Consider the following figure:
The value of a is

Answer:

[tex]\sf b) \quad \dfrac{y^3}{4x}[/tex]

Explanation:

[tex]\sf \left(\dfrac{6x^2}{5y}\right) \left(?}\right) = \left(\dfrac{3xy^2}{10}\right)[/tex]

cross multiply variables

[tex]\sf ? = \left(\dfrac{3xy^2 (5y)}{10(6x^2)}\right)[/tex]

distribute inside parenthesis

[tex]\sf ? = \left(\dfrac{15xy^3}{60x^2}\right)[/tex]

remove parenthesis and simplify

[tex]\sf ? = \dfrac{y^3}{4x}[/tex]

Answer:

7 weeks, £35, and £21.

Step-by-step explanation:

Every week, Suzie saves £5 and gets £3 from her Mum. Altogether, Suzie gets £8 every week. All we need to do is divide 56 by 8, which gives us 7. Suzie will take 7 weeks to collect enough money. To find out how much she has saved and been given by her mum individually, we need only times these values by 7. 5x7=35, and 3x7=21.

The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.

The data shows that:

E(x) = 1

E(y) = 2

E(z) = 3

Var(X) = 2² = 4

Var(Y) = 4² = 16

Var(Z) = 5² = 25.

Cov(U, V) = 16

Var(U) = Var(Z - Y)

= 25 - 0 + 16

= 41

The correlation coefficient will be:

= -16/✓(20 × 41)

= -0.5587

The correlation coefficient between U and V is -0.5587 and it illustrates to at there's a negative relationship between U and V.

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By solving a quadratic equation we will see that the number can be:

8 or -5.

The product of a number N, and 3 less than the number, is equal to 40.

This is written as:

[tex]N*(N - 3) = 40[/tex]

Now we need to solve this for N.

[tex]N^2 - 3N = 40[/tex]

[tex]N^2 - 3N - 40 = 0[/tex]

Then we need to solve this quadratic equation:

[tex]N = \frac{-(-3) \pm \sqrt{(-3)^2 - 4*1*(-40)} }{2} \\\\N = \frac{3 \pm 13 }{2}[/tex]

Then we have two solutions:

These are the two possible solutions.

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Using the normal distribution, there is a 0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

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]

Researching this problem on the internet, the parameters are given as follows:

[tex]\mu = 150, \sigma = 9, n = 10, s = \frac{9}{\sqrt{10}} = 2.85[/tex]

The probability is one subtracted by the p-value of Z when X = 157, hence:

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

By the Central Limit Theorem

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

Z = (157 - 150)/2.85

Z = 2.46

Z = 2.46 has a p-value of 0.993.

1 - 0.993 = 0.007.

0.007 = 0.7% probability that the mean score for 10 randomly selected people who took the LSAT would be above 157.

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The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

The quadratic expression in its standard form is;

ax² + bx + c

Given the expression in the question;

x² - 2x + ------

Compared with the standard for a quadratic expression

Let the missing value be represented by "c"

x² - 2x + c

Now, to find the value of c, we divide the coefficient of x by 2 and then square the result.

Note that, coefficient of x is b

c = ( b/2 )²

We substitute

c = ( -2/2 )²

c = ( -1 )²

c = 1

The perfect square trinomial is x² - 2x + 1.

Hence, the value needed to complete the square of the expression ( x² - 2x + --- ) is 1.

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Answer: 4.9

Step-by-step explanation:

[tex]AB=\sqrt{(-4-3)^2 +(6-4)^2}=\sqrt{53}\\\\A'B'=\frac{2}{3}\sqrt{53} \approx \boxed{4.9}[/tex]

The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

According to the statement

we have given that the Smith family's sprinkler was 25L per hour and

Stewart family's sprinkler was 30L per hour and The families used their sprinklers for a combined total of 65 hours, resulting in a total water output of 1750L.

And we have to find the How long was each sprinkler used.

So, For this purpose,

The given statements in the equation form become:

Let Smith family's sprinkler be x

Let Stewart family's sprinkler be y then

The equation become

x + y = 65 -(1)

25x + 30y = 1750 -(2)

Here we use the elimination method.

So, Multiply (1) by 25 and (2) by 1 then

25x + 25y = 1625

25x + 30y = 1750

Now eliminate x from the equations then

-5y = -125

y = 25

then x value becomes

x + y = 65

x + 25 = 65

x = 40.

So, The Smith family's and Stewart family's sprinkler was used 40 and 25 hours.

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The theoretical probability of randomly getting a black counter is P = 2/5.

In this case, we have 8 black counters and 12 white counters, so there is a total of 20 counters.

We assume that all the counters have the same probability of being randomly selected, then the probability of randomly selecting a black counter is just given by the quotient between the number of black counters and the total number of counters.

There are 8 black counters and 20 in total, then the probability is given by:

P = 8/20

Now we can simplify that fraction to get:

P = 2/5

The theoretical probability of randomly getting a black counter is P = 2/5.

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Step-by-step explanation:

[tex] = \frac{6}{7} \times \frac{2}{3} \\ [/tex]

[tex] = \frac{12}{21} \\ [/tex]

Change into lowest term...

[tex] = \frac{4}{7} \\ [/tex]

...

The value of the probability P(A and D) is 0.30

Using the probabilities on the tree diagram, we have the following parameters

P(A) = 0.5

P(D/A) = 0.6

The probability P(A and D) is then calculated using the following formula

P(A and D) = P(A) * P(D/A)

Substitute the known values in the above equation

P(A and D) = 0.5 * 0.6

Evaluate the product

P(A and D) = 0.30

Hence, the value of the probability P(A and D) is 0.30

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Answer:

[tex]P(x) -0.1(x+1)(x-3)^2[/tex]

Step-by-step explanation:

So you can express a polynomial in factored form, where each factor of the polynomial is being multiplied by each other to get the original polynomial as such: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex] notice the a in front? Sometimes the value is 1, sometimes it's not, and I'm assuming it's not 1, since the y-intercept is given.

Anyways, when we express a polynomial in factored form: [tex]p(x) = a(x+a)(x+b)(x+c)...[/tex], it's pretty easy to see that -a, -b, and -c are roots, since if we plug in -a, the factor (x+a) becomes (-a + a) = 0, and since the factors are being multiplied by each other, the value p(-a) will be 0, since 0 * some value = 0.

The next thing to know is what multiplicity means. It essentially means when you have the same root "multiple times", or in other words it's the degree of the factor. For example: [tex]f(x) = (x+a)^3(x+b)^2(x+c) = (x+a)(x+a)(x+a)(x+b)(x+b)(x+c)[/tex], if you took each factor, you would see that the root -a shows up 3 times, thus the multiplicity is 3, which can also be determined by just looking at the initial degree... 3. The same thing goes for b and c, except for c, the degree isn't explicitly said, it's just 1.

Since we have a zero at x=3 one of the factors will be (x-3) since plugging in 3 to this makes it 0. But this has a multiplicity of 2, so the degree of the this factor is 2. So for we have the polynomial: [tex]p(x) = (x-3)^2[/tex]

Since we have a zero at x=-1, one of the factors will be at (x+1), since plugging in 1 into this makes the value 0. This has a multiplicity of 1, and you can write the degree 1, but if you don't explicitly write it, it can just be assumed to be 1, since a^1=a

So now we have the polynomial: [tex]p(x) = (x+1)(x-3)^2[/tex]

So let's just assume we have an "a" value in front as mentioned in the very beginning, we have the polynomial: [tex]p(x) = a(x+1)(x-3)^2[/tex] and we can solve for this value, using any point except for the zeroes. We can use the y-intercept given to solve for a

Plug in 0 as x (by definition of y-intercept) and set p(x) = -0.9

[tex]-0.9 = a(0+1)(0-3)^2[/tex]

Subtract/add values

[tex]-0.9 = a(1)(-3)^2[/tex]

Simplify

[tex]-0.9 = 9a[/tex]

Divide both sides by 9

-0.1 = a

So now let's plug this into our polynomial to get the final result!

[tex]P(x) -0.1(x+1)(x-3)^2[/tex]

The revenue function in terms of q will be 200q - 3q².

The following can be deduced based on the information given:

P(q) = 200 - 3q

C(q) = 75 + 80q - q²

The revenue function in terms of q will be:

= Price × Quantity

= (200 - 3q) × q

= 200q - 3q²

The profit will be:

= Total revenue - Total cost

= (200q - 3q²) - (75 + 80q - q²)

= 200q - 3q² - 75 + 80q + q²

= -2q² + 280q - 75

= 2q² - 280q + 75

The average cost function will be:

= Total cost / Quantity

= (75 + 80q - q²) / q

= 75/q + 80 - q

The marginal cost will be 80 - 2q.

The marginal revenue will be 200 - 6q.

The marginal cost when q = 20 will be:

= 80 - 2q

= 80 - 2(20)

= 80 - 40

= 40

The marginal revenue when q = 20 will be:

= 200 - 6q

= 200 - 6(20)

= 200 - 120

= 80

The company should decrease production from 20 units in order to gain more profit.

The production level that gives the largest profit for the company will be gotten by finding the second derivative for the profit function as illustrated in the question. The profit function is 2q² - 280q. Then the production level will be 4.

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The volume of the solid is which is a cone is 100.48 [tex]km^{3}[/tex].

Given a cone of radius 4 km and height being 6 km.

We are told to find the volume of the cone.

Volume is basically the amount of a substance that a container can hold in its capacity.Its value cannot be equal to zero or negative. It is basically amount of filling in a container.

Volume of cone is 1/3 [tex]\pi r^{2} h[/tex].

Volume =1/3 [tex]\pi 4^{2} *6[/tex]

=1/3 π*16*6

=32π

=32*3.14

=100.48[tex]km^{3}[/tex]

Hence if the radius of the cone is 4 km and height be 6 km then the volume of the cone is 100.48[tex]km^{3}[/tex].

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Answer:

B

Step-by-step explanation:

Every (x,y) pair is equal to each other, thus making them proportional :)

Answer:

[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]

=

[tex]\frac{ \sqrt{2} }{a + b} [/tex]

Step-by-step explanation:

[tex]\left(a-b\right)\sqrt{\frac{2}{a^2-b^2}}[/tex]

[tex](a - b)( \frac{ {2}^{ \frac{1}{2} } }{(a + b)(a - b)} )[/tex]

[tex] \frac{(a - b)( {2}^{ \frac{1}{2} }) }{(a - b)(a + b)} = \frac{ \sqrt{2} }{a + b} [/tex]

The area of this regular polygon is 46.8 square units

The given parameters are:

Perimeter, p = 54 m

Apothem, a = √3

The area of this regular polygon is then calculated as:

Area = 0.5 * Apothem * Perimeter

Substitute the known values in the above equation

Area = 0.5 * √3 *  54

Evaluate the product

Area = 46.8

Hence, the area of this regular polygon is 46.8 square units

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The slope of the graph is 1 / 5.

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Slope describes the steepness of a line. The slope of any line remains constant along the line.

Therefore,

slope  = y₂ - y₁ / x₂ - x₁

Hence, let's take two coordinates in the graph,

(2, 2)(7, 3)

x₁ =  2

x₂ = 7

y₁ = 2

y₂ = 3

Therefore,

slope = 3 - 2 / 7 - 2

slope = 1 / 5

Therefore, the slope of the graph is 1 / 5.

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a) [tex]\angle QST[/tex]

b) Arc QT

c) Arc QRS

d) 105 degrees

e) 255 degrees

Answer:

  no

Step-by-step explanation:

The angle subtended by the radius of the target at Emily's distance can be found using the tangent relation.

  tan(α) = opposite/adjacent = (1/4 ft)/(150 ft) = 1/600

The angle is found using the inverse relation:

  α = arctan(1/600) ≈ 0.095°

If Emily's aim is off by 0.2°, she will miss the target by several inches.

__

Additional comment

Emily's projectile will miss her aiming point by ...

  (150 ft)tan(0.2°) ≈ 0.524 ft ≈ 6.28 in

The monetary policy that the Central Bank is using to address the downturn in the economy is the reduction of the reserve requirement from 17% t 14%.

It should be noted that the monetary policy is the set of actions to control money supply in the economy.

The macroeconomic issues resulting from the pandemic on Trinidad and Tobago are that there are less money in circulation and there's a reduction in the standard of living.

The reduction of the reserve requirement will impact the money supply as it will lead to more money in circulation.

Complete question:

1. What form of monetary policy can the Central Bank use to address the downturn in the economy resulting from the pandemic?

2. Identity and explain two macroeconomic issues resulting from the pandemic on Trinidad and Tobago.

3. Identify how the reserve requirement will impact the money supply.

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Answer:

6t tomato plants

Step-by-step explanation:

There are 6 rows, Tamala places t in each row. We multiply 6 by t.

If t were 5, the tomato plants would be 30 since we multiply the rows by the number of tomato plants

Answer:

6t

Step-by-step explanation:

number of rows × number of plants per row = total number of plants

6 × t = 6t

Answer: 6t

Answer:

Step-by-step explanation:

e^-6 = 1/e^6 = about 0.00248

The number sets that each number belong too are given as follows:

1. Rational.

2. Irrational.

3. Rational.

4. Whole.

5. Whole.

6. Integer.

It is a terminating decimal, hence it is a rational number.

The square root of 5 is not exact, hence it is a non-terminating decimal, meaning that is an irrational number.

It is a fraction, hence it is a rational number.

It is a positive non-decimal number, hence it is a whole number.

The square root of 16 is of 4, which is a positive non-decimal number, hence it is a whole number.

The result of the division is of -4, which is a negative non-decimal number, hence it is an integer number.

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Using the combination formula, it is found that six of these five-ball selections contain exactly five red balls.

The order in which the balls are selected is not important(as balls A, B, C, D and E is the same outcome as balls B, A, C, D and E), hence the combination formula is used to solve this question. If the order was important, then the permutation formula would be used.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, five red balls can be chosen from a set of six, hence the number of selections is the combination of 5 elements from a set of 6, that is calculated from the formula given above:

[tex]C_{6,5} = \frac{6!}{1!5!} = 6[/tex]

Hence six of these five-ball selections contain exactly five red balls.

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The value of the evaluation of logarithm e^in4 is 4

Given the expression as;

e^in4

To put in logarithmic form, equate to the power of the "Lin,ln value"

Now, let's equate it to the value of the exponential

e^in4 = 4

We have that'

[tex]loge x = loge 4[/tex]; this is the logarithmic form of the expression but we need to find the value of 'x'

To find the value, let's cancel out the like variables, we have

[tex]x = 4[/tex]

Then we have the value to be

x = 4

Thus, the value of the evaluation of logarithm e^in4 is 4

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The equation for the horizontal asymptote will be y = -2.

Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:

y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)

= y = -2/1

= y = -2

The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0

= x + 3 = 0

= x = -3

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Answer:60 ml

Step-by-step explanation:20 % of 300 = 60 and snce the rest of the the l are coffee thats 20%

The measure of the unknown angles are as shown below;

m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

An angle is the point where the two lines meet. From the given diagram, the lines B and D are parallel to each other with a transversal.

Given the following parameters

m<1 = 52 degrees

From the given diagram, the following are true

m<1 = m<3 (corresponding angle)

m<3 = m<8 (vertical angles)

m<1 = m<6 (vertical angles)
m<2 = m<5 (vertical angles)

m<4 = m<7 (vertical angles)

Also;

m<1 + m<2 = 180

m<2 = 180 - m<1

m<2 = 180 - 52
m<2 = 128 degrees = m<4

m<5 = 128 degrees

m<6 = 52 degrees

m<3 = 52 degrees = m<8

m<7 = 128 degrees

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