A taxi driver uses this formula to work out fares, Fare = £2. 50 + £0. 90 x miles


Use the formula to work out:

a. The fare for a 9-mile journey.


give your answer in pounds

ASAP PLEASE

Team B will need to sell at least 192 candies to avoid losing money.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given total amount to be raised by each team is $100,

Team B wants to sell cotton candy,

rent of candy machine = $25

total cost to be earned for team B = $100 + $25 = $125

let the number of candies sold be x

cost used in candy sticks = $0.10 per stick

cost used in x candy sticks = $0.10x

the selling price of each candy = $0.75

the selling price of x  each candy  = $0.75x

total gain = $0.75x - $0.10x

total gain = $0.65x

minimum candies to be sold for no loss

$0.65x = $125

x = 125/0.65

x = 192.30

x = 192

Hence for no loss, at least 192 candies are to be sold.

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If a rigid motion of the plane—that is, a combination of rotations, translations, and reflections—can turn one tile into the other while without stretching or contracting, then two tiles are said to be congruent.

What is congruent ?

Congruent refers to having a precise match in size and shape. Even after the forms have been flipped, turned, or rotated, the shape and size ought to remain constant.

We are surrounded by tiling. Human nature makes us curious about how various small bits fit together when presented.

In the broadest sense, tiling simply refers to the process of breaking up a large area into several little parts (tiles) that seamlessly interlock one another.

Even human bodies, for instance, can be thought of as tilings with cells serving as the "tiles." The earth's surface is tiled by land ownership! There are tiles almost everywhere.

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Answer:

Approximately 6.78

Step-by-step explanation:

–3x + 10y = –7 - - - - - - > (1)

–3x + 4y = –19 - - - - - - > (2)

(1) - (2) Because if same sign then you have subtract to cancel out the equal numbers therefore - 3x and - 3x is cancelled out

6y = +2

y = 2 ÷ 6

y = 1/3

Then to find the value of x substitute value of y

-3x + (4 × 1/3) = - 19

-3x + 4/3 = - 19

- 3x = - 19 - 4/3

- 3x = - 61/3

x = ( - 61/3 ÷ -3)

x = 6.78

The marginal benefit is the additional number of benefit associated with an increase in the activity.

The marginal benefit is the amount of benefit that is gained from a one-unit increase in the activity, and is measured by the additional satisfaction or utility that the individual or organization receives from the increase in the activity.

The marginal benefit is the additional number of benefit associated with an increase in the activity.

The marginal benefit is the additional benefit or satisfaction that is derived from an increase in the activity or product. It is the amount of pleasure or utility that a person or organization receives from the marginal increase in the activity or product. This is measured by the additional revenue, utility, or satisfaction that is experienced from the increase in activity. Marginal benefit can also refer to the additional money, time, or other resources that are invested in an activity or product, as well as the amount of value that is gained from the increase in the activity or product.

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Answer:

Step-by-step explanation:

4x+5y=15

-4x. -4x

5y=-4x+15

divide by 5 on both sides

y = 4/5x+3

Two points would be : (0,3) & (7,5)

extra : 4/5 means on the graph you go up 4 spaces, and to the right 5 spaces, in reverse you would go down 4 spaces and 5 spaces to the left

hope this helped =)

-YinAhara

The test statistic be Pearson's correlation test.

What is Null hypothesis ?

The null hypothesis assumes that any difference between the selected attributes in a set of data is attributable to chance.

The test statistic could be Pearson's correlation coefficient, which measures the linear association between two continuous variables (here, amygdala activity and memory score).

The null hypothesis would be that there is no association between amygdala activity and memory score, which can be represented as:

H0: r = 0

The type of test would be a Pearson's correlation test, which is a parametric test that assesses the strength and direction of the linear relationship between two continuous variables.

Hence, The test statistic be Pearson's correlation test.

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The required six algebraic equations to relate the given different pairs of angles are in the solution part.

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

Given: AD, BE and FC intersect at point P.

AD⊥FC.

According to the given figure, the required equations would be as:

m∠APB = m∠EPD  (vertical angles)

m∠FPD = m∠APC  (right angles are congruent)

m∠EPC + m∠EPF = 180 degrees (linear pair)

m∠BPC = m∠EPD (vertical angles)

m∠APB + m∠BPC = 90 degrees (complementary angles)

m∠FPB + m∠BPC = 180 degrees (linear pair)

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About 68% of the data in a typical normal curve is within one of the mean's standard deviation. Accordingly, 68% of the data should fall between -1 and 1 if the data's mean was 0 and its standard deviation was 1.

A theoretical continous probability distribution known as the "standard normal curve" depicts a bell-shaped, symmetrical curve. The normal distribution or the Gaussian distribution are other names for it. The standard normal curve, which serves as a benchmark for other normal distributions, has a means of 0 and a variance of 1. For simpler analysis and comparison, data sets can frequently be translated into the normal form standards. The distributions of many real-world events, including IQ scores, length, weight, and heart rate, to mention a few, is described by the curve, which is significant in statistics. Among other uses, the normalised curve is employed in statistical inference, quality control, and hypothesis testing.

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Fraction amount left 21/50

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The limit of 1/2x + 2 as x approaches 2 is equal to 3.

The definition of a limit states that as the x-value approaches a specific number, in this case 2, the y-value of the expression 1/2x + 2 approaches 3. The definition states that for any ε > 0, there exists a δ > 0, such that for all 0 < |x - 2| < δ, we have |1/2x + 2 - 3| < ε. We can rearrange this to find that for all 0 < |x - a| < δ, we have |f(x) - L| < ε. This means that when x is close to 2, the difference between 1/2x + 2 and 3 is less than ε. Therefore, if we take ε to be very small, we see that 1/2x + 2 gets very close to 3, so the limit is 3. To prove this statement, we can calculate the y-value of the expression when x is equal to 1.5, 1.99, and 1.999. As we can see, the y-values get closer and closer to 3 as the x-values get closer and closer to 2. As x gets closer and closer to 2, the y-values of 1/2x + 2 get closer and closer to 3, so the limit of 1/2x + 2 as x approaches 2 is equal to 3.

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Answer:

15 CDs

Step-by-step explanation:

The total percentage of the CDs is 100% because it basically means all the CDs. Therefore, the percentages of types need to add up to 100%. If 30% are country and 40% are pop, 100 - 30 - 40 = 30% are other.

30% is equivalent to 30/100 or 0.3 when written as a decimal. You would then multiply this by the number of CDs to get the number of other CDs:

[tex]50 * 0.3 = 15[/tex]

Therefore, 15 CDs are other types of music

Answer: Apples: $2      Mangos: $1.50

Step-by-step explanation:

8m+3a = 183m+5a=14.5

Multiply the first equation by 5 and multiply the second equation by 340m+15a=909m+15a=43.5

Subtract the equations

31m=46.5m=46.5/31m=1.5

Substitute to find the price of apples

8(1.5)+3a=1812+3a=183a=18-123a=6a=2

Apples cost $2.00 each mangoes cost $1.50 each

A. KP = ST is given

B. Given as PR = TV is known

C. KP + PR = ST + TV using the addition property.

D. Segment addition in KP + PR = KR

E. ST + TV = SV

F. Segment addition has obtained this answer

G. KR = SV by substitution property

The solution has been obtained by using the concept of mathematical reasoning.

What is mathematical reasoning?

In mathematics, reasoning entails making logical deductions from data or presumptions.

A. For this, we are stated a reason that it is given.

So, the statement is KP = ST.

B. We are given the statement as PR = TV

The reason is that it is given.

C. For this, we are stated a reason that it is obtained by addition property.

So, the statement is KP + PR = ST + TV.

D. We are given the statement as KP + PR = KR

The reason is that it is obtained by segment addition.

E. ST + TV = SV is the statement

F. The reason for the statement is that it is obtained by segment addition.

G. For this, we are stated a reason that it is obtained by substitution property.

So, the statement is KR = SV.

Hence, the statements and their respective reasons have been arranged.

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The length of side DB can be expressed as [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]

To solve this, we can use the Pythagorean theorem:

[tex]DB^2 = AE^2 + EC^2[/tex]

Substituting the values of AE and EC:

[tex]DB^2 = (6x - 55)^2 + (3x - 16)^2[/tex]

[tex]DB^2 = 36x^2 - 720x + 3025 + 9x^2 - 96x + 256[/tex]

[tex]DB^2 = 45x^2 - 816x + 3281[/tex]

[tex]DB =[/tex] [tex]\sqrt{ (15x - 55)(3x - 28).}[/tex]

Key points:

The Pythagorean theorem states:

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The complete question is:

In a quadrilateral ABCD, the length of sides AB and CD are equal and measure x units. If AE = 6x - 55 and EC = 3x - 16, find the length of side DB.

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If he p-value is used for hypothesis testing , then the Null Hypothesis is rejected if (a) p-value ≤ α .

In a hypothesis testing, the p-value represents the probability of observing a test statistic as extreme or more extreme than the one observed, provided that the null hypothesis is True.

The significance level, represented by "α" , is a pre-determined threshold which determines the level of evidence required to reject the null hypothesis.

If the p-value is less than or equal to α, this indicates that the observed test statistic is sufficiently unlikely to occur under the null hypothesis, and therefore the null hypothesis is rejected.

Therefore , the Null hypothesis is rejected if (a) p-value ≤ α .

The given question is incomplete , the complete question is

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

(a) p-value ≤ α

(b) α < p-value

(c) p-value ≥ α

(d) p-value = 1 - α

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The correct answer is a) p-value ≤ α. In hypothesis testing, the null hypothesis is typically assumed to be true initially. The p-value is used to determine the probability of observing a test statistic as extreme or more extreme than the one obtained from the data, assuming that the null hypothesis is true.

The significance level (α) is chosen beforehand and represents the maximum acceptable probability of rejecting the null hypothesis when it is actually true.

If the p-value is less than or equal to the significance level (p-value ≤ α), then the result is considered statistically significant and the null hypothesis is rejected. This implies that the observed effect is unlikely to have occurred by chance alone and that the alternative hypothesis is more likely to be true.

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The area of △ABC is equal to 6√6 / 2.

What is the area of triangle 3-dimensional space?

The area of a triangle in 3-dimensional space can be found using the cross product of two vectors formed by the three vertices of the triangle.

The formula for the area of a triangle with sides u and v is given by:

Area = |u × v| / 2

Where × represents the cross product of the two vectors u and v, and |•| represents the magnitude of the resulting vector.

To find the area of △ABC, we can form the vectors AB and AC and find their cross-product:

AB = B - A = (1 - 2, -3 - (-1), 2 - (-1)) = (-1, -2, 3)

AC = C - A = (2 - 2, -3 - (-1), 0 - (-1)) = (0, -2, 1)

Cross product of AB and AC: AB × AC =

| i j k |

|-1 -2 3 |

| 0 -2 1 |

= (6, 6, -6)

Area of △ABC = |AB × AC| / 2 = |(6, 6, -6)| / 2 = √(6^2 + 6^2 + (-6)^2) / 2 = 6√6 / 2

Hence, the area of △ABC is equal to 6√6 / 2.

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The probability of Hans winning the competition and taking no more than three shots is 0.784.

To calculate the probability that Hans wins after taking no more than 3 shots, we can use the cumulative distribution function (CDF) of the binomial distribution.

The CDF gives the probability of getting k or fewer successful shots in n trials, with a success probability of p.

In this case, n = 3, p = 0.4, and k = 2 (since Hans wins if he hits the bull's-eye with 2 shots or fewer).

Using the cumulative binomial distribution formula, the probability of Hans winning the competition and taking no more than three shots is 0.784.

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It suggests that the communities are unsaturated and that the size of the regional pool determines local species richness.

The correct option is (A)

Now, According to the question:

This suggests that the processes structuring the butterfly community are likely related to the presence and abundance of resources such as food plants and suitable habitat for the butterflies. As the number of individuals in the community increases, the number of different species that can be supported also increases, resulting in a linear relationship between the two. Additionally, this indicates that the butterfly community is likely experiencing a relatively stable and predictable environment, where resources are available to support a diverse population of butterflies.

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The complete question in the form is:

Now examine the lower panel (butterflies), where the curve continues to rise linearly. What does this indicate about the processes structuring the butterfly community?

(A) It suggests that the communities are unsaturated and that the size of the regional pool determines local species richness.

(B) It suggests that the communities are becoming saturated and that local processes are likely becoming increasingly important.

(C) It does not tell us anything about the relative importance of the regional species pool and local interactions.

The celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).

The right ascension and declination of a particular point in the sky can be used to calculate its corresponding celestial coordinates. Right ascension (RA) is measured in hours, minutes and seconds, while declination (Dec) is measured in degrees, minutes and seconds.

The RA of the given point is 15 h 06 m 53.62 s. This can be converted to degrees by multiplying by 15. The result is 225.1045 degrees. The Dec of the given point is 62° 20' 10.0" which can be converted to radians by multiplying by pi/180. The result is 1.08269 radians.

The celestial coordinates can then be calculated using the formula:

sin(RA)cos(Dec) = sin(225.1045)*cos(1.08269) = 0.92868

cos(RA)cos(Dec) = cos(225.1045)*cos(1.08269) = 0.36983

sin(Dec) = sin(1.08269) = 0.04921

Therefore the celestial coordinates of the given point are (0.92868, 0.36983, 0.04921).

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Consider the initial value problem y' = 3y^2, at the value of y(0) = 1/6 will the solution have a vertical asymptote at t = 2.

The differential equation is y'=3y^2.

We can write this equation as:

dy/dt = 3y^2

dy/y^2 = 3dt

Now integrating on both side

[tex]\int \frac{dy}{y^2} = \int 3dt[/tex]

After integrating we get,

- 1/y = 3t + c

Multiply by y on both side, we get

(3t + c)y = -1

Divide by (3t + c) on both side, we get

y = -1/(3t + c).................(1)

Since there is vertical asymptote at t = 2

So 3t + c = 0 at t = 2

3(2) + c = 0

6 + c = 0

Subtract 6 on both side, we get

c = -6

Put the value of c in equation 1

y = -1/(3t - 6)

At t = 0

y(0) = -1/(3(0) - 6)

y(0) = 1/6

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the percent discount is 14% when the original price and new price are given $36 and $30.96.

Given that,

Original price of item = $36       (that is before discount and the tax)

Price after discount = $30.96

Let the percentage discount be = x

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

To get the percent discount :

x = (original cost - new price)/original price

x = (36 - 30.96)/36

x = 5.06/36

x = 0.14

Percentage discount x , in percentage = 0.14 x 100

Percentage discount = 14%

therefore, the percent discount is 14%

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Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.

What is vector ?

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction. The term also denotes the mathematical or geometrical representation of such a quantity. Examples of vectors in nature are velocity, momentum, force, electromagnetic fields and weight.

Let W be a subspace of a vector space V and let a1, a2, and a3 be vectors in V. The vector a2 is in the subspace W if and only if it can be written as a linear combination of the vectors a1, a2, and a3. That is, there exist scalars c1, c2, and c3 such that:

a2 = c1 * a1 + c2 * a2 + c3 * a3

This equation can be written in matrix form as:

[a2] = [a1 a2 a3] * [c1; c2; c3]

where [a2] is the column vector representation of a2, [a1 a2 a3] is the matrix with a1, a2, and a3 as columns, and [c1; c2; c3] is the column vector of scalars c1, c2, and c3.

Vector a2 is in the subspace spanned by vectors a1, a2, and a3 if it can be written as a linear combination of these vectors.

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A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event, is an exponential probability distribution.

The probability density function or pdf of the exponential distribution is given by the formula

[tex]$$f(x) = \begin{cases} \lambda e^{-\lambda x} & \text{for } x \ge 0 \ 0 & \text{otherwise} \end{cases}$$[/tex]

where λ is the rate parameter and e is the natural logarithm base.

The pdf gives the probability distribution of a random variable x, which represents an exponential distribution.

The exponential distribution is a continuous probability distribution that simulates the interval between events with an average occurrence rate that is constant.

In this distribution, the likelihood that an event will occur in the future is independent of when that event occurred in the past

The time interval between customers joining a line, the interval between device failures, or the separation between two places in space are all frequently modeled using the exponential distribution.

The rate parameter, which denotes the average number of events per unit of time or space, is what defines the exponential distribution.

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The largest digit number that can be formed from 1720 is 7210

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

Examples of integers include -2, 567, -1000, 0, e.t.c

Numbers that can be formed from 1720 are:

1270,

1072,

1027

1207

7201

7102

7210

Among all the numbers , 7210 is the highest number that can be formed from 1720

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The numerical measure of angle A is 49 degrees.

Vertical angles are simply angles that are opposite one another when two starlight lines cross. They are congruent.

Given the data in the question;

∠A and ∠B are vertical angles

Since ∠A and ∠B are vertical angles and vertical angles are congruent,

∠A = ∠B

(8x - 23)° = (6x - 5)°

Solve for x

8x - 23 = 6x - 5

8x - 6x  = -5 + 23

2x = 18

x = 18/2

x = 9

Now, the numerical value of angle A will be;

mA = ( 8x - 23)°

Plug in x = 9

mA = ( 8(9) - 23)°

mA = ( 72 - 23)°

mA = 49°

Therefore, the measure of mA is 49°.

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37.7 °Celsius = 99.8 °Fahrenheit. Your normal body temperature is approximately 37°C. A fever is usually when your body temperature is 37.8°C or higher.

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Yes, we may install 90 square feet of flooring with 360 nails, as the total number of nails and screws used shouldn't exceed 500.

The facility is a method to problem-solving and involves essentially figuring out the price of a single unit, following multiplication that value to figure out the desired value. Clearly explained, the unit method is employed to derive a single property value out of a specified multiple. For contrast, 40 pens should cost (400 rupees, which is equal to the cost among one pen. This procedure might be standardized. undivided nation. anything does indeed have a distinctive element. Its adjoint and reciprocal are equal in terms of mathematics (algebra), abstract algebra, mathematical analysis, or mathematics of matrices or operators.

given

Let x be the number of screws and y be the number of nails,

then the answer to the question is 500.

For 90 square feet, it takes

144 = (2x + 4y) nails, or

4 nails per square foot, for a total of 360 nails.

Yes, we may install 90 square feet of flooring with 360 nails, as the total number of nails and screws used shouldn't exceed 500.

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The domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function (f o g)(-5) as follows:

(f o g) = 4(x² + x) + 8

(f o g) = 4x² + 4x + 8

(f o g)(-5) = 4(-5)² + 4(-5) + 8

(f o g)(-5) = 100 - 20 + 8

(f o g)(-5) = 88

Therefore, the domain of the composite function (f o g)(-5) for f(x) = 4x + 8 and g(x) = x² + x is equal to 88.

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Answer:102+31-180 = 47

so x = 47

Step-by-step explanation:

this is very simple

The matrix is now in row echelon form. The inverse is the right side of the augmented matrix: [tex]$$\begin{bmatrix}1 & 1 & 0 \\2 & 1 & 3 \\0 & 1 & 2\end{bmatrix}$$[/tex]

We will use the algorithm for finding the inverse of a matrix by row reducing.

Step 1: Augment the matrix with the identity matrix.

[tex]$$\begin{bmatrix}1 & 1 & 0 & | & 1 & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]

Step 2: Use row operations to transform the matrix into the identity matrix.

1. Multiply the first row by [tex]$\frac{1}{2}$[/tex] to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\2 & 1 & 3 & | & 0 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]

2. Subtract two times the first row from the second row to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 1 & 2 & | & 0 & 0 & 1\end{bmatrix}$$[/tex]

3. Subtract the first row from the third row to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 2 & | & -\frac{1}{2} & 0 & 1\end{bmatrix}$$[/tex]

4. Multiply the third row by [tex]$\frac{1}{2}$[/tex] to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 1 & | & -\frac{1}{4} & 0 & \frac{1}{2}\end{bmatrix}$$[/tex]

5. Subtract [tex]$\frac{3}{2}$[/tex]times the second row from the third row to get:

[tex]$$\begin{bmatrix}\frac{1}{2} & \frac{1}{2} & 0 & | & \frac{1}{2} & 0 & 0\\0 & 0 & 3 & | & -1 & 1 & 0\\0 & 0 & 0 & | & \frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]

Step 3: The matrix is now in row echelon form. The inverse is the right side of the augmented matrix:

[tex]$$\begin{bmatrix}1 & 0 & 0\\-1 & 1 & 0\\\frac{7}{4} & -1 & \frac{1}{2}\end{bmatrix}$$[/tex]

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