(b)
Factorise the following:
4x²-4

(2) 8y2 - 2

5n²-20
(6)
12x²y-27y³ (10)
3p²q-48q³
(14)
-x² +16
(18)
-3n³+3n
(22)
(5)
(9)
(13)
(17)
(21)
8y²-2
100m² - 25
75a²-126²
2ax * - 50a
-9x² +1
-8b +32b

Answer:279 cm2

Step-by-step explanation:

The area of a rhombus is calculated by multiplying the length of the base by the height.

The base of the rhombus is 18 cm and the height is 15.5 cm.

Therefore, the area of the rhombus is:

18 cm × 15.5 cm = 279 cm²

So the answer is 279 cm².

Jenny can completely fill the glass with 1 1/11 (one and one eleventh) gallons of water approximately 11 times by using division method.

What is division?

Division is an arithmetic operation that involves splitting a quantity or number into equal parts or groups. It is the multiplication inverse operation.

To determine how many times Jenny can completely fill the glass with 1 1/11 gallons of water, we need to calculate the number of times 1 1/11 gallons can be divided by 1 1/11 gallons.

1 1/11 gallons can be represented as 12/11 gallons. Dividing 12/11 by 1 1/11 gives us:

(12/11) ÷ (1 1/11) = (12/11) ÷ (13/11) = (12/11) × (11/13) = 12/13

Therefore, 1 1/11 gallons can be divided by 1 1/11 gallons approximately 12/13 times.

Since 12/13 is approximately equal to 0.923, Jenny can completely fill the glass approximately 0.923 * 11 = 10.153 times.

Rounding to the nearest whole number, Jenny can completely fill the glass approximately 11 times.

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The measures are m ∠RBM = 52.2°, m ∠WNH = 23.5° and m ∠WKH = 80.8°

Given that a triangle BKN, and H is the incenter of the triangle, we need to find the missing measures,

We know that the incenter of a triangle is the point where the angle bisectors meet,

So, we can say, BW, MN and RK are the angle bisectors.

So, using the property of angle bisectors, we have,

1) m ∠RBM = 2 × ∠RBH

m ∠RBM = 52.2°

2) m ∠WNH = ∠WNR / 2

m ∠WNH = 23.5°

3) m ∠WKH = 2 × ∠MKH

m ∠WKH = 80.8°

Hence the measures are m ∠RBM = 52.2°, m ∠WNH = 23.5° and m ∠WKH = 80.8°

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The general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false

The general fertility rate refers to the number of live births reported in an area during a given time interval per 1,000 women of reproductive age (usually defined as 15 to 44 years old) in the same area.

Therefore, it is a rate or a ratio that expresses the number of births in relation to the number of women of reproductive age in a population.

Hence, the statement is False that the general fertility rate refers to the number of live births reported in an area during a given time interval divided by the number of women age 15 to 44 years in the area is false

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x = 58/3 = 19 1/3 = 19.333333

I'm attaching a screenshot showing this rule.

I'm using the letters from the rule shown on the screenshot bc this is the common formula used.

AB x AD = AC x AE

In your problem:

AB = 16+26=42
AD = 16

AC = 18+x

AE = 18

Substitute:

AB x AD = AC x AE

42 x 16 = (18+x)(18)

672 = 18x+18*18

672 = 18x + 324

672-324 = 18x

348 = 18x

x = 348/18 = 58/3 = 19 1/3 = 19.333333

Check:

AB x AD = AC x AE

42x16 = (18+(58/3))(18)

672 = 672

The distance across the lake PQ will be 496.8 meters.

Given that:

Sides, OS = 210 m, SQ = 70 m, and RS = 124.2 m

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The distance across the lake PQ is calculated as,

PQ / RS = OQ / SQ

PQ / 124.2 = (210 + 70) / 70

PQ / 124.2 = 280 / 70

PQ = 496.8 m

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The length of side LJ is equal to 11.48 units.

In Mathematics and Geometry, two (2) triangles are only similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the diagram, we can logically deduce the following proportion based on the congruent sides:

XY/JK = YZ/KL = ZX/LJ

8.7/12.18 = 8.2/LJ = 7.8/KL

By cross-multiplying and solving for the length of side LJ, we have the following:

LJ = (12.18 × 8.2)/8.7

LJ = 11.48 units.

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Answer:

x=9

Step-by-step explanation:

Since x is a midsegment this means that it bisects the side with a length of 16. Now using ratio and proportion between the large triangle and the small triangle to find the length of x you have to do

18/16=x/(16/2)

16x=18(8)

x= 144/16

x=9

The coefficient of determination will be 0.36.

the coefficient of correlation measures the strength and direction of the linear relationship between two variables, while the coefficient of determination measures the proportion of the total variation in one variable that is explained by the other variable.

The coefficient of determination is equal to the square of the coefficient of correlation, so if the coefficient of correlation is -0.6, we can square it to get 0.36. Therefore, the coefficient of determination will be 0.36.

knowing the coefficient of correlation between two variables can help us determine the coefficient of determination, which represents the proportion of the variation in one variable that is explained by the other variable.

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According to the information, The Least Common Multiple (LCM) and the greatest common divisor (GCD) allow us to simplify fractions and solve proportion problems.

The Least Common Multiple (LCM) and  greatest common divisor (GCD) are two ways to calculate the smallest number that is a multiple of all given numbers (LCM) and is the largest number that is a common divisor of all the given numbers (GCD)

The usefulness of the LCM and GCD lies in the fact that they allow us to simplify fractions and solve proportion problems. In addition, they are useful in factoring polynomials and solving linear equations.

Note: This question is in Spanish. The answer is in English
Question:
What is th least common multiple and the greatest common divisor?

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The volume of the cube is greater than 5.4 cubic inches.

The volume of a cube of side length a is given by the cube of the side length, as follows:

V = a³.

The side length in the context of this problem is given as follows:

a = 5.4 in.

Hence the volume of the cube is given as follows:

V = 5.4³

V = 157.5 cubic inches.

(to obtain the volume of the cube, we apply the formula obtaining the cube of the side length).

157.5 > 5.4, hence the volume of the cube is greater than 5.4 cubic inches.

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Yes, since the set of invertible matrices is closed under addition and scalar multiplication and contains the zero matrix.

Yes, since the set of symmetric matrices is closed under addition and scalar multiplication and contains the zero matrix.

Yes, since the set of matrices with integer entries is closed under addition and scalar multiplication and contains the zero matrix.

Yes, since the set of upper triangular matrices is closed under addition and scalar multiplication and contains the zero matrix.

No, since the set of singular matrices is not closed under scalar multiplication.

Yes, since the set of matrices with trace 0 is closed under addition and scalar multiplication and contains the zero matrix.

No, since the set of matrices in reduced row-echelon form is not closed under addition.

No, since the set of matrices with all zeros in the first row is not closed under addition.

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answer

(1.2, 1) if its asking what i think it is

Step-by-step explanation:

Answer:

p(girl) = 12/31

Step-by-step explanation:

p(event) = (number desired outcomes)/(total number of possible outcomes)

Here, we have 12 girls and 19 boys. The total is 12 + 19 = 31. When we pick one out of all of them, we are picking one out of 31, so the total number of possible outcomes is 31, every single one of the girls and boys.

The desired outcome is picking one girl. How many ways can you pick a girl? The answer is 12 since there are 12 different girls. The number of desired outcomes is 12.

p(girl) = (number of desired outcomes)/(total number of possible outcomes)

p(girl) = 12/31

so hmmm let's call them P(2, 4) and Q(10, 8)

[tex]\textit{internal division of a segment using a fraction}\\\\ P(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad Q(\stackrel{x_2}{10}~,~\stackrel{y_2}{8})~\hspace{8em} \frac{1}{4}\textit{ of the way from P to Q} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_2}{10}-\stackrel{x_1}{2}~~,~~ \stackrel{y_2}{8}-\stackrel{y_1}{4})\qquad \implies \qquad \stackrel{\stackrel{\textit{component form of}}{\textit{segment PQ}}}{\left( 8 ~~,~~ 4 \right)} \\\\[-0.35em] ~\dotfill\\\\ \left( \stackrel{x_1}{2}~~+~~\frac{1}{4}(8)~~,~~\stackrel{y_1}{4}~~+~~\frac{1}{4}(4) \right) \implies \boxed{(4~~,~~5)}[/tex]

The trigonometric ratios for tangent indicates that the height of the kite, where the distance between the observers is 500 m, and the angle of elevation are 30° and 20° is h ≈ 492.4 meters

Trigonometric ratios are mathematical functions that express the relationships between an interior angle of a right triangle and two of the sides of the triangle.

The distance between the two observers = 500 m

The angle of observation of the kite by each of the two observers = 30° and 20°

Let h represent the height of the kite, and let x represent the horizontal distance from the kite to the closer observer (The observer observing with an angle of elevation of 30°), we get;

The horizontal distance from the kite to the other observer = x + 500

Therefore, according to the trigonometric ratios for tangent;

tan(20°) = h/(x + 500)

tan(30°) = h/x

h = x × tan(30°)

Therefore;

tan(20°) = (x × tan(30°))/(x + 500)

(x + 500) × tan(20°) = x × tan(30°)

(x + 500) × 0.36397 = x × (1/(√3))

0.36397·x + 500 × 0.36397 = x/√3

x/√3 - 0.36397·x = 500 × 0.36397 = 181.985

x·(1/√3 - 0.36397) = 181.985

x = 181.985/((1/√3 - 0.36397))

h = 181.985/((1/√3 - 0.36397)) × tan(30°)

h = 181.985/((1/√3 - 0.36397)) × (1/√3) ≈ 492.4

The height of the kite, h ≈ 492.4 meters

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The probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%.

To find the probability of having both lab work and a referral, we can use the formula P(A and B) = P(A) + P(B) - P(A or B), where A and B are events and P is the probability of those events occurring.

Let A be the event of having lab work and B be the event of having a referral.

We know that P(A) = 0.41, P(B) = 0.53, and P(neither A nor B) = 0.21.

To find P(A or B), we can use the formula P(A or B) = P(A) + P(B) - P(A and B). We don't know P(A and B), but we can find it by using the fact that P(neither A nor B) = 0.21:

P(A or B) = P(A) + P(B) - P(A and B)
1 - P(neither A nor B) = P(A) + P(B) - P(A and B)
1 - 0.21 = 0.41 + 0.53 - P(A and B)
0.78 = 0.94 - P(A and B)
P(A and B) = 0.16

Therefore, the probability of having both lab work and a referral is 0.16.


The probability of having both lab work and a referral during a visit to a primary care physician's office can be found using the formula P(A and B) = P(A) + P(B) - P(A or B). Given that the probability of having lab work is 0.41, the probability of having a referral is 0.53, and the probability of having neither is 0.21, we can solve for P(A and B) and get a probability of 0.16. This means that there is a 16% chance of a patient having both lab work and a referral during their visit.


In conclusion, the probability of having both lab work and a referral during a visit to a primary care physician's office is 0.16 or 16%. This calculation was done using the formula P(A and B) = P(A) + P(B) - P(A or B), with the probabilities of having lab work, a referral, and neither being given.

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Answer:

9.25 inches

Step-by-step explanation:

9.25 inches

Answer:U₁ = 2
.

Step-by-step explanation:

Un+1 = 2U₁ + 6 (Equation 1)

Uo = 10

We want to find U₁. We can start by using Equation 1 with n = 1 to get:

U2 = 2U₁ + 6

We can then use the value of Uo = 10 to find U₂ as follows:

U₂ = 2U₁ + 6

U₂ = 2U₁ + 2(3)

U₂ = 2(U₁ + 3)

We can then use the value of U₂ to find U₃:

U₃ = 2U₂ + 6

U₃ = 2(2U₁ + 2(3)) + 6

U₃ = 4U₁ + 12 + 6

U₃ = 4U₁ + 18

We can keep using this process to find Un in terms of U₁, until we reach the value of n we need. For example, we can find U₄ as follows:

U₄ = 2U₃ + 6

U₄ = 2(4U₁ + 18) + 6

U₄ = 8U₁ + 36

So we have:

Uo = 10

U₂ = 2(U₁ + 3)

U₃ = 4U₁ + 18

U₄ = 8U₁ + 36

and so on.

To find U₁, we need to use the equation for U₂:

U₂ = 2(U₁ + 3)

Substituting U₂ = 10 (from the given value of Uo), we get:

10 = 2(U₁ + 3)

Simplifying, we get:

5 = U₁ + 3

Subtracting 3 from both sides, we get:

U₁ = 2

Therefore, U₁ = 2.

Janet's Athletic Company can ship 15 basketballs in the round containers with a volume of 208,592.

To figure out how many basketballs Janet's Athletic Company can ship, we need to divide the volume of the round containers by the volume of each basketball. So we can set up the following equation:
Number of basketballs = Volume of round containers / Volume of each basketball
Plugging in the given values, we get:
Number of basketballs = 208,592 / 13906
Simplifying the division, we get:
Number of basketballs = 15
Therefore, Janet's Athletic Company can ship 15 basketballs in the round containers with a volume of 208,592.

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Answer:

x + (x + 1) + (x + 2) is an example, or

x x + 1 (x + 1) + 1 = x + 2

Step-by-step explanation:

Therefore, the probability distribution of x is:

x    P(X=x)

0    1/64

1    3/64

2    9/64

3    27/64

Let's use a probability tree to determine the probability distribution of x, the number of tails observed after 3 tosses of a biased coin where tails is three times as likely as heads.

On the first toss, the probability of observing tails is 3/4, and the probability of observing heads is 1/4. Let's label the branches T and H, respectively.

For each of the T and H branches, we repeat the same probabilities for the second and third tosses, resulting in the following probability tree:

        / T \

    / T /     \ H \

   /   /       \   \

  T   H         T   H

 / \ / \       / \ / \

T  T T  H     T  H T  H

Now, we can determine the probability of each possible outcome for x, the number of tails observed after 3 tosses:

x = 0: This can only occur if all three tosses are heads (H, H, H). The probability of this is (1/4) * (1/4) * (1/4) = 1/64.

x = 1: This can occur in three ways: (T, H, H), (H, T, H), and (H, H, T). The probability of each is (3/4) * (1/4) * (1/4) = 3/64.

x = 2: This can occur in three ways: (T, T, H), (T, H, T), and (H, T, T). The probability of each is (3/4) * (3/4) * (1/4) = 9/64.

x = 3: This can only occur if all three tosses are tails (T, T, T). The probability of this is (3/4) * (3/4) * (3/4) = 27/64.

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Answer: To determine the time it would take to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000, we can use the continuous compound interest formula:

A = Pe^(rt)

Where:

A = the final amount in the account ($5000 in this case)

P = the initial amount in the account ($3400 in this case)

e = the mathematical constant e (approximately equal to 2.71828)

r = the annual interest rate (0.12% = 0.0012 as a decimal)

t = the time in years

We can rearrange this formula to solve for t:

t = ln(A/P) / r

Substituting the values given, we get:

t = ln(5000/3400) / 0.0012

t = 28.58 years (rounded to two decimal places)

Therefore, it would take approximately 28.58 years to save $3400 in an account with a 0.12% interest rate compounded continuously to end up with $5000.

Step-by-step explanation:

Yes, it is possible to solve x(t) for t and substitute it into y(t) to eliminate the parameter t and write it as a rectangular equation with x and y instead.

Starting with the given equation:

x(t) = 0.5507t^2 - 1.5393t - 86.1

To solve for t, we can use the quadratic formula:

t = [-(-1.5393) ± sqrt((-1.5393)^2 - 4(0.5507)(-86.1))]/(2(0.5507))

Simplifying the equation:

t = [1.5393 ± sqrt(1.5393^2 + 190.2122)]/1.1014

t = [1.5393 ± 13.9769]/1.1014

t = -11.098 or 25.682

Since we're interested in the positive value of t, t = 25.682.

Now, substituting t = 25.682 into y(t):

y(t) = 0.5054t - 78.9

y(25.682) = 0.5054(25.682) - 78.9

y(25.682) = 1.504

Therefore, the rectangular equation for the given parametric equations is:

x = 0.5507t^2 - 1.5393t - 86.1

y = 0.5054t - 78.9

Substituting t = 25.682:

x = 358.6

y = 1.504

So the rectangular equation is:

(x, y) = (358.6, 1.504)

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Answer:

a) 1 : 3 and 1 : 27. b) 1728 inches³

Step-by-step explanation:

a) if ratio of areas is 1:9, then the ratio of lengths is √1 : √9 = 1:3

ratio of volumes is 1³ : 3³ = 1 : 27

b) volume of smaller = 64.

ratio of volumes = 1 : 27

volume of larger sphere = 27 X 64 = 1728 (inches³)

The length of the arc is approximately 4.5 to the nearest 10th.

To find the length of the arc intercepted by an angle in a circle, we can use the formula:

Arc length = radius × angle (in radians)

In this case, the radius is 4.5, and the angle is 1 radian. So, we can calculate the arc length as follows:

Arc length = 4.5 × 1 ≈ 4.5

Therefore, the length of the arc is approximately 4.5 to the nearest 10th.

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b)i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward. b)ii)  we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5. b)iii) the only value of x when y = 1 is x = 2.

a)

| x | y

| -3 | 12

| -2 | 1

| -1 | -4

| 0 | -3

| 1 | -2

| 2 | -3

| 3 | 0

b) i) The curve that matches y = x² - 2x - 3 is the middle one, which is a parabola opening upward.

ii) To estimate the value of y when x = 2.5, we can use the values of y when x = 2 and x = 3 to find the average rate of change, and then add or subtract that from the value of y when x = 2 or x = 3, respectively.

Using x = 2 and x = 3, we have:

Average rate of change = (y(3) - y(2)) / (3 - 2) = 3

So we can estimate that y(2.5) ≈ y(2) + 3/2 = -3 + 3/2 = -1.5.

iii) To find the values of x when y = 1, we can set y = 1 in the equation y = x² - 2x - 3 and solve for x:

x² - 2x - 3 = 1

x² - 2x - 4 = 0

(x - 2)² = 0

x - 2 = 0

x = 2

So the only value of x when y = 1 is x = 2.

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