Linda is buying wool to knit a baby’s blanket.

She needs 1800 yards of wool.


Linda chooses some balls of wool.

There are 245 metres of wool in each ball of wool.


Linda knows that


1 yard is 36 inches

1 inch is 2. 54 centimetres


How many balls of wool does Linda need to buy?

You must show all your working

Given variables p, v, t, and T related by the equations: pv = 4T, T = 100 - t, and v = 10 - t. We are to find the value of p for the interval from t = 0 to t = 1.pv = 4T ...(1)T = 100 - t ...(2)

v = 10 - t ...(3)By substituting the value of T from equation (2) in equation (1), we get:pv = 4T ⇒ p(10 - t) = 4(100 - t)⇒ 10p - pt = 400 - 4t⇒ pt + 4t = 10p - 400 ...(4)By substituting the value of v from equation (3) in equation (1), we get:pv = 4T⇒ p(10 - t) = 4(100 - t)⇒ 10p - pt = 400 - 4t⇒ 10p - p(10 - t) = 400 - 4t⇒ 10p - 10 + pt = 400 - 4t⇒ pt + 4t = 10p - 390 ...(5)Subtracting equation (4) from equation (5), we get:pt + 4t - (pt + 4t) = 10p - 390 - (10p - 400)⇒ - 10 = 10⇒ 0 = 20This is not possible since 0 cannot be equal to 20.

Therefore, there is no value of p for the interval from t = 0 to t = 1.Option a. 4 is not the answer. Option b. 1 is not the answer. Option c. 40 is not the answer. Option d. -40 is not the answer.

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The lengths of the legs of a right triangle 4.884 units and 14.18 units

In this question, we have been given a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long.

We need to find the lengths of the legs of a right triangle.

Consider a right triangle ABC with ∠B = 90° and ∠C = 19°

Consider sine of angle C

sin(C) = AB/AC

sin(19°) = AB / 15

AB = 0.3256 * 15

AB = 4.884

Using Pythagoras theorem,

AC² = AB² + BC²

15² = 4.884² + BC²

BC = √(225 - 23.85)

BC = 14.18 units

Therefore, the lengths of the legs of a right triangle:

AB = 4.884 units

BC = 14.18 units

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The Excel function used when deciding to reject or fail to reject the null hypothesis is the T.TEST function.

This function is used to calculate the probability of obtaining the observed results or more extreme results, assuming that the null hypothesis is true. If the probability, also known as the p-value, is less than the significance level, typically 0.05, the null hypothesis is rejected, and it is concluded that there is sufficient evidence to support the alternative hypothesis.

Otherwise, if the p-value is greater than the significance level, the null hypothesis is not rejected, and it is concluded that there is not enough evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the level of significance (alpha) chosen for the test, typically 0.05 or 0.01, then the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the chosen alpha level, then the null hypothesis is not rejected.

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Answer: 4 hours

Step-by-step explanation:

Assume x is the number of hours taken.

Garage A would therefore charge a total of:

= $9 + $1.50 * x

= 9 + 1.50x

Garage B would charge:

= $5 + $2.50 * x

= 5 + 2.50x

To find the number of hours it would take for them to be the same, equate both equations:

9 + 1.50x = 5 + 2.50x

9 - 5 = 2.50x - 1.50x

4 = 1x

x = 4 hours

That cost would be:

= 9 + 1.50 * 4

= 9 + 6

= $15

Answer:

585

Step-by-step explanation:

3 years + 3 months

=3years + 3/12 years

=3years + 1/4 years

=13/4 years

SI = 1500× 12/100 × 13/4

= 585

Answer:

(0,4)

Y =2.5X +4

Step-by-step explanation:

Answer:

because you can technically add a negative to a positive so you could do 10 + -11 and it would be a proper equation and it is -1 so they can be negative sums

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given that the radius of a bubble increases by 4%.

Let r be the radius of the spherical bubble, so the new radius of the sphere

\(R= r+0.04r = 1.04r\cdots(i)\)

(a) Surface area of the bobble,

\(s=4\pi r^2\)

So, the rate of increase of surface area = \(4\pi R^2 -4\pi r^2= 4\pi(R^2-r^2)\)

The percentage change in the surface area \(= \frac {4\pi(R^2-r^2)}{4\pi r^2}\times 100\)

By using equation (i)

The percentage change in the surface area = \(\frac {(1.04r)^2-r^2}{ r^2}\times 100\)

\(=(1.04^2-1)\times 100\)

=8.160%

Therefore, the percentage change in the surface area is 8.160%

(b) The volume of the sphere = \(4/3 \pi r^3\)

So, the change in the volume = \(4/3 \pi R^3-4/3 \pi r^3\)

Percentage change in the volume =

\(\frac {4/3 \pi R^3-4/3 \pi r^3}{4/3 \pi r^3}\times 100\)

\(=(1.04^3-1)100\) [by using equation (i)]

=12.486%

Therefore, the percentage change in the volume is 12.486%.

Triangle pairs are similar polygons if they have the same shape but not necessarily the same size. In order for two triangles to be similar, they must satisfy the following conditions:

They must have the same angles. This means that the measures of the angles in one triangle must be the same as the measures of the corresponding angles in the other triangle.

The lengths of the sides must be in the same ratio. This means that if you divide the lengths of the corresponding sides of one triangle by the lengths of the corresponding sides of the other triangle, you must get the same ratio for all pairs of sides.

For example, if triangle ABC is similar to triangle DEF, the ratios of AB/DE, AC/DF, and BC/EF must all be the same.

To determine if two triangles are similar, you can use one of several theorems and postulates, such as the Side-Side-Side (SSS) Similarity Theorem, the Side-Angle-Side (SAS) Similarity Theorem, or the Angle-Angle (AA) Similarity Postulate. These theorems and postulates provide different sets of conditions that must be satisfied in order for two triangles to be similar.

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Answer:

Cost of 20 boxes = RS. 188

Step-by-step explanation:

Given:

Length of box = 30 cm  = 0.3m

Width of box = 40 cm = 0.4 m

Height of box = 50 cm = 0.5 m

Cost per m² = Rs. 10

Find:

Cost of 20 boxes

computation:

TSA of box = 2[lb + bh + hl]

TSA of box = 2[(0.3)(0.4) + (0.4)(0.5) + (0.5)(0.3)]

TSA of box = 2[0.12 + 0.2 + 0.15]

TSA of box = 0.94 m²

Cost of 20 boxes = 0.94 x 20 x 10

Cost of 20 boxes = RS. 188

Answer: 142.7

Step-by-step explanation:

Answer:

first one is A. I have no idea what the second is. good luck, it might be D.

Answer:

1) 3x³ - x² - 15x + 5

2) x² - 4

3) (5, 3)

4) f⁻¹(x) = 1/3x - 4

Step-by-step explanation:

1......................

Correct option is A.

2......................

Correct option is D.

3......................

Point (5, 3) is the inverse of point (3,5)

Correct option is C

4......................

To get the inverse of the function, switch over domain and range:

Correct option is D.

The values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.

Compute the mean and standard deviation for the new sample.

The mean of the original sample Soriginal is 0.625.

Moriginal = 0.625.

For the given sample of n = 8 scores: 0, 1, 1/2, 0, 3, 1/2,0,1.

We have to simplify the arithmetic by first multiplying each score by 2 to obtain a new sample of 0, 2, 1, 0, 6, 1, 0, and 2. Then, we will compute the mean and standard deviation for the new sample.

The calculations are:

\($\overline{x}_{\text{new}}=\frac{\sum x_{\text{new}}}{n}=\frac{0+2+1+0+6+1+0+2}{8}=1.25$$\)

This implies that the mean of the new sample is 1.25.Mnew = 1.25

Now, let us calculate the standard deviation.

To do so, we have to calculate the variance of the data. The variance is the average of the squared deviation from the mean.

That is,

\($\sigma_{\text{new}}^2=\frac{\sum(x_{\text{new}}-\overline{x}_{\text{new}})^2}{n-1}\)

\(=\frac{(0-1.25)^2+(2-1.25)^2+(1-1.25)^2+(0-1.25)^2+(6-1.25)^2+(1-1.25)^2+(0-1.25)^2+(2-1.25)^2}{8-1}\\=3.7321\)

This implies that the variance of the new sample is 3.7321.

Now, we calculate the standard deviation as:

\($\sigma_{\text{new}}=\sqrt{3.7321}=1.9322$\)

Thus, the standard deviation of the new sample is 1.9322.

Snew = 1.9322

We will use the formula for calculating the standard deviation of a new sample from an old sample, as follows:

\($\sigma_{\text{old}}=\frac{\sigma_{\text{new}}}{2}=\frac{1.9322}{2}=0.9661$$\)

So, the standard deviation of the original sample is 0.9661.

Soriginal = 0.9661

To find the mean of the original sample, we will use the following formula:

\($\overline{x}_{\text{old}}=\frac{\overline{x}_{\text{new}}}{2}=\frac{1.25}{2}=0.625$$\)

Therefore, the mean of the original sample is 0.625.

Moriginal = 0.625

Thus, the values for the mean and standard deviation for the original sample are Moriginal = 0.625 and Soriginal = 0.9661, respectively.

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Answer:

y = -3/4x -7

Step-by-step explanation:

hope this helps!

Answer:

c=120x+200y

Step-by-step explanation:

La expresión algebraica debería indicar que el valor total que debe cobrar Flor es igual a 10 que representa el número de bolsas por el resultado de la suma del precio de cada item por la cantidad, lo que se puede expresar de la siguiente forma:

c=10(12x+20y)

c=120x+200y

De acuerdo a esto, la expresión algebraica que permite saber cuánto debe cobrar Flor por 10 bolsas que contengan x cantidad de lápices y "y" cantidad de bolígrafos es c=120x+200y.

Answer:

After 250 messages

Step-by-step explanation:

45+0.25x=70+0.15x

O.25x-0.15x = 70-45

0.10x = 25

X = 25/.10

X = 250 messages

The 98% confidence interval for the mean number of personal computers is :

(2.50, 2.66).

To construct a 98% confidence interval for the mean number of personal computers, you'll need to use the sample mean (2.58), population standard deviation (0.48), and sample size (180). You'll also need to find the critical value (z-score) for a 98% confidence interval.

1. Determine the z-score for a 98% confidence interval: For a 98% confidence interval, the z-score is approximately 2.33 (you can find this in a standard normal distribution table).

2. Calculate the standard error: Standard error = (population standard deviation) / √(sample size) = 0.48 / √180 ≈ 0.0357

3. Multiply the z-score by the standard error: 2.33 * 0.0357 ≈ 0.0832

4. Construct the confidence interval:
- Lower limit = sample mean - (z-score * standard error) = 2.58 - 0.0832 ≈ 2.50
- Upper limit = sample mean + (z-score * standard error) = 2.58 + 0.0832 ≈ 2.66

So, the 98% confidence interval for the mean number of personal computers is (2.50, 2.66).

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Answer:

€120

Step-by-step explanation:

Let us represent

Ann = x

Brian = y

Carol = z

€400 is divided between Ann, Brian and Carol

Hence: x + y + z = €400...... Equation 1

Ann has twice as much as Brian

Hence:

x = 2y

Brian has three times as much as Carol.

y = 3z

z = y/3

We substitute

x + y + z = €400...... Equation 1

2y + y + y/3= €400

Multiply both sides by 3

2y × 3 + y × 3 + y/3 × 3 = €400 × 3

6y + 3y + y = €1200

10y = €1200

y = €1200/10

y = €120

How much does Brian receives ?

Since, Brian = y

Brian receives €120

Answer:

9/34

Step-by-step explanation

There are a total of 17 animals out of which 9 are Labradors

Probability of picking a labrador the first time is P(L1) = 9/17.

If the first animal picked is a labrador, then there will be 8 labradors and a total of 16 animals left. So he probability of picking a second labrador is Probabaility of picking second labarador given that the first pick was a labrador is expressed as P(L2 | L1) = 8/16 = 1/2

P(2 labradors) = P(L1 and L2) = 9/17 x 1/2 = 9/34

Given the expression:

Let's simplify the polynomials by adding them.

Here, the polynomials have like terms because their variables are the same and the expoenents of the variables are also equal.

Since the polynomials have like terms, let's add the coefficients.

Therefore, the simplified expression after adding is:

ANSWER:

Answer:

Step-by-step explanation:

In order for us to be able to find our answer, we need to show our work.

-3(x-y=3) → -3x + 3y = -9

                 +2x - 3y = -1

____________________________

                  -1x = -10

                   -1      -1

We need to divide -1 both sides in order for us to be able to find our x-value but there's more to this than just solving for X.

x = 10

x - y = 3

10 - y = 3

-10       -10

_________________

-y = -7

-1     -1

We need to divide -1 both sides in order for us to be able to find our y-value. Please note that each y is equivalent to an invisible 1.

y = 7

As a result, your answer will be B.

Answer:

m = 3

Step-by-step explanation:

Slope of first one is -1/3

Perpendicular therefore m = -(-1/3)^(-1) = 3

m = 3

Answer:

Given the equation line 4x+12y=8

Step-by-step explanation:

The equation is y=mx+5y=mx+5

The line passes through A(3,14)A(3,14)

Putting (x,y)=(3,14)(x,y)=(3,14), we have…

14=3m+514=3m+5

⟹3m=9⟹3m=9

⟹m=3

The missing length indicated on the right triangle is 120 units

To start with:

The missing length in the right triangle can be represented with the variable x

Next, we have the following equivalent ratio from the given triangle

64 : x = x : 289 - 64

Express the ratio as a fraction

64/x = x/(289 - 64)

Evaluate the difference on the right-hand side

64/x = x/225

Cross multiply in the above equation

x * x = 64 * 225

This gives

x^2 = 64 * 225

Take the square root of x^2 (do not approximate)

x = 64 * 225

Take the square root of 64 and 225 (do not approximate)

x = 64 * 225

Evaluate the product of 8 and 5

x = 120

Based on the given parameters, the missing length indicated on the right triangle is 120 units

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Answer:

The answer to your question is 152

Step-by-step explanation:

46+56+3+17+30= 152

I hope this helps!

Answer:

152

Step-by-step explanation:

46+56= 102. 102+3= 105. 105+17= 122. 122+30= 152

Answer:

\((2x+3)(2x+3)\)

Step-by-step explanation:

The given expression is

\(4x^2+12x+9\)

Here, a=4, b=12, c=9.

Step 1: Multiply \(a\cdot c=4\cdot 9=36\)

Step 2: Find the factors of ac that add to b.\(6\cdot 6=36\) and \(6+6=12=b\) So, two factors of ac are 6 and 6.

Step 3:\(4x^2+6x+6x+9\)

Step 4:\((4x^2+6x)+(6x+9)\)

Step 5:\(2x(2x+3)+3(2x+3)\)

Step 6:\((2x+3)(2x+3)\)

Therefore, the required factor form is \((2x+3)(2x+3)\). It can also written as \((2x+3)^2\).

Answer:

Possible answer: 5a/ -6

Step-by-step explanation:

Not 100% sure to be honest.

The product (3+√8)(3-√8) can be simplified using the difference of squares formula. The simplified form is 9 - 8 = 1.

To find the product (3+√8)(3-√8), we can use the difference of squares formula, which states that (a+b)(a-b) = a^2 - b^2.

In this case, we have (3+√8)(3-√8). Applying the difference of squares formula, we get:

(3+√8)(3-√8) = 3^2 - (√8)^2.

Simplifying further, we have:

= 9 - 8.

Finally, evaluating the expression, we find:

= 1.

Therefore, the product (3+√8)(3-√8) simplifies to 1.

In summary, by applying the difference of squares formula, we simplified the given product to the value of 1.

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