Kevin ate 2/3 of a pizza and Louisa ate 1/12 of the same pizza. How
much pizza is left? *

There are many strategies we can use to solve a system of equations, such as elimination or substitution.

\(y=3x+6\\y=(x+4)^2-10\)

Since y has already be isolated in both equations, we can just use substitution to equate them:

\(3x+6=(x+4)^2-10\)

Now, combine like terms:

\(3x=(x+4)^2-16\)

Expand the binomial:

\(3x=x^2+8x+16-16\\3x=x^2+8x\\0=x^2+5x\)

Find the zeroes:

\(0=x(x+5)\)

Therefore, x can be 0 or -5.

Now, we can plug these values of x back into one of the equations to determine the y coordinate:

\(y=3x+6\\y=3(0)+6\\y=6\)

Therefore, one solution is (0,6).

\(y=3x+6\\y=3(-5)+6\\y=-15+6\\y=-9\)

Another solutions is (-5,-9).

(0,6), (-5,-9)

The probability that on any given day the office receives exactly 3 calls is 0.0076.

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, we let

Let X be the number of calls received in an office per day.

X≈Poison(λ=10)

P(X = x) = e^(-λ)λˣ/x!; x = 0, 1, 2.....

= 0, otherwise

The probability that on any given day the office receives exactly 3 calls: 0.0076

P(X = 3) = e^(-10)10³/3!

P(X=3) = 0.0076

Hence, the probability that on any given day the office receives exactly 3 calls is 0.0076.

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Answer:

In order to prove that (x+3) is a factor of p(x), Serena must show that p(-3) = 0. This means that if we plug -3 into the polynomial p(x), the resulting value must be 0. Therefore, the correct answer is option D, p(-3)=0.

Step-by-step explanation:

Answer: x= -3.25

Step-by-step explanation:

R=4x+6y   11=4x+6(4)     11=4x+ 24     11-24=4x   -13=4x  -13/4=x  x=-3.25

11=4(-3.25)+ 6(4)  11= -13+24

Step-by-step explanation:

first of all you times every number with two 2(n-7) then collect like terms then divide

The double integral ∬dxcosyda, where d is bounded by y=0, y=x2, and x=4 can be evaluated as (-1/2)cos(16) + (1/2).

The integration of a function of two variables, commonly represented as f(x,y), over a two-dimensional region in the xy-plane is done using a double integral, a sort of definite integral. Its definition is given by: f(x,y) dx dy

We can evaluate the integral using iterated integrals. First, we integrate with respect to x:

∫[0, 4] ∫[0, x²] cos(y) dy dx

Using u-substitution with u = y and du = dy, we have:

∫[0, 4] sin(x²) - sin(0) dx

Next, we integrate with respect to x:

[(-1/2) cos(x²)]|[0, 4]

= (-1/2)cos(16) + (1/2)cos(0)

= (-1/2)cos(16) + (1/2)

Therefore, the value of the double integral is (-1/2)cos(16) + (1/2).

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The multiplication shows that the total steps for the ramp will be 28 inches.

From the information given, the school has 4 steps to the front door and each step is 7 inches tall.

In this case, the total steps of the ramp will be gotten by multiplying the values. This will be:

= 4 × 7 = 28 inches.

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Answer:

The z score of the 65-mph speed limit is -0.75

Step-by-step explanation:

The z score is given by the relation;

\(z = \frac{x- \mu}{\sigma}\)

Where:

Z = Normal (Standard) or z score

x = Observed speed  score

μ = Mean, expected speed

σ = Standard deviation

Where we plug in the values for x = 65-mph, σ = 8 mph and μ = 71 mph, into the z-score equation, we get;

\(z = \frac{65-71}{8}= \frac{-6}{8} = -\frac{3}{4}\)

Hence the z score of the 65-mph speed limit =-3/4 or -0.75.

The volume of the triangular base prism with a base of 9 ft, the height of the base 8 ft, and the height of the prism 2.5 ft is 90 ft³.

Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object.

volume = 1 / 2 bhl

where

Therefore,

b = 9 feet

h = 8 feet

l  = 2.5 feet

Therefore,

volume  = 1 / 2 × 9 × 8 × 2.5

volume = 180 / 2

volume = 90 ft³

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Answer:

Step-by-step explanation:

a) To determine if the polynomials 1+2t, 3+6t^2, 1+3t+4t^2 are linearly dependent in P2, we need to check if there exist constants c1, c2, and c3 such that c1(1+2t) + c2(3+6t^2) + c3(1+3t+4t^2) = 0, where 0 is the zero polynomial in P2.

Rewriting this equation in terms of the standard basis B = {1, t, t^2}, we have:

(c1 + c3) + (2c1 + 3c3)t + (4c2 + 3c3)t^2 = 0

This gives us the system of equations:

c1 + c3 = 0

2c1 + 3c3 = 0

4c2 + 3c3 = 0

Solving this system of equations, we get c1 = -3c3/2, c2 = -3c3/4. Therefore, any choice of c3 that is not equal to zero would give us a nontrivial solution, which implies that the polynomials are linearly dependent in P2.

b) To determine if the polynomials 1+2t+t^2, 3-9t^2, 1+4t+5t^2 are linearly dependent in P2, we need to check if there exist constants c1, c2, and c3 such that c1(1+2t+t^2) + c2(3-9t^2) + c3(1+4t+5t^2) = 0, where 0 is the zero polynomial in P2.

Rewriting this equation in terms of the standard basis B = {1, t, t^2}, we have:

(c1 + c3) + (2c1 + 4c3)t + (c1 + 5c3)t^2 - 9c2t^2 = 0

This gives us the system of equations:

c1 + c3 = 0

2c1 + 4c3 = 0

c1 + 5c3 - 9c2 = 0

Solving this system of equations, we get c1 = -2c3, c2 = (1/9)(c1 + 5c3). Therefore, any choice of c3 that is not equal to zero would give us a nontrivial solution, which implies that the polynomials are linearly dependent in P2.

Answer:

8 - 6x

Step-by-step explanation:

16-2(4+3x)

16 - 8 - 6x

8 - 6x

So, the answer is 8 - 6x

Answer:

Step-by-step explanation:

all values are true

Answer:

his tank can hold 24 gallons

Step-by-step explanation:

5/6 - 1/2 = 2/6 2/6 of tank = 8 gallons So, tank can hold 24 gallons.

The 95% confidence interval for the population mean is (16.426, 26.574

To find the 95% confidence interval, we can use the formula:

Confidence interval = sample mean ± (z-score)*(population standard deviation/√n)

where the z-score for a 95% confidence level is 1.96.

Plugging in the values given in the question, we get:

Confidence interval = 21.5 ± (1.96)*(19.4/√49)

Simplifying this expression, we get:

Confidence interval = 21.5 ± 5.074

Therefore, the 95% confidence interval for the population mean is (16.426, 26.574) as an open-interval.

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Answer:

3/4

Step-by-step explanation:

Answer:

D = 1120

Step-by-step explanation:

Given:

Substitute the values into the equation:

⇒ D = WT²

\(\text{D = WT}^{2} \ \text{can also be written as D = (W)(T)(T)}\)

⇒ D = (W)(T)(T)

⇒ D = (70)(4)(4)

Simplify the RHS:

⇒ D = 280(4)

⇒ D = 1120

When starting a problem, almost every single problem needs to be understood by the person answering so they can see what needs to be done.  In this example, we are given an expression and told to solve the equation which means that we need to solve for the unknown, in this case x.

Now that we know what we must do, we can start to solve the problem. Looking at the problem we can see that the step that we must take is to distribute 3 into the parenthesis.

Distribute

Now that we distributed the values inside of the parenthesis we can move onto the next step which is to help isolate x.  What we should do is subtract 6 from both sides which will help leave x with its coefficient alone.

Subtract 6 from both sides

The next step that we should take to help solve for the unknown is to subtract 3x from both sides.

Subtract 3x from both sides

The final step that we must take to help isolate the unknown would be to divide both sides by 3.  This would remove the coefficient from x and we would get -21 divided by 3.

Divide both sides by 3

Therefore, after simplifying the expression that was given to solve for the unknown we were able to determine that the option that would best match the solution is option A, x = -7.

Answer:

a) x = -7

Step-by-step explanation:

Given: 3(2x + 2) = 3x - 15

1. Distribute:

3(2x) + 3(2) = 3x - 15

⟹ 6x + 6 = 3x - 15

2. Subtract 3x from both sides:

6x - 3x + 6 = 3x - 3x - 15

⟹ 3x + 6 = -15

3. Subtract 6 from both sides:

3x + 6 - 6 = -15 - 6

⟹ 3x = -21

4. Divide both sides by 3:

3x ÷ 3 = -21 ÷ 3

⟹ x = -7

5. Check your work:

3(2x + 2) = 3x - 15

3(2(-7) + 2) = 3(-7) - 15

3(-14 + 2) = -21 - 15

3(-12) = -21 - 15

⟹ -36 = -36 ✔

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The following distributions has a mean that varies

II. The distribution of sample data

III. The sampling distribution of the sample mean

The correct answer is option v) II and III."

Here, we have,

In the context of statistical distributions:

I. The population distribution refers to the distribution of a specific variable within the entire population. The mean of the population distribution which is fixed and does not vary.

II. The distribution of sample data refers to the distribution of a variable within a specific sample. The mean of the sample data can vary from one sample to another.

III. The sampling distribution of the sample mean refers to the distribution of sample means taken from multiple samples of the same size from a population. The mean of the sampling distribution of the sample mean is equal to the population mean, but the individual sample means can vary from sample to sample.

Therefore, the mean varies in both the distribution of sample data (II) and the sampling distribution of the sample mean (III), but not in the population distribution (I).

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In Milgram's first study of obedience, the majority of teachers initially complied but refused to deliver more than slight levels of shock.

In Milgram's first study of obedience, participants were assigned the role of 'teacher' and were instructed to administer electric shocks to a 'learner' whenever they answered a question incorrectly. The shocks ranged from mild to severe, with the highest level labeled as 'XXX.' The learner was actually an actor, and no real shocks were administered.

The study found that the majority of teachers initially complied with the experimenter's orders and delivered shocks, but they refused to deliver more than slight levels of shock. This suggests that while they were willing to follow the instructions to some extent, they had moral reservations about causing significant harm to another person.

It is important to note that the study has been criticized for ethical concerns and the potential psychological harm it may have caused to participants. However, it remains a significant contribution to our understanding of obedience and the power of authority figures.

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Answer:

8

Step-by-step explanation:

Use PEMDAS.

P-Parenthesis/Brackets

E-exponents

M-multiply

D-divide

A-add

S-subtract

Answer:

34°

Step-by-Step Explanation:

(4x) + (3x-8) = 90° (90° for right angles)

x = 14

3(14)-8 =34°

Step-by-step explanation:

4x+3x-8=90

7x=98

x=14

angle CDJ=3×14-8=34

Equatiοns that can be used tο find s, the tοtal distance Kurt swam is as fοllοws:

• s = 2 x 4/8 and

• s = 4/8 + 4/8

Bοth οf these equatiοns can be used tο find s, the tοtal distance Kurt swam.

The equatiοn s = 2 x 4/8 can be used tο find s, the tοtal distance Kurt swam. This equatiοn represents the fact that Kurt swam acrοss the lake and back, which is a tοtal οf twο times the distance acrοss the lake. Since the lake is 4/8 miles acrοss, the equatiοn simplifies tο s = 2 x 4/8, which equals 1 mile.

The equatiοn s = 4/8 + 4/8 can alsο be used tο find s, but it represents the distance Kurt swam in οne directiοn οnly. It adds the distance acrοss the lake and back tοgether, but since Kurt οnly swam in οne directiοn, this equatiοn οnly gives half οf the tοtal distance.

The equatiοn s = 1 is incοrrect because it dοes nοt take intο accοunt the distance acrοss the lake.

The equatiοn s = 2 x 8 is alsο incοrrect because it assumes that the lake is 8 miles acrοss, which is nοt given in the prοblem.

The equatiοn s = 2 + 4+8 is incοrrect because it adds three different distances tοgether, which dοes nοt accurately represent the distance Kurt swam.

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We can be 80% confident that the true value of the parameter falls within the range of our estimate plus or minus 1.282 standard errors of the estimate.

The value of zα that would result in a 80% one-sided confidence interval is 1.282. A confidence interval is a range of values that represents the uncertainty of an estimate.

A confidence level is the probability that the interval actually contains the true value of the parameter.

Confidence intervals are typically expressed as a range of values with an associated level of confidence. In a one-sided confidence interval, all of the values are on one side of the estimate.

For example, if we want to construct a one-sided confidence interval for the mean of a population, we would either be interested in the upper or lower end of the range, but not both.

A one-sided confidence interval is also known as a one-tailed confidence interval.

The formula for a one-sided confidence interval is given by:

zα × (σ / √n), where zα is the z-score for the desired level of confidence, σ is the population standard deviation, and n is the sample size.

For an 80% one-sided confidence interval, the z-score is 1.282.

This means that we can be 80% confident that the true value of the parameter falls within the range of our estimate plus or minus 1.282 standard errors of the estimate.

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Answer:

x = 36

Step-by-step explanation:

The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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Answer:

Point B and point G

Step-by-step explanation:

the second quadrant is above the x axis and left to y axis

Answer:

point B AND G

Step-by-step explanation:

THAT IS THE CORRECT ANSWER ABOVE

the second quadrant is located at the top left of the XY plane

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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Answer:

y = 120

Step-by-step explanation:

Interior angles of a triangle add up to 180°

So,

x+87+33 = 180

x + 120 = 180

Subtracting 120 to both sides

x = 180-120

x = 60°

Now

Angles on a straight line also add up to 180°

So,

x+y = 180

60 + y = 180

Subtracting 60 to both sides , we get

y = 180-60

y = 120

Since the data set does not contain any extreme outliers and appears to be relatively symmetric, the mean is likely to be a better measure of the center. The correct answer is: Mean.

To determine whether the mean or the median is a better measure of the center for the given data set: 31, 28, 30, 33, 29, 32, 29, 30, we can compare their values.

First, let's calculate the mean:

Mean = (31 + 28 + 30 + 33 + 29 + 32 + 29 + 30) / 8 = 242 / 8 = 30.25

Now, let's arrange the data set in ascending order:

28, 29, 29, 30, 30, 31, 32, 33

The median is the middle value in the data set, which is 30.

In this case, both the mean and the median are close in value, with the mean being 30.25 and the median being 30. However, since the data set does not contain any extreme outliers and appears to be relatively symmetric, the mean is likely to be a better measure of the center.

Therefore, the correct answer is: Mean.

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Given the following list of values, is the mean or the median likely to be a better measure of the center of the data set? 31, 28, 30, 33, 29, 32, 29, 30 Select the correct answer