f(9) - 4f(3) = 2(2f(3) + 2f(1)) - 4f(3) = 4f(3) + 4f(1) - 4f(3) = 4f(1)

Therefore, we have shown that f(1) = f(3) = f(9) = f(27) = f(81).

Answer:

9) 15

10)22

11)25

Step-by-step explanation:

9)

[tex]area=\frac{bh}{2} \\30=\frac{(2x+1)4}{2} \\\\30=4x+2\\\\28=4x\\x=7\\[/tex]

substitute:

=2x+7

=2(7)+1

=15

10)

[tex]area=\frac{bh}{2} \\114=\frac{12(3x-2)}{2} \\114=18x-12\\126=18x\\7=x[/tex]

substitute:

=3x-2

=3(7)+1

=22

11)

[tex]area=h\frac{b1+b2}{2} \\\\69=\frac{4x-2}{2} \\\\69=\frac{24x-12}{2} \\\\69=12x-6\\75=12x\\x=6.25\\\\=4x\\=4(6.25)\\=25[/tex]

The container holds 99.223 grams of tablets.

One-sixteenth of a pound is represented by the weight measurement called an ounce (oz). A slice of bread and a pencil are two items that weigh about one ounce. One fluid ounce is the same as one-eighth of a cup in terms of volume. A medication cup has a volume of roughly one liquid ounce.

To convert ounces to grams, we can use the conversion factor 1 oz = 28.3495 g.

So, the container holds:

[tex]$3.5\ \text{oz} \times 28.3495\ \frac{\text{g}}{\text{oz}} = 99.223\ \text{g}$[/tex]

Therefore, the container holds 99.223 grams of tablets.

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The correlation coefficient for the SAT math score and the GPA of the students is given as follows:

r=0.94668.

A correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables. It is represented by the symbol "r" and ranges from -1 to 1.

The value of the correlation coefficient indicates the strength of the linear relationship between the variables. The closer the value of "r" is to -1 or +1, the stronger the linear relationship between the variables. A value of 0 indicates that there is no linear relationship between the variables.

The correlation coefficient is calculated inserting the points of the data-set into a correlation coefficient calculator.

The points from the graph are given as follows:

(595, 3.4), (520, 3.2), (715, 3.9), (405, 2.3), (680, 3.9), (490, 2.5), (565, 3.5).

Inserting these points into a calculator, the coefficient is given as follows:

r = 0.94668.

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The probability that the next patient arrives during the following 20 minutes is approximately 0.776.

(a) The probability that exactly 7 patients will arrive during a 90-minute period can be found by using the Poisson distribution formula.Poisson distribution formula:P(X = x) = (e-λ * λx) / x!Where: λ is the average number of events per unit of time or space, x is the number of occurrences, e is the exponential constant equal to 2.71828.x! means x factorial that is x(x − 1)(x − 2)⋯(2)(1).Here, λ = 9/60 = 0.15 (since there are 9 arrivals in one hour, there would be 9/60 arrivals in 1 minute)We are to find the probability of exactly 7 patients arriving in 90 minutes.The time period is 90/60 = 1.5 hours. Hence, λ = 0.15 × 1.5 = 0.225P(X = 7) = (e-λ * λ7) / 7! = (e-0.225 * 0.2257) / 7! = 0.085 ≈ 0.09Therefore, the probability that exactly 7 patients will arrive during a 90 minutes period is approximately 0.09(b) We can calculate the probability of at least 30 minutes passing until the next patient arrives by using the cumulative distribution function (CDF) of the exponential distribution.Exponential distribution formula:f(x) = λe-λxwhere λ is the rate parameter, x is the time period, and e is the exponential constant equal to 2.71828.The mean waiting time between two successive arrivals is 60/9 = 6.67 minutes.Hence, λ = 1/6.67 = 0.15The probability of at least 30 minutes passing until the next patient arrives can be calculated as follows:P(X > 0.5) = 1 - P(X ≤ 0.5) = 1 - (1 - e-λx) = e-λx = e-0.15×0.5 ≈ 0.776Therefore, the probability that at least 30 minutes will pass until the next patient arrives is approximately 0.776.(c) The probability that the next patient arrives during the following 20 minutes can be calculated as follows:P(X > 1) = 1 - P(X ≤ 1) = 1 - (1 - e-λx) = e-λx = e-0.15×1/3 ≈ 0.776Therefore, the probability that the next patient arrives during the following 20 minutes is approximately 0.776.

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Answer:

Let x be the price of one adult ticket, and y be the price of one student ticket.

From the information given in the problem, we can set up the following system of equations:

15x + 5y = 265 (equation 1)

15x + 16y = 419 (equation 2)

We can solve for x by subtracting equation 1 from equation 2:

15x + 16y - (15x + 5y) = 419 - 265

11y = 154

y = 14

Now we can substitute y = 14 into either equation 1 or equation 2 to solve for x. Let's use equation 1:

15x + 5(14) = 265

15x + 70 = 265

15x = 195

x = 13

Therefore, one adult ticket costs $13, and one student ticket costs $14.

For each of the following situations the critical value are:

a) H0: μ=115 vs. HA: μ ≠115 at α= 0.05; n= 41,  the critical values are ±1.96.
b) H0: p=0.14 vs. HA: p>0.14 at α= 0.10,  the critical value is 1.28.
c) H0: p= 0.6 vs. HA: p≠ at α=0.01 - z = 2.326, the critical values are ±2.58.
d) H0: p=0.8 vs. HA: p<0.8 at α=0.01; n=500, the critical value is -2.33.
e) H0​: p=0.9 vs. HA: p< at α=0.01, the critical value is -2.33.

a) Since n=41 is greater than 30, we can use a z-test. The test is two-tailed because the alternative hypothesis is μ≠115. Using a significance level of 0.05, the critical values are ±1.96. Therefore, the rejection region is z < -1.96 or z > 1.96.

b) Since we are testing a proportion, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p > 0.14. Using a significance level of 0.10, the critical value is 1.28. Therefore, the rejection region is z > 1.28.

c) Since we are testing a proportion, we can use a z-test for proportions. The test is two-tailed because the alternative hypothesis is p≠0.6. Using a significance level of 0.01, the critical values are ±2.58. Therefore, the rejection region is z < -2.58 or z > 2.58.

d) Since n=500 is greater than 30, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p < 0.8. Using a significance level of 0.01, the critical value is -2.33. Therefore, the rejection region is z < -2.33.

e) Since we are testing a proportion, we can use a z-test for proportions. The test is one-tailed because the alternative hypothesis is p < 0.9. Using a significance level of 0.01, the critical value is -2.33. Therefore, the rejection region is z < -2.33.

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Answer: 0.72 pts.

Step-by-step explanation:

so yeah the answers

Answer:

6*3

n=26

Given:-

To find:-

Solution:-

Here the sum of the two unknown angles will be 90° as they are the angles which make up 90° . So that;

[tex]\implies x^o + 42^o + 3x^o = 90^o \\[/tex]

[tex]\implies 4x^o = 90^o - 42^o \\[/tex]

[tex]\implies 4x^o = 48^o \\[/tex]

[tex]\implies x =\dfrac{48}{4} \\[/tex]

[tex]\implies \boxed{ x = 12} \\[/tex]

Hence the value of x is 12 .

and we are done!

Answer:

True

Step-by-step explanation:

A factorial means a number multiplied by all of the positive integers before it. That means both n+3! and n! have a common factor of n!. When you take out this factor of N, the fraction (n+3)!/n! ‘s denominator would be one, and the numerator would have all of the positive integers before n+3 and also being greater than n. Thus, (n+1)(n+2)(n+3)

Step-by-step explanation:

Your debt ratio is the ratio of the credit limit you have spent.

Your debt ratio is the amount you have spent on the credit card/ the limit

You have spent $9000- $3200 = $5800

Debt ratio = 5800/9000

=58/90 = 29/45

2. Acceptable ratio is less than 43%

Is 29 out of 45 less than 43%

Convert 29/45 to percentage

29/45 /100/1 = 64.44%

You have exceeded acceptable ratio at 64.4%

Answer:

Your debt ratio is the percentage of your credit limit that you have spent.

spent $9000- $3200 = $5800

Debt to income ratio = 5800/9000 = 58/90 = 29/45

2. A satisfactory ratio is less than 43%.

Is 29 percent of 45 less than 43%?

29/45 converted to a percentage 29/45 /100/1 = 64.44%

Step-by-step explanation:

Brainliest pls

From the right triangle figure the sides are solved to be

The side b and side d is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figure describes a right triangle, and side b is calculated using sin, SOH

Sin 45 = opposite / hypotenuse

Sin 45 = b / 8

b = 8 * sin 45

b = 4√2

Solving for side d

sin 60 = d / 7

d = 7 * sin 60

d = 7√3 / 2

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Answer:

x = 15

Step-by-step explanation:

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.

Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& Roots)

Multiplications

Divisions

Additions

Subtractions

~

First, add 10 to both sides of the equation:

[tex]4x - 10 = 50\\4x - 10 (+10) = 50 (+10)\\4x = 50 + 10\\4x = 60[/tex]

Next, divide 4 from both sides of the equation:

[tex]4x = 60\\\frac{4x}{4} = \frac{60}{4} \\x = \frac{60}{4} = 15\\x = 15[/tex]

~

x = 15 is your answer.

~

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Answer:

Step-by-step explanation:

[tex]\tt 4x -10 = 50[/tex]

Add 10 to both sides:-

Divide both sides by 4:-

___________________

Hope this helps!

If you are rolling two dice and one coin. the probability of rolling a three on the first dice, a four on the second dice, and flipping a heads on the coin is B. 1/72.

Probability of rolling a three on the first dice is 1/6, the probability of rolling a four on the second dice is 1/6, and the probability of flipping a heads on the coin is 1/2.

To find the probability of all three events happening together, we need to multiply the probabilities of each individual event:

(1/6) x (1/6) x (1/2) = 1/72

Therefore, the probability is B. 1/72.

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The exponential function between (-1, 2/5) and (3, 250) is as follows:

[tex]f(x) = 2 * 5^x[/tex]

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

[tex]f(x) = 2 * 5^x[/tex]

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

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

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * [tex]b^(-1)[/tex] = 2/5 (equation 1) 

a *[tex]b^3[/tex]= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *[tex]b^3[/tex] = 250

Simplifying, we get:

[tex]b^4 = 3125[/tex]

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

[tex]f(x) = 2 * 5^x[/tex]

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The value of the calculated perimeter, in inches, of the floor in the scale drawing is 50 inches

The dimensions of the rectangular floor is calculated as

Dimension = 28 feet in length and 22 feet in width

The length of the scale is given as

Scale length = 14 inches

When the above is compared, we can see that

The length is divided by 2 to get the scale length

So, we have

Scale width = 22 inches/2

Evaluate

Scale width = 11 inches

The perimeter is then calculated as

Perimeter = 2 * (Length + width)

So, we have

Perimeter = 2 * (14 + 11)

Evaluate

Perimeter = 50 inches

Hence, the perimeter is 50 inches

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The area of the sector is ≈134 sq units and the length of the arc is ≈16.75

The sector of a circle produced by a portion of the circumference (arc) and the circle's radii at both ends of the arc. A sector of a circle can be compared to a piece of pizza or a pie in shape.

The length of an arc is the distance between two point in the section of a curve.

According to the given information:

Given that radius= 16 in, ∅ = 60°

The formula for finding the area of sector= (∅/360°)[tex]\pi r^{2}[/tex]

Substituting values in the formula we get

= (60°/360°)*3.14*[tex]16^{2}[/tex]

=133.9733

≈134 sq units.

The formula for Finding Arc Length =  (∅/360°)[tex]2\pi r[/tex]

On substituting the values

= (60°/360°)*2*3.14*16

=16.74666

≈16.75 in

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Answer:I could possibly be wrong but I say no. From what I remember, with these things you can put the points wherever as long as it follows the rules you were given for each triangle.

Step-by-step explanation:

I actually drew it out, and to me it appears as it’s not, yet I could be wrong and I’m sorry if I am! Angles aren’t my best, but I’m really good at math! If you have other problems I can go over them

Answer:

dghcŕhĝt5dfg9yd6grdy6cjbjbknygug4ximpohyvug5h7h6g6