Factorise fully 15x² + 10x​

Answer:

The True answer is -2>-3

Answer: 4.5

Step-by-step explanation:

2 + 0.5x

x = 5

2 + 0.5 ( 5 )

2 + 2.5

2 + 2.5 = 4.5

Hope this helps!

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Type II error in this context: The chef believes the complaint rate is not less than 8%, when in fact it is less than 8%

Consequence: The chef continues to use the new recipe but experiences a large number of unsatisfied customers.

A Type II error, in the context of hypothesis testing, occurs when the null hypothesis (H₀) is not rejected even though it is false. In other words, it's the failure to reject a false null hypothesis.

In this scenario, the null hypothesis states that the complaint rate is 8%, and the alternative hypothesis (Hₐ) states that the complaint rate is less than 8%.

A Type II error would occur if the chef believes that the complaint rate is not less than 8% (failing to reject the null hypothesis), when in fact it is less than 8% (the alternative hypothesis is true).

Consequences of a Type II error in this context:

The consequence of a Type II error would be that the chef continues to use the new gluten-free recipe for the topping even though the actual complaint rate is less than 8%.

This means that the chef would miss out on an opportunity to improve the recipe and potentially satisfy more customers.

In this case, the chef might continue to experience a significant number of unsatisfied customers who might have been pleased with an improved recipe.

This could lead to negative customer reviews, loss of customer loyalty, and a potential negative impact on the restaurant's reputation and business.

To summarize:

Type II error in this context: The chef believes the complaint rate is not less than 8%, when in fact it is less than 8%.

Consequence: The chef continues to use the new recipe but experiences a large number of unsatisfied customers, potentially harming the restaurant's reputation and business.

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A Type II error in this scenario would occur if the chef wrongly assumes the complaint rate is less than 8%, leading to continued use of the disliked recipe and unsatisfied customers.

In this context, a Type II error in the chef's hypothesis test would occur if the chef believes the complaint rate for the new gluten-free recipe is less than 8%, when in fact, it is not. That means the chef is under the false impression that the customers are more satisfied with the new recipe than they truly are. The consequence would be that the chef continues to use the new recipe, despite a higher complaint rate. This would lead to a significant number of unsatisfied customers because the recipe is not meeting their taste preferences as much as the chef thinks. This could subsequently affect the restaurant's reputation and customer loyalty.

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The amount of sugar in the entire shipment is 97(1)/(2) tons.

We are given that a shipment of sugar fills 2(1)/(5) containers. If each container holds 3(3)/(4) tons of sugar, we need to find the amount of sugar in the entire shipment.

Step-by-step explanation:

One container of sugar holds 3(3)/(4) tons of sugar. There are 2(1)/(5) containers of sugar in the shipment.

Amount of sugar in one container = 3(3)/(4) tons

Amount of sugar in 2(1)/(5) containers

= 2(1)/(5) × 3(3)/(4) tons

= 13/5 × 15/4 = 195/20

= 97(1)/(2) tons

Therefore, the amount of sugar in the entire shipment is 97(1)/(2) tons.

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If we want to provide a 99% confidence interval for the mean of a population, the confidence coefficient will be 0.99. This means that there is a 99% probability that the true population mean falls within the calculated interval.

The confidence coefficient for a confidence interval represents the level of confidence we have in our estimate.

In the case of a 99% confidence interval, the confidence coefficient is 0.99. This means that we are 99% confident that the true population mean falls within the calculated interval. The confidence coefficient is derived from the desired level of confidence, which is typically expressed as a percentage.

A higher confidence level corresponds to a larger confidence coefficient. In practical terms, a 99% confidence interval indicates that if we were to repeat the sampling process multiple times and construct 99% confidence intervals, approximately 99% of those intervals would contain the true population mean.

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Answer:

5 is the answer

Step-by-step explanation:

The equation of the line that is parallel to y = -3x + 6 is: y = -3x - 20.

The equation of the line that is perpendicular to y = -3x + 6 is: y = 1/3x + 20/3.

Recall the following facts:

Given the equation of a line as y = -3x + 6, the slope of the line is m = -3. This implies that, the line that is parallel to y = -3x + 6 will have the same slope of m = -3, and the slope of the line that is perpendicular to y = -3x + 6 will be m = 1/3.

To write the equation of the perpendicular line, substitute m = 1/3 and (a, b) = (-8, 4) into y - b = m(x - a):

y - 4 = 1/3(x - (-8))

y - 4 = 1/3x + 8/3

y = 1/3x + 8/3 + 4

y = 1/3x + 20/3

To write the equation of the parallel line, substitute m = -3 and (a, b) = (-8, 4) into y - b = m(x - a):

y - 4 = -3(x - (-8))

y - 4 = -3x - 24

y = -3x - 24 + 4

y = -3x - 20

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The Stackelberg outcome is represented by the intersection of the best-response function of firm 2 with the reaction function of firm 1.

In this problem, we are given the demand function Q = 150 - P and two firms with no production costs.

We are asked to find the subgame-perfect equilibrium of the Stackelberg version of the game where firm 1 chooses q1 first and then firm 2 chooses q2. We are also asked to add an entry stage after firm 1 chooses q1, in which firm 2 decides whether to enter, and compute the threshold value of K2 above which firm 1 prefers to deter firm 2's entry.

Finally, we are asked to represent the Cournot, Stackelberg, and entry-deterrence outcomes on a best-response function diagram.

In the Stackelberg version of the game, firm 1 chooses q1 first and firm 2 chooses q2 based on the quantity chosen by firm 1.

The subgame-perfect equilibrium is q1 = 75 and q2 = 37.5. When we add an entry stage, we find that firm 2 will only enter the market if K2 < 37.5. If K2 > 37.5, firm 1 will deter firm 2's entry.

The threshold value of K2 is 37.5. We can represent the outcomes of the Cournot, Stackelberg, and entry-deterrence games on a best-response function diagram.

The Cournot outcome is represented by the intersection of the best-response functions of the two firms.

f the best-response function of firm 2 with the horizontal line at q2 = 0, which represents the situation where firm 1 deters firm 2's entry by choosing a high quantity.

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Answer:

yea i can help

Step-by-step explanation:

Answer:

MN = 20

QR = 80

PR = 100

AB = 76

The standard deviation of the amount paid for monthly water usage is $35.25

From the summary statistics, we have:

Standard deviation, σ = 2350

Rate = $0.015

The standard deviation of the amount is calculated using:

σ = Standard deviation * rate

This gives

σ = 2350 * $0.015

Evaluate

σ = $35.25

Hence, the standard deviation of the amount paid for monthly water usage is $35.25

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Answer:

521.96

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

Explanation:

Here, we want to solve for the missing parts of the triangle

we have the value of a as 5 and b as 12

What we have is a right triangle since one of the internal angles is 90 degrees

We can start by getting the value of c

Mathematically, we can get this by the use of Pythagoras' theorem

c faces the right angle and thus, it is the hypotenuse of the triangle

Mathematically, the square of the length of the hypotenuse equals the sum of the squares of the length of the two other sides of a right anlged triangle

We have this as:

Now, we need to get the other internal angles

We can use the appropriate trigonometric ratios here

The question specifically asks to get the value of internal angle A

From what we have, A faces a and that makes a the opposite

The trigonometric ratio that compares the opposite and the hypotenuse is the sine

It is the ratio of the length of the opposite to the length of the hypotenuse

Mathematically, we have this as:

Answer:

There is no attachment

Step-by-step explanation:

The derivative of f(x) = -4e^(5x) with respect to x is -20e^(5x). The chain rule is used to differentiate the composite function, applying the derivatives of the outer and inner functions.

To differentiate the function f(x) = -4e^(5x), we can use the chain rule of differentiation.

The chain rule states that if we have a composite function of the form f(g(x)), where f(u) and g(x) are differentiable functions, then the derivative of f(g(x)) with respect to x is given by f'(g(x)) * g'(x).

Applying the chain rule to our function:

f(x) = -4e^(5x)

Let u = 5x, so we have f(x) = -4e^u.

Now, differentiating f(u) = -4e^u with respect to u gives us f'(u) = -4e^u.

Differentiating u = 5x with respect to x gives us du/dx = 5.

Now, applying the chain rule, we have:

df/dx = f'(u) * du/dx = (-4e^u) * 5

Substituting u = 5x back into the equation, we get:

df/dx = (-4e^(5x)) * 5

Therefore, the derivative of f(x) = -4e^(5x) with respect to x is df/dx = -20e^(5x).

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The given question is incomplete, the complete question is,

Differentiate the following function.

f(x)=-4e^(5x)

Answer:

ur missing a x in the equation

Answer:

x = 8

y = -8

Step-by-step explanation:

1. у = - 2х +8

2. - 7x - бу = - 8

Substitute y in equation 2 using equation 1

-7x - 6(-2x+8) = -8

-7x -(-12x) - 48 = - 8

Two negatives = positive

-7x + 12x - 48 = -8

5x - 48 = - 8

Plus 48 on both sides

5x = 40

Isolate x by dividing both sides by 5

x = 8

Using the value of x, find what y is.

y = -2(8) + 8

y = -16 + 8

y = -8

Hope this helps :)

Have an awesome day!

Answer:

0.2343 m per year or 1/4 m per year

Step-by-step explanation:

3/8 divided by 1 3/5 = 0.2343 m per year = 1/4 m per year

After working 8 hours and grading 9 papers per hour, it is expected Autumn has 11 papers left.

To calculate the number of papers she can grade during this time, let's use the rate provided:

This means in 9 hours she can grade 72 papers.

Now, let's calculate the number of papers left:

Based on this, the total of papers left after working for 8 hours is 11 papers.

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we have found constants c1, c2, c3, and c4 such that f(t) can be expressed as a linear combination of the polynomials in s.

To determine whether s is a basis for p3, we need to check whether the polynomials in s are linearly independent and span p3.

First, we check for linear independence by setting up the equation:

c1(3 − 4t2 t3) + c2(−4 t2) + c3(3t t3) + c4(5t) = 0

where c1, c2, c3, c4 are constants. This equation must hold true for all values of t in order for the polynomials in s to be linearly independent.

Simplifying the equation and grouping like terms, we get:

(3c1 + 3c3)t3 + (-4c1 - 4c2)t2 + (3c3)t + (5c4) = 0

Since this equation must hold for all values of t, each coefficient must be equal to zero. Solving for c1, c2, c3, and c4, we get:

c1 = 0
c2 = 0
c3 = 0
c4 = 0

Therefore, the polynomials in s are linearly independent.

Next, we need to check if the polynomials in s span p3. This means that any polynomial in p3 can be expressed as a linear combination of the polynomials in s.

Let f(t) = at3 + bt2 + ct + d be an arbitrary polynomial in p3.

We need to find constants c1, c2, c3, c4 such that:

c1(3 − 4t2 t3) + c2(−4 t2) + c3(3t t3) + c4(5t) = at3 + bt2 + ct + d

Equating the coefficients of like terms, we get the following system of equations:

3c1 = a
-4c1 - 4c2 = b
3c3 = c
5c4 = d

Solving for c1, c2, c3, and c4, we get:

c1 = a/3
c2 = (-4a-3b)/12
c3 = c/3
c4 = d/5

Therefore, we have found constants c1, c2, c3, and c4 such that f(t) can be expressed as a linear combination of the polynomials in s.

Since the polynomials in s are linearly independent and span p3, we can conclude that s is a basis for p3.

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To find the volume generated by rotating the function g(x) = -1(x + 5)² around the x-axis over the domain [-3, 20], we can use the method of cylindrical shells.

The volume of a cylindrical shell can be calculated as V = ∫[a,b] 2πx f(x) dx, where f(x) is the function and [a,b] represents the domain of integration.

In this case, we have g(x) = -1(x + 5)² and the domain [-3, 20]. Therefore, the volume can be expressed as:

V = ∫[-3,20] 2πx (-1)(x + 5)² dx

To evaluate this integral, we can expand and simplify the function inside the integral, then integrate with respect to x over the given domain [-3, 20]. After performing the integration, the resulting value will give the volume generated by rotating the function g(x) = -1(x + 5)² around the x-axis over the domain [-3, 20].

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Answer:

\( \large{ \tt{❃ \: EXPLANATION}} : \)

\( \large{ \tt{❁ \: LET'S \: START}} : \)

\( \boxed{ \large{ \tt{❈ \: y = mx + c}}}\)

- Plug the values :

\( \large{ \tt{↬y = 12x + ( - 5)}}\)

\( \large{ \tt{↬ \: y = 12x - 5}}\)

\( ↬\large{\tt{12x - 5 = y}}\)

\(↬ \large{ \boxed{ \bold{ \tt{12x - y - 5 = 0}}}}\)

\( \tt{✺ \: STUDY \: MORE \: PROCASTINATE \: LESS !\:♪ }\)

۵ Hope I helped! ツ

☃Have a wonderful day / evening ! ☼

# StayInAndExplore ! ☂

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Answer:

p=1/5t

Step-by-step explanation:

Since t is 100% of the items sold and p is 20% of that, the profit, p is 20% of t, or 1/5t.

Answer:

p = t(0.2)

Step-by-step explanation:

The profit is 20% of the total price. So if you multiply the total price by 0.2, you will get 20% of the total price which is the profit.

No, because the test value 0.28 is in the noncritical region.

The null hypothesis (H₀) is the hospital's success rate is equal to the national average.

H₀: p = 0.78 (hospital's success rate is equal to the national average)

The alternative hypothesis (H₁) is the hospital's success rate is different from the national average.

H₁: p ≠ 0.78 (hospital's success rate is different from the national average)

We can use a significance level (α) of 0.05 for this test.

z = (p(hat) - p₀) / √(p₀(1 - p₀) / n)

P(hat) is the sample proportion (successful operations / total operations)

p₀ is the hypothesized proportion under the null hypothesis (0.78)

n is the sample size

p(hat) = 42 / 52 ≈ 0.8077

z = (0.8077 - 0.78) / √(0.78 × 0.22 / 52)

z = 0.28

Now, we compare the test statistic to the critical values. Since it is a two-tailed test, we divide the significance level (α = 0.05) by 2 to get α/2 = 0.025.

Looking up the z-value corresponding to α/2 = 0.025 in the standard normal distribution table, we find that the critical z-values are approximately -1.96 and 1.96.

Since the calculated test statistic (z = 0.28) falls within the noncritical region (-1.96 < z < 1.96), we fail to reject the null hypothesis.

A) No, because the test value 0.28 is in the noncritical region.

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Answer:

B

Step-by-step explanation:

ye

Answer:

Quamir = 20 and since Quamir is twice Taaj's age you simply divide Taaj's age by two

The limit of the given expression is approximately 0.87928.

To evaluate the limit lim x→0 (sin(14) cos(12) tan(14)), we can apply the properties of limits and trigonometric identities. Let's break it down step by step:

First, let's simplify the expression using the trigonometric identity:

tan(14) = sin(14) / cos(14)

Now, we can rewrite the limit as:

lim x→0 (sin(14) cos(12) tan(14)) = lim x→0 (sin(14) cos(12) (sin(14) / cos(14)))

Next, we can cancel out the common factor of cos(14):

lim x→0 (sin(14) cos(12) (sin(14) / cos(14))) = lim x→0 (sin(14) cos(12) sin(14))

Now, we have:

lim x→0 (sin(14) cos(12) sin(14))

Using the double angle formula for sin(2θ):

sin(2θ) = 2sin(θ)cos(θ)

We can rewrite the expression as:

lim x→0 (2sin(14)cos(14) cos(12) sin(14))

Next, we can rearrange the terms:

lim x→0 (2sin(14)sin(14) cos(14) cos(12))

Using the trigonometric identity sin(θ)cos(θ) = 1/2 sin(2θ), we get:

lim x→0 (2 * 1/2 sin(2*14) * cos(14) * cos(12))

Simplifying further:

lim x→0 (sin(28) * cos(14) * cos(12))

Now, we can use the trigonometric identity sin(2θ) = 2sin(θ)cos(θ) to simplify sin(28):

sin(28) = sin(2 * 14) = 2sin(14)cos(14)

Substituting back into the expression:

lim x→0 (2sin(14)cos(14) * cos(14) * cos(12))

Simplifying:

lim x→0 (2cos(14)² * cos(12))

Now, we can evaluate the limit numerically. Since there are no variables approaching 0, the limit is simply the value of the expression:

lim x→0 (2cos(14)² * cos(12)) ≈ 2 * (cos(14))² * cos(12)

Approximating the numerical value using a calculator, we have:

lim x→0 (2cos(14)² * cos(12)) ≈ 0.87928

Therefore, the limit of the given expression is approximately 0.87928.

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Answer:

The lowest common multiple 3 and 4 is 12.

Step-by-step explanation:

The total multiples of both 3 and 4 between 1 - 100 are 100/12 = 8 4/12 i.e. 8.

what is the rate of increase of the function f(x) = 1/3(^3 √24)^2x

Step-by-step explanation:

let M be the midpoint of x and y

xM= (xX+xY)/2 =(0+88)2=44

yM=(Yx+yY)/2=(21_103)/2=_41

M(44,_41)