The price of a roll of fabric is reduced by 20%
to £60.
What was its original price?

Answer:

80

Step-by-step explanation:

mean = 140+20=160

160/2

= 80

Answer: 160

Step-by-step explanation:

Just took it

Answer:

x > 9

Step-by-step explanation:

Hello!

First let's solve the inequality for x.

Flip the sign if you are dividing by a negative number.

Now let's graph it on a number line. If it is a greater or less than symbol, we use an open circle. If it is a greater than or equal to or a less than or equal to, we use a closed circle.

Plot the point of 9 with an open circle, and shade in a line towards the right (all values greater than 9).

Answer:1981

Step-by-step explanation:

The value of x would make the triangles similar by the SSS similarity theorem would be 30 . Option C

The SSS similarity theorem of triangles holds that if the three sides of two triangles are proportional, then the triangles are similar.

If the two triangles are to be similar, we have that:

45/x = 75/50

Cross multiply

x = (45 × 50)/75

x = 2250/75

x = 30

Therefore, the value of x would be 30 . Option C

Learn more about SSS similarity theorem here:

https://brainly.com/question/4163594

#SPJ1

The sample size which will produce sample proportion of 0.3 and 95% confidence interval is 36.

Given sample proportion of 0.3, confidence level 95%.

A confidence interval of proportions is given by:

π±z[tex]\sqrt{}[/tex]π(1-π)/n

In which :

π is the sample proportion,

z is the critical value

n is the sample size.

Margin of error=z[tex]\sqrt{}[/tex]π(1-π)/n

z value for confidence level of 95% is 1.96

Margin of error=1.96[tex]\sqrt{0.3*0.7/n}[/tex]

The widest interval has the highest margin of error, since the margin of error and since the margin of error is inversely proportional to the sample size , a lower sample size generates a higher margin of error.

Hence sample size which is correct is 36.

Learn more about margin of error at https://brainly.com/question/24289590

#SPJ4

Question is incomplete as it also includes options like:

a)46

b)68

c)56

d)36.  

The solution of the linear equation 2.8y+6+0.2y=5y-14 is y=10.

Given linear equation 2.8y+6+0.2y=5y-14 and we have to find the solution of the equation.

An equation is relationship between two or more variables which is expressed in equal to form. It is solved in order to find the values of variables. Equation of two variables look like ax+ by=x.

The given linear equation is 2.8y+6+0.2y=5y-14 which can be solved as under:

2.8y+6+0.2y=5y-14

We have to add the coefficients of same variables. Coefficients are the numbers which are present with the variable.

3y+6=5y-14

We have to take same variables at one side.

3y-5y=-14-6

-2y=-20

y=-20/-2

y=10

Hence the solution of the linear equation 2.8y+6+0.2y=5y-14  is y=10.

Learn more about equation at https://brainly.com/question/2972832

#SPJ4

There is no solution for the equation | 3x+7|-5.

When asked to explain why there is no solution to |3x+7|-5 Jack said, "It is not a solution because the 5 is negative." Jack is on the right track but his reasoning is incomplete

equation are format of a link which process over mathematical operators like addition, subtraction etc.

| 3x+7|-5 has no solution because the data is incomplete. Without know there limits or equal to zero, less than zero or greater than zero this system of equation cannot be defined. That is why there is no solution for | 3x+7|-5.

Learn more about equation here:
https://brainly.com/question/10413253

#SPJ1

Answer:

the widths of the wire :)

Step-by-step explanation:

Answer:

b) The two triangles are similar by SAS

Step-by-step explanation:

From the diagram below, we can tell that

SAS similarity (Side-Angle-Side similarity) is a criterion used to determine whether two triangles are similar.

It states that if two sides of one triangle are proportional to two sides of another triangle, and the included angles between these sides are congruent, then the two triangles are similar.

In other words, if in two triangles, the ratio of the lengths of corresponding sides is equal, and the included angles between these sides are congruent, then the two triangles are considered similar.

The corresponding angles are congruent and the sides are in proportion

Learn more about similar triangles here:

https://brainly.com/question/29333623

#SPJ2

Answer:

3x-10=x+40

X=25

Angels are 65

Ans:c

The average speed of Ken is 70 m/min. Using the relation between the speed and distance, the required speed for Ken is calculated.

The relationship between speed S and distance D with a period T is formed as

S = D/T

Units: m/sec (basic unit)

Given that,

Jaylen and Ken started jogging from the same place in opposite directions along a straight path.

This means, that the sum of distances traveled by both of them in opposite directions = 13.6 km (since it is given that at the end of their jogging, they are 13.6 km apart)

Consider,

The distance traveled by Jaylen = x km

Then the distance traveled by Ken = x - 2.4 km (since Jaylen jogged 2.4 km more than Ken)

Step 1: Finding the distance traveled by them:

x + x - 2.4 = 13.6

⇒ 2x = 13.6 + 2.4

⇒ 2x = 16

⇒ x = 8 km

So, the distance travelled by Jaylen = 8 km and by Ken = 8 - 2.4 = 5.6 km

Step 2: Finding the average speed traveled by Ken:

Since it is given that,

Jaylen's speed was 30 m/min faster than Ken's speed.

So,

For 30 m, the time = 1 min

then for 2.4 km i.e., 2400 m, the time = 80 min.

Therefore,

the average speed of Ken S = D/t

⇒ S = 5600 m / 80 min

∴ S = 70 m/min.

So, the average speed of Jaylen will be 70 m/min + 30 m/min = 100 m/min.

Thus, the average speed of Ken is 70 m/min.

Learn more about the relation between speed, distance, and time here:

https://brainly.com/question/3004254

#SPJ2

Answer:

12

Step-by-step explanation:

Time=D/S

T1=PQ/20

T2=PQ/30

Total Time=T1+T2

1=PQ/20+PQ/30

PQ=12

Step-by-step explanation:

[tex] = \frac{ \frac{10}{3} }{ \frac{2}{3} } [/tex]

[tex] = \frac{10}{3} \div \frac{2}{3} [/tex]

[tex] = \frac{10}{3} \times \frac{3}{2} [/tex]

[tex] = \frac{9 + 1}{3} \times \frac{3}{2} [/tex]

[tex] = 3 \frac{1}{3} \times \frac{3}{2} [/tex]

[tex] = 3 \frac{1}{3} .( \frac{3}{2} )[/tex]

The answer is B.

Answer:

0.3 gallon

Step-by-step explanation:

To do this problem, we must divide the amount of cement by the number of feet to see how much cement he used for each foot.

15/50 = 0.3 gallon

Answer:

0.3 gallons per foot

Step-by-step explanation:

We know that he used 15 gallons of cement for 50 feet.

We want to find the amount per foot or the amount per each 1 foot.

So we have to divide the 15 gallons by the 50 feet.

15 / 50 = 0.3 gallons per foot.

Considering the problem described, we have that:

a) The normal distribution can be used, as both [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex].

b) There is a 0.0132 = 1.32% probability that proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters of the binomial distribution are:

n = 2000, p = 0.92.

Hence:

Since both [tex]np \geq 10, n(1 - p) \geq 10[/tex], a normal approximation can be used. The mean and the standard deviation of the approximation are given as follows:

The probability that proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less, using continuity correction, is P(X < 175.5), which is the p-value of Z when X = 175.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{175.5 - 184}{3.8367}[/tex]

Z = -2.22.

Z = -2.22 has a p-value of 0.0132.

0.0132 = 1.32% probability that proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less.

More can be learned about the normal distribution at https://brainly.com/question/24537145

#SPJ1

Answer:

55

Step-by-step explanation:

[tex] \frac{n(n + 1)}{2} \\ n = 10 \\ substitutig \\ \frac{10(10 + 1)}{2} \\ \\ \frac{10(11)}{2} \\ \\ \frac{110}{2} = 55 [/tex]

Answer:

b. The graph of g(x) is a translation 10 units right and 8 units up from the graph of f(x).

Step-by-step explanation:

See attached image.

Mickey, Making errors could be that he must be found out that cost of one carton is $0.50, by dividing 12 cartons with total cost and by this  e figured it out the cost of 7 carton is just $3.5.

In this question is  arithmetic, what we have in, the question is 12 cartons of eggs cost $22.20. we need to find out the cost of seven cartons.

In mathematics it deals with numbers of operations according to the statements.

Here, the cost of one carton is given by;
  =  22.20/12  = $1.85

now the cost of seven cartons,

   = 1.85 x 7 = 12.95 ≅ $ 13

Thus, Mickey made the mistake in his calculation and didn't get the right cost for seven cartons which is $13.

Learn more about arithmetic here:
https://brainly.com/question/14753192

#SPJ1

The estimated probability that at least one of the next four fish Roxanne catches will be a perch is 34%

Probability is the likeliness of an event to happen. It has a range of 0 to 1, where 0 indicates uncertainty and 1 indicates certainty.

It is given that

0, 1, and 2 represent trout , 3 and 4 represent bass , 5 represent perch , 6, 7, 8, and 9 represent other fish

From the data it can be observed that

Total number of single digits numbers = 80

No. of Perch , "5 " = 8

Probability of getting a perch in next fish = 8/80 = 0.1

Probability that at least one of the next four fish Roxanne catches will be a perch = 1- P(no perch)

P ( no perch) = 1 - 0.1 = 0.9

for 4 fishes

= 1 - 0.9⁴

= 0.3439

= 34.39%

≈ 34%

Therefore the estimated probability that at least one of the next four fish

Roxanne catches will be a perch is 34%.

To know more about Probability

https://brainly.com/question/11234923

#SPJ1

Answer:

it means y intercept

Step-by-step explanation:

Answer: θ≈48,81°.

Step-by-step explanation:

[tex]sin\theta=\frac{8}{\sqrt{113}}\\sin\theta } =\frac{8*\sqrt{113} }{\sqrt{113}*\sqrt{113} } \\sin\theta=\frac{8*\sqrt{113} }{113} \\sin\theta\approx0,75258\\\theta\approx48,81^0.[/tex]

Good luck an' have a nice day!

The graph which represents the solution to the compound inequality is; -2 ≤ x < 5.

The inequalities given in the task content can be solved as follows;

For –2x + 4 ≤ 8

-2x ≤ 8 -4

x >= -2

For –2x + 4 > –6

–2x > –6 -4

x < 5

Hence, the graph which represents the solution to the compound inequality is; -2 ≤ x < 5.

Read more on compound inequality;

https://brainly.com/question/7070563

#SPJ1

Answer:

The correct answer would be B) 2

Answer:

C 1/2

Step-by-step explanation:

Since the angels of these triangles are same,they are totally similar.

The ratios of their sides are

10/20=1/2

8/16=1/2

6/12=1/2

So, The scale factor is 1/2.

Using the Poisson distribution, it is found that there is a 0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Considering the average of 15 birds every 2 hours during daylight hours, the mean for a 45-minute period is given by:

[tex]\mu = 15 \times \frac{45}{120} = 5.625[/tex]

The probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours is given by:

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-5.625}(5.625)^{0}}{(0)!} = 0.004[/tex]

[tex]P(X = 1) = \frac{e^{-5.625}(5.625)^{1}}{(1)!} = 0.02[/tex]

[tex]P(X = 2) = \frac{e^{-5.625}(5.625)^{2}}{(2)!} = 0.057[/tex]

[tex]P(X = 3) = \frac{e^{-5.625}(5.625)^{3}}{(3)!} = 0.107[/tex]

[tex]P(X = 4) = \frac{e^{-5.625}(5.625)^{4}}{(4)!} = 0.150[/tex]

[tex]P(X = 5) = \frac{e^{-5.625}(5.625)^{5}}{(5)!} = 0.169[/tex]

Then:

[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.004 + 0.02 + 0.057 + 0.107 + 0.15 + 0.169 = 0.507[/tex]

0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

More can be learned about the Poisson distribution at https://brainly.com/question/13971530

#SPJ1

Answer:

[tex]\boxed{Circuit_{\Delta ABC} = 15~cm }[/tex]

Step-by-step explanation:

The ABC triangle is an equilateral triangle.

[tex]\mid AB\mid = \mid BC\mid = \mid AC\mid[/tex]

The drawing in the attachment.

I am entering meaningfully:

a - side length of an equilateral triangle

[tex]a=\mid AB\mid = \mid BC\mid = \mid AC\mid[/tex]

[tex]P_{\Delta} =\dfrac{a^{2} \sqrt{3} }{4}[/tex]  -   equilateral triangle area formula

[tex]P_{\Delta} =\dfrac{25 \sqrt{3} }{4}~~\land~~P_{\Delta} =\dfrac{a^{2} \sqrt{3} }{4}~~\Rightarrow~~\dfrac{a^{2} \sqrt{3} }{4}=\dfrac{25 \sqrt{3} }{4}\\\\\\\dfrac{a^{2} \sqrt{3} }{4}=\dfrac{25 \sqrt{3} }{4}~~\mid~~\div ~~\dfrac{\sqrt{3} }{4} \\\\\\\dfrac{a^{2} \sqrt{3} }{4}\cdot \dfrac{4}{\sqrt{3} } =\dfrac{25 \sqrt{3} }{4}\cdot \dfrac{4}{\sqrt{3} } \\\\a^{2} =25~~\\\\a^{2} =5^{2} ~~\land~~a > 0~~\Rightarrow~~\boxed{a=5~cm}\\\\\\[/tex]

[tex]Circuit_{\Delta ABC} =a+a+a\\\\Circuit_{\Delta ABC} =3a~~\land~~a=5~cm\\\\\boxed{Circuit_{\Delta ABC} =3\cdot 5 = 15~cm }[/tex]

Parallel lines are lines in a plane that are always the same distance apart.

☆...hope this helps...☆

_♡_mashi_♡_

Lines with the same slope that never touch each other.

Parallel lines share the same slope (direction). Attached is an example of two lines parallel to each other, [tex]y=2x-1[/tex] in red and [tex]y=2x+1[/tex] in green. They both have a slope of [tex]2[/tex], which is what makes them parallel.

1+3-2+0=2

-3-2+1+2=-2

Answer:

d.-½ ,represent change of y with respect to x

Step-by-step explanation:

The values of y with respect to x are :-

Thus, -½ in the value of the change in y with respect to x.

Step-by-step explanation:

here we have to know that, if A/B=A'/B' is equal to 1 it means it doesn't cut. if it isn't equal to 1, it does.

A=3 B=4

A'=4 B'=3

3/4=4/3 it cuts. Now, they are straight lines because we don't have x² or anything, so they can just intersect once between them.

Answer:

2 Pas

Step-by-step explanation:

pressure = force/area

p= 30N/2m²

p=15pas

Answer:

Pressure = 15 N/m²  =  15 Pa

Step-by-step explanation:

[tex]Pressure = \frac{Force \space\ \space\ applied}{Area}[/tex]

[tex]Pressure= \frac{30}{2} \\\\Pressure = 15 \space\ N/m^2[/tex]

A circle and a triangle can intersect in a point.

This refers to the fact that two lines are able to meet at a given point. The point where they meet is the point of intersection.

A circle is known to be able to intersect with a triangle in three different ways and at one point.

Read more on intersection here:

https://brainly.com/question/2065148

#SPJ1