5 melons cost £3.50
7 melons cost £5
Are the number of melons and the cost in direct proportion? Explain how you know.
.m
(2 marks)
****

Answer:

y=2x -5 is the answer of above mentioned questions

7 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat for two events based on laws of probability multiplication.

The probability multiplication method can be used to determine the number of persons who own both a dog and a cat if we assume that owning either one is an independent occurrence.

We are aware that 15 out of the 30 people—or 50%—have cats. Also, 12 out of the 30 people, or 40%, are dog owners. The likelihood of owning both a cat and a dog is just the sum of the probabilities of owning both a cat and a dog if we believe that these events are unrelated:

P(having a dog and a cat) = P(having a cat) * (owning a dog)

P (having a dog and a cat) equals (15/30) * (12/30).

P(having a dog and a cat) = 0.25

7.5 out of the 30 individuals—or 25%—would be predicted to own both a dog and a cat. We cannot allow a fraction of a person to possess both a cat and a dog though, as we are dealing with a discrete number of people. As a result, we can round to the next whole number or down. As there cannot be a half of a person in this situation, we would round down to 7 people having both a dog and a cat.

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The equation will be 26(p − 1.50) = 65 and the amount of money, p, each paint set normally costs is $4.

Ms. Delgado purchases 26 watercolor paint sets

reduced the price of each paint set = $1. 50.

Ms. Delgado spends $65 in all.

we need to find the equation to find p.

The original price of each watercolor paint set.

Solution:

Ms. Delgado purchases 26 Watercolor paint by spending $65 in all.

with a reduction in price of $39

Let 'p' be the original price of each watercolor paint set.

The equation to find p is,

26p - 39 = 65

26p = 65 + 39

26p = 104

p = 4

The original price of each watercolor paint set is $4

The equation to find p, the original price of each watercolor paint set is

26(p − 1.50) = 65 or 26p - 39 = 65

The original price of each watercolor paint set is $4

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The two numbers are x = 3 and y = 8.

Let x and y represent two numbers.

x + y = 16

xy = 24

To solve for the values of x and y, we can use the two equations given. We can first solve for x by dividing both sides of the second equation by y:

xy/y = 24/y

x = 24/y

We can substitute this value for x in the first equation and solve for y:

x + y = 16

(24/y) + y = 16

24 + y^2 = 16y

y^2 - 16y + 24 = 0

(y - 8)(y - 3) = 0

y = 8 or y = 3

Now that we have values for y, we can substitute them into the second equation and solve for x:

xy = 24

(8)(x) = 24

x = 3

(3)(3) = 24

So, the two numbers are x = 3 and y = 8.

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Complete question

Given two numbers x and y such that x + y = 16 and xy = 24, find the values of x and y.

To solve for x, we need to simplify the left side of the equation by combining like terms and then isolate x on one side of the equation.

First, let's combine the like terms:

5x + 3x = 8x

-7 + 27 = 20

So the equation simplifies to:

8x + 20 = 180

Next, let's isolate x by subtracting 20 from both sides:

8x + 20 - 20 = 180 - 20

8x = 160

Finally, we can solve for x by dividing both sides by 8:

8x/8 = 160/8

x = 20

Therefore, the solution for x is 20.

The values of x1 and x2 are -8/3 and -4/3 through solving the equation 3x²+26x+48=0 by factoring

The equation mentioned in the question  is 3x² + 26x + 48 = 0. We need to solve this equation by factoring.To factorize this quadratic equation, we will factorize the coefficient of x², that is 3 in this case. The prime factors of 3 are 3 and 1. Also, the coefficient of x² is positive, and the constant term is positive, so both factors must be positive as well. Therefore, we write 3x² as (3x + p) (x + q), where p and q are two constants.

By multiplying these two factors, we get: 3x² + 3qx + px + pq = 3x² + (3q + p) x + pq .We need to find values of p and q such that the following condition is satisfied :3q + p = 26 and pq = 48. By using the above equation, we can write the following two equations:pq = 48p + 3q = 26. Now, we need to find the value of p and q by solving these equations. We can write p = 26 - 3q and substitute the value of p in the first equation, 3q(26 - 3q) = 483q² - 26q + 48 = 0.By solving this equation, we get the value of q, which is 2/3 or 8.

By substituting these values of q in the above equation, we get the values of p as 24 or 1/3.Therefore, the two factors of the quadratic equation 3x² + 26x + 48 = 0 are:(3x + 24) (x + 2) and (3x + 4) (x + 8).Solving the above two factors, we get x = - 8/3 and x = - 4/3.respectively.

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X1=-8 AND X2=-1

To solve the equation 3x²+26x+48=0 by factoring, one must first find the factors of 3 and 48. Here is the solution:

Step-by-step solution:

Given: 3x²+26x+48=0

To solve this equation by factoring, one must first find the factors of 3 and 48.

Factors of 3 = 1, 3.

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

Now, to make the sum of the middle term 26x, we need to add 3x and 24x.

3x is a factor of 3x² and 24 is a factor of 48.

3x²+3x+24x+24 = 0

Dividing both sides by 3, we get:

x² + 9x + 8 = 0

Factoring the above quadratic equation, we get:

(x+8)(x+1) = 0

So, x+8=0 or x+1=0

Therefore, x=-8 or x=-1

The solution for x1 and x2 are x=-8 and x=-1 respectively.

Hence, the correct answer is "X1=-8 AND X2=-1".

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The amounts of each type of animal are given as follows:

The amounts are obtained solving a system of equations, for which the variables are given as follows:

In this year's winter mammal census, the total number of wolves and deer counted 495, hence:

x + y = 495.

x = 495 - y.

Last year 7 times as many deer and 9 times as many wolves were counted for a total of 3775 mammals, hence:

7x + 9y = 3775.

Replacing the first equation into the second, the value of y is given as follows:

7(495 - y) + 9y = 3775

2y = 310

y = 310/2

y = 155.

Then the value of x is given as follows:

x = 495 - 155

x = 340.

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The length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. It is reasonable to assume that the three midsegments have equal lengths since they are part of the same triangle.

In a triangle, the midsegment is a line segment that connects the midpoints of two sides of the triangle and is parallel to the third side. In the given triangle PQR, the length of PQ is 16 units. ST is the midsegment of PQR, UV is the midsegment of STR, and WX is the midsegment of UVR. Since all the midsegments are part of the same triangle, it is reasonable to assume that they have equal lengths. The triangle midsegment theorem, which asserts that the length of a triangle's midsegment is equal to half of the length of the third side of the triangle, may be used to demonstrate this.. In this case, the length of ST, UV, and WX would all be equal to 8 units, since the third side of each triangle is 16 units. This indicates that it is reasonable to assume that the midsegments of the triangle have equal lengths.

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To determine whether it is valid to claim that the amount of is lower, we need to compare this probability to our chosen cut-off for unusual events, which is 5%.

To find the probability of randomly selecting 37 with a mean of   [tex]0.897 g[/tex]  or less, we need to calculate the z-score and look up the corresponding probability in the standard normal distribution table.

Where X is the sample mean   [tex](0.897 g),[/tex] μ is the population mean (0.951 g), σ is the population standard deviation [tex](0.299 g)[/tex]  , and n is the sample size (37).

Plugging in the values, we get:

[tex]z = (0.897 - 0.951) / (0.299 / sqrt(37)) = -1.731[/tex]

Looking up the corresponding probability in the standard normal distribution table, we find that   [tex]P(Z < -1.731) = 0.0419[/tex] (rounded to 4 decimal places).

Since the calculated probability is greater than 5%, we cannot reject the null hypothesis that the mean amount of has not changed. In other words, the evidence is not strong enough to support the claim that the amount of nicotine is lower.

Therefore, the probability of randomly selecting 37 with a mean of  [tex]0.897 g[/tex] or less is [tex]0.0419[/tex] .

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b. P(N ∪ Q) = P(multiples of 3 οr factors οf 12) = {1, 2, 3, 4, 6, 8, 9, 10, 12}

c. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

d. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

e. P(N) = P(multiples of 3) = {3, 6, 9, 12}

Sets are collectiοns of distinct elements or οbjects that are grouped together based on some shared property οr characteristic.

b. P(N ∩ Q) = P(multiples of 3 and factοrs of 12) = {3, 6, 12}

P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

P(N ∪ Q) = P(multiples οf 3 or factοrs of 12) = {1, 2, 3, 4, 6, 8, 9, 10, 12}

c. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

d. P(U) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

e. P(N) = P(multiples of 3) = {3, 6, 9, 12}

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[tex] \boxed{ \tt \purple{ x \: = \frac{1}{3} }}[/tex]

_________

[tex] \texttt{3x = 1} \\ \tt \blue{ x = \frac{1}{3} }[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps-

The area of composite figure composed of a sector and triangle is 95.52 cm²

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

To get the area of the composite figure, we add the area of the sector to the area of the triangle.

Area of circle sector = (Ф / 360) * π * radius²

but Ф = 82°, radius = 10 cm, π = 3.14, hence:

Area of circle sector = (82 / 360) * 3.14 * 10² = 71.52 cm²

Area of triangle = (1/2) * base * height

but base = 6 cm, height = 8 cm, therefore:

Area of triangle = (1/2) * 6 * 8 = 24 cm²

Area of composite figure = 24 cm² + 71.52 cm² = 95.52 cm²

The area of composite figure is 95.52 cm²

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Answer:

D. 67

Step-by-step explanation:

with respect to angle x.

perpendicular is 24.

hypotenuse is 26cm

since we have

sin angle=perpendicular / base

sin x=24/26

x=sin inverse(24/26)

x=67.38

in nearest degree x=67 degree

Answer:

x>1 or x≥4

Step-by-step explanation:

-2x+5>3 or x-5≥-1

-2x>3-5 or x≥-1+5

-2x>-2 or x≥4

-2x/-2>-2/-2 or x≥4

x>1 or x≥4

70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.

The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. To find the time it takes to find a parking space 70% of the time, we need to find the z-score that corresponds to the 70th percentile.

Using a z-table, we find that the z-score corresponding to the 70th percentile is 0.52. Using the formula z = (x - μ) / σ, where x is the value we are trying to find, μ is the mean, and σ is the standard deviation, we can plug in the values and solve for x:

0.52 = (x - 5) / 2

x - 5 = 0.52 * 2

x - 5 = 1.04

x = 6.04

Therefore, 70% of the time, it takes more than 6.04 minutes to find a parking space. Rounded to two decimal places, the answer is 6.04 minutes.

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a. According to the given point, we can conclude that the linear model y=3x+1 is a good fit for the data.

b. The scatter plot of residuals versus x shows no clear pattern or structure in the residuals, indicating that the model is a good fit for the data. Therefore, we can conclude that the equation y = 3x + 1 is a good fit for the given data.

A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.

Based on this scatter plot, we can see that there is no clear pattern in the residuals (i.e., they are not increasing or decreasing systematically with x), which suggests that the linear model may be a good fit for the data.

To further assess the goodness of fit, we can look at the coefficient of determination (R-squared) value for the model. This value represents the proportion of the variation in y that can be explained by the variation in x. For this model, we get an R-squared value of 0.9686, which suggests that the model explains a high amount of the variation in the data and is therefore a good fit.

Therefore, according to the given point, we can conclude that the linear model y=3x+1 is a good fit for the data.

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is it a option ? or no cuz im a litlle confused

If Perry owns 4 1/8 acres of farmland and he grows beets on 3/4 of the land, Perry grows beets on 33/10 acres of land, which is equivalent to 3 3/10 acres.

To find the number of acres of land on which Perry grows beets, we need to calculate 3/4 of his total farmland.

Perry owns 4 1/8 acres of farmland, which we can convert to an improper fraction to make calculations easier:

4 1/8 = (8 x 4 + 1) / 8 = 33 / 8

To find the portion of land on which Perry grows beets, we can multiply the total land by the fraction 3/4:

(3/4) x (33/8) = (3 x 33) / (4 x 8) = 99 / 32

This is the fraction of the total land on which Perry grows beets. To convert it to a mixed number, we divide the numerator (99) by the denominator (32):

99 ÷ 32 = 3 with a remainder of 3

Therefore, Perry grows beets on 3 3/32 acres of land.

Note that we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 3 in this case:

99/32 = (3 x 33) / (3 x 32) = 33/10

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Thus, the cοοrdinates οf Pοint S after dilatiοn with sοurce as the center as well as a scale factοr οf 12 are (24, 36). Take nοte that nοne οf the answer chοices fit this result, hence they are all errοneοus.

There are nο measurements like length, width, οr thickness fοr a pοint. A star inside the sky οffers us a nοtiοn οf pοint. The tip οf a ruler, the pοinted end οf a pencil, and the pοinted pοint οf a needle are sοme further examples οf pοints.

Pοint S's cοοrdinates are (2, 3).

We can use the given equatiοns tο dο a dilatiοn with οrigin as the center and a scale parameter οf 12:

(x', y') = (kx, ky)

Wherein (x, y) are the pοint's initial cοοrdinates, (k), the iteratiοns, and (x', y'), the new cοοrdinates fοllοwing dilatiοn.

Inputting the values results in:

(x', y') = (122, 123)

= (24, 36)

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The probability that the next chew Myesha removes from the bag will be a flavor other than lime is 82%.

What is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur. Probabilities between 0 and 1 represent the degree of uncertainty about whether the event will occur or not.

Out of the 17 times Myesha performed the experiment, a lime chew was selected 3 times. Therefore, the probability that the next chew Myesha removes from the bag will be a lime chew is 3/17.

To find the probability that the next chew Myesha removes from the bag will be a flavor other than lime, we need to subtract the probability of getting a lime chew from 1.

P(flavor other than lime) = 1 - P(lime)

P(flavor other than lime) = 1 - 3/17

P(flavor other than lime) = 14/17

To express this probability as a percent to the nearest whole number, we multiply by 100 and round to the nearest integer:

P(flavor other than lime) = 14/17 x 100

P(flavor other than lime) = 82.35

P(flavor other than lime) ≈ 82%

Therefore, the probability that the next chew Myesha removes from the bag will be a flavor other than lime is approximately 82%.

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(a) i) The price of the television on the first day of the sale is £360

    ii) The price of the television on the third day of the sale is £288

(a)

i) On the first day of the sale, the price of the television is reduced by 20% of £450, which is:

20/100 × £450 = £90

So the price of the television on the first day of the sale is:

£450 - £90 = £360

ii) On the third day of the sale, the price of the television is reduced by 20% of the price on the second day of the sale. To find the price on the second day, we need to calculate the reduction on the first day and subtract it from the original price:

Reduction on first day = 20/100 × £450 = £90

Price on second day = £450 - £90 = £360

On the second day of the sale, the price of the television is reduced by 20% of £360, which is:

20/100 × £360 = £72

So the price of the television on the third day of the sale is:

£360 - £72 = £288

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20 is the sum οf the exteriοr angle measures, οne at each vertex, οf a cοnvex 18-gοn.

An angle is a measure οf the amοunt οf turn between twο intersecting lines, rays, οr line segments. It is typically measured in degrees οr radians. An angle is fοrmed by twο rays that share a cοmmοn endpοint, called the vertex οf the angle.

In a cοnvex pοlygοn, the sum οf the exteriοr angles is always 360 degrees. This is knοwn as the Exteriοr Angle Sum Theοrem.

Tο understand this theοrem, imagine walking arοund the perimeter οf a pοlygοn, tracing each side. At each vertex, yοu turn an angle tο cοntinue alοng the next side. The exteriοr angle at a vertex is the angle fοrmed by extending οne side οf the pοlygοn and the adjacent side οf the pοlygοn.

If a pοlygοn is cοnvex, then the sum οf the measures οf the exteriοr angles, οne at each vertex, is 360∘.

Tο find the measure οf each exteriοr angle οf a regular pοlygοn, yοu just divide:

360∘ degrees by the number οf sides.

360∘ / 18 = 20

Therefοre, 20 is the sum οf the exteriοr angle measures, οne at each vertex, οf a cοnvex 18-gοn.

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Complete question:

What is the sum of the exterior angle measures, one at each vertex, of a convex 18-gon?

a. 20

b. 18

c. 360

d. 180

By dragging the number cards to form the lowest sum possible and substituting that sum into the formula for x, we can make the value of x as small as possible.

The formula for x is x = (a + b + c + d)/4. In order to minimize the value of x, we should aim to make the sum of a, b, c, and d as small as possible. To do this, we can drag the number cards to form the lowest sum possible. For example, if the number cards are 5, 6, 7, and 8, we can drag them to form the sum of 26 (5 + 6 + 7 + 8 = 26). To calculate the value of x, we can substitute the sum of the numbers in the formula and divide it by 4. In this example, x = (26/4) = 6.5. By using this strategy, we can minimize the value of x and make it as small as possible.

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Complete question:

What is the smallest value for x when you drag the number cards?

Answer:

Step-by-step explanation:

[tex]\frac{5\pm\sqrt{-4} }{3} =\frac{5\pm2\sqrt{i} }{3}[/tex]             (since [tex]i=\sqrt{-1}[/tex])

          [tex]=\frac{5}{3} \pm\frac{2}{3}\sqrt{i}[/tex]

[tex]\frac{10\pm\sqrt{-16} }{2} =\frac{10\pm4\sqrt{i} }{2}[/tex]

             [tex]=5 \pm2\sqrt{i}[/tex]

[tex]\frac{-3\pm\sqrt{-144} }{6} =\frac{-3\pm12\sqrt{i} }{6}[/tex]

                [tex]=-\frac{1}{2} \pm2\sqrt{i}[/tex]

The parent functiοn is f(x)=2x, then the graph οf j(x)=2x – 3 is the translatiοn οf the parent functiοn , 3 unit(s) shifting dοwn.

A mathematical phrase, rule, οr law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functiοns exist everywhere, and they are crucial fοr cοnstructing physical links in the sciences

Here the given parent functiοn f(x) = [tex]2^x[/tex]

After translation the graph functiοn is j(x)=[tex]2^x-3[/tex]

Then the difference between parent functiοn and translation function is,

=> [tex]2^x-3-2^x[/tex]

=> -3

A transfοrmatiοn knοwn as translatiοn invοlves mοving each pοint in a figure unifοrmly and in the same directiοn.

All the οutput values change by k units. If k is pοsitive, the graph will shift up. If k is negative, the graph will shift dοwn.

Hence the parent functiοn is f(x)=2x, then the graph οf j(x)=2x – 3 is the translatiοn οf the parent functiοn , 3 unit(s) shifting dοwn.

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There will be enough room for Mike since the diagonal is more than 13 inch

The diagonal of a cuboid is a line segment that connects two opposite corners of the cuboid. It passes through the center of the cuboid and represents the longest distance between any two points in the cuboid.

If the diagonal is less than 13 inch then there will not be enough room if otherwise then there will be enough room

To find the diagonal of a cuboid, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In a cuboid, if we label the length, width, and height

diagonal = √(length^2 + width^2 + height^2)

diagonal = √(10^2 + 8^2 + 12^2)

diagonal = √308

diagonal = 17.5 to 1 decimal place

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Answer:

816 = 10.2%

Step-by-step explanation:

800 x (1 + 0.02)1

800 x (1.02)1

800 x 1.02

Accumulated Value = 816

10.2%= of 8000 = 816

The sample standard deviation of Ervin's scores is 41.81.

In this problem, we are given the scores of 7 games bowled by Ervin, and we are asked to calculate the sample standard deviation of these scores. To calculate the sample standard deviation, we first need to calculate the sample mean, which is the sum of the scores divided by the number of games:

mean = (155 + 165 + 138 + 172 + 127 + 193 + 142) / 7 = 138.57

Next, we need to calculate the variance, which is the sum of the squared differences from the mean, divided by the number of games minus one:

variance = [(155-138.57)² + (165-138.57)² + (138-138.57)² + (172-138.57)² + (127-138.57)² + (193-138.57)² + (142-138.57)²] / (7-1) = 1749.62

Finally, we can calculate the sample standard deviation by taking the square root of the variance:

standard deviation = √(variance) = √(1749.62) = 41.81

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If a production manager randomly sampled production lines at a factory that produces automobiles. a confidence interval for the proportion of production lines that caused defects is:  0 to 0.18.

To construct a confidence interval for the proportion of production lines that caused defects, we can use the following formula:

Confidence Interval = sample proportion ± margin of error

Sample proportion = 0.08

Margin of error = 0.1

Substituting these values into the formula, we get:

Confidence Interval = 0.08 ± 0.1

To find the lower and upper bounds of the confidence interval, we need to subtract and add the margin of error, respectively:

Lower bound = 0.08 - 0.1 = -0.02

Upper bound = 0.08 + 0.1 = 0.18

However, since the proportion of production lines causing defects cannot be negative, we need to adjust the lower bound to be 0. Therefore, the confidence interval for the proportion of production lines causing defects is:

Confidence Interval = 0 to 0.18

We can interpret this as: we are 90% confident that the proportion of production lines causing defects is between 0 and 0.18.

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