Expand, and simplify the following expressions a. (2x+y)(x+y) + (2x-y)(x+y)​

Answer: 18

Step-by-step explanation:

360/20 = 18

Given the biconditional statement: "It is a leap year if and only if the year has 366 days.", the converse to form it is "If the year has 366 days, then this is a leap year". (Right choice: C)

According to logics, propostions are truth bearers that makes sentences true or false. In linguistics, propositions are the meaning of declarative sentences. There are simple and composite propositions, the latter are formed by one simple proposition at least and logic connectors. There are five logic connectors:

By logic rules we know that the double implication/biconditional is commutative operator:

(X ⇔ Y) ⇔ (Y ⇔ X)

In addition, a double implication/biconditional has the following equivalence:

(X ⇒ Y) ∧ (Y ⇒ X)

Where Y ⇒ X is the converse of X ⇒ Y.

Therefore, the converse to form the statement "It is a leap year if and only if the year has 366 days" is Y ⇒ X: "If the year has 366 days, then this is a leap year".

To learn more on propositions: https://brainly.com/question/14789062

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Answer:

The correct answer is "0.3410, 0.4990".

Step-by-step explanation:

Given values are:

[tex]n=150[/tex]

[tex]p=\frac{63}{150}[/tex]

  [tex]=0.42[/tex]

At 95% confidence interval,

C = 95%

z = 1.96

As we know,

⇒ [tex]E=z\sqrt{\frac{p(1-p)}{n} }[/tex]

By substituting the values, we get

       [tex]=1.96\sqrt{\frac{0.42\times 0.58}{150} }[/tex]

       [tex]=1.96\sqrt{\frac{0.2436}{150} }[/tex]

       [tex]=0.0790[/tex]

hence,

The confidence interval will be:

= [tex]p \pm E[/tex]

= [tex]0.42 \pm 0.079[/tex]

= [tex](0.3410,0.4990)[/tex]

Answer:

0.2979 = 29.79  probability that a single randomly selected policy has a mean value between 172595.6 and 196608.1 dollars.

0.982 = 98.2% probability that a random sample of size 60 has a mean value between 172595.6 and 196608.1 dollars.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 181000 dollars. Assume the standard deviation is 31000 dollars.

This means that [tex]\mu = 181000, \sigma = 31000[/tex]

Find the probability that a single randomly selected policy has a mean value between 172595.6 and 196608.1 dollars.

This is the p-value of Z when X = 196608.1 subtracted by the p-value of Z when X = 172595.6. So

X = 196608.1

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

[tex]Z = \frac{196608.1 - 181000}{31000}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915

X = 172595.6

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

[tex]Z = \frac{172595.6 - 181000}{31000}[/tex]

[tex]Z = -0.27[/tex]

[tex]Z = -0.27[/tex] has a p-value of 0.3936

0.6915 - 0.3936 = 0.2979

0.2979 = 29.79  probability that a single randomly selected policy has a mean value between 172595.6 and 196608.1 dollars.

Sample of 60:

This means that [tex]n = 60, s = \frac{31000}{\sqrt{60}}[/tex]

Now, the probability is given by:

X = 196608.1

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

By the Central Limit Theorem

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

[tex]Z = \frac{196608.1 - 181000}{\frac{31000}{\sqrt{60}}}[/tex]

[tex]Z = 3.9[/tex]

[tex]Z = 3.9[/tex] has a p-value of 0.9999

X = 172595.6

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

[tex]Z = \frac{172595.6 - 181000}{\frac{31000}{\sqrt{60}}}[/tex]

[tex]Z = -2.1[/tex]

[tex]Z = -2.1[/tex] has a p-value of 0.0179

0.9999 - 0.0179 = 0.982

0.982 = 98.2% probability that a random sample of size 60 has a mean value between 172595.6 and 196608.1 dollars.

Given:

Chung has 6 trucks and 5 cars in his toy box.

Brian has 4 trucks and 5 cars in his toy box.

To find:

The correct comparison of their ratios of trucks to cars.

Solution:

The ratio of trucks to cars is defined as:

[tex]\text{Ratio}=\dfrac{\text{Number of trucks}}{\text{Number of cars}}[/tex]

Chung has 6 trucks and 5 cars in his toy box. So, the ratio of trucks to cars is:

[tex]\text{Ratio}=\dfrac{6}{5}[/tex]

Brian has 4 trucks and 5 cars in his toy box.

[tex]\text{Ratio}=\dfrac{4}{5}[/tex]

We know that,

[tex]6>4[/tex]

[tex]\dfrac{6}{5}>\dfrac{4}{5}[/tex]

Therefore, the correct option is D.

Answer:

what the guy above me said

Step-by-step explanation:

so yeah he is right points

Answer:

0.9

Step-by-step explanation:

To find the mean temperature, we have to add all of the numbers together and divide that by the amount of numbers there are.

6 + 5 + 3 + -4 + 3 + -3 + 2 + -1 + -2 + 0 = 9

There are 10 numbers.

Our mean, or average, would be 9 / 10 = 0.9

Answer: 0.876, 9.123

Step-by-step explanation:

The function is [tex]y=-x^2+10-8[/tex]

It meets the ground level when [tex]y[/tex] is 0

[tex]\Rightarrow -x^2+10x-8=0\\\Rightarrow x^2-10x+8=0\\\\\Rightarrow x=\dfrac{10\pm \sqrt{(-10)^2-4(1)(8)}}{2}\\\\\Rightarrow x=\dfrac{10\pm \sqrt{68}}{2}\\\\\Rightarrow x=5\pm \sqrt{17}\\\Rightarrow x=0.876,\ 9.123[/tex]

Thus, it touches the ground at two points given above

Answer:

HI=15

Step-by-step explanation:

HI=sqrt(17^2-8^2)=sqrt(225)=15

P=8+15+17=40

S=8*15/2=60

Answer:

Step-by-step explanation:

for side HI

hypotenuse = 17

other two sides are 8 and HI . Hi has to be find so let it be x.

using pythagoras theorem

a^2 + b^2 = c^2

x^2 + 8^2 = 17^2

x^2 + 64 = 289

x^2 = 289 - 64

x^2 = 225

x = [tex]\sqrt{225[/tex]

x = 15

for angle G

take angle G as reference angle

using sin rule

sin G = opposite / hypotenuse

sin G = 15 / 17

sin G = 0.882

G = [tex]sin^{-1} (0.882)[/tex]

G = 61.884°

G = 61.88°

for angle I

angle G + angle H + angle I = 180 degree (being sum of interior angles of a triangle)

61.88° + 90° + angle I = 180°

151.88° + angle I =180°

angle I = 180°- 151.88°

angle I = 28.12°

Answer:

Step-by-step explanation:

Intervals are always x values. When x = 5, y = 4 (look at the graph to se this); when x = 6, y = 2. The rate of change is the same thing as the slope. We can't get an exact slope here because this isn't a straight line, but we can find the average rate of change. We use the slope formula to do this: with the coordinates (5, 4) and (6, 2):

[tex]m=\frac{2-4}{6-5}=\frac{-2}{1}=-2[/tex]. Third choice down is the one you want.

Answer:

Step-by-step explanation:

I don't know what the answer is if I am not given choices, but here is one possibility.

2(x^2 - 12x - 7)

You could factor what is inside the brackets.

2(x - 12.557) (x + 0.557)

Answer:

Step-by-step explanation:

since it is in the form of quadration equation , we can use quadratic formula . In quadratic equation we get the two values of x . one will be positive and another will be negative.

Answer:

83.5%

Step-by-step explanation:

90% × 20% + 85% × 30% + 80%× 50%

Step-by-step explanation:

a=16

r=3

48/16=3

144/16=3

6th term

=ar^(n-1)

= 16(3)^(6-1)

=3888

Answer:

£70.00

Step-by-step explanation:

You basically want to find what she spent in total, then subtract the amount she spent on ingredients.

50 glasses of lemonade at £2.10 each would be £105. (50*2.1)

Subtract the cost of ingredients, which is £35, with the total she made, £105, to get £70 (105-35)

Answer:

volume quantity is hjaj

9514 1404 393

Answer:

  B.  horizontal stretch by a factor of 3

Step-by-step explanation:

Replacing x by x/k in a function causes its graph to be stretched horizontally by a factor of k. (This makes sense because it means x needs to be k times as large to give the same argument to the function.)

Here, the value of k is 3, so the function graph is horizontally stretched by a factor of 3.

yes

Substitute x and y into the

equation  we have

0+4 .(-5)=-20

<=>-20=-20

satisfy the condition

Answer:

bukhayung saging my faborito

Step-by-step explanation:

The given equation is :

[tex](2x-1)^2=8[/tex]

or

[tex](2x-1)=\sqrt{8}\\\\2x-1=\pm 2\sqrt2\\\\2x=\pm 2\sqrt2 +1\\\\x=\dfrac{2\sqrt2 +1}{2}\\\\x=\pm (\sqrt 2+\dfrac{1}{2})\\\\or\\\\x=\sqrt2+\dfrac{1}{2},-\sqrt2-\dfrac{1}{2}[/tex]

Hence, this is the required solution.

Answer:

1.333333333333

Step-by-step explanation:

7/9÷4/9=7/4

= 1/3/4

Hence, a=1, b=3, c=4.

hope it helps:)))

Answer:10.25-r= hourly rate

Step-by-step explanation:

Answer:

Remember that, for a rectangle of length L and width W, the area is:

A  =L*W

And the perimeter is:

P = 2*(L + W)

In this case, we know that:

W = x

Let's assume that one of the "length" sides is on the part where the farmer uses the wall.

Then the farmer has 72 m of fencing for the other "length" side and for the 2 wide sides, then:

72m = L + 2*x

isolating L we get:

L = (2x - 72m)

Then we can write the area of the rectangle as:

A = L*x = (2x - 72m)*x

A = 2*x^2 - 72m*x

(you wrote  A = 72x - 21, I assume that it is incorrect, as the area should be a quadratic equation of x)

Answer:

30 and 45 degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let Terri spent the 'x' hours in the river,

Per hour rental charged by Timmy's Tubes = [tex]\frac{\text{Rental charged}}{\text{Hours spent}}[/tex]

                                                                        = [tex]\frac{18.75}{2.5}[/tex]

                                                                        = $7.5

Charges for 'x' hours = $7.5x

Therefore, function that defines the rental of Timmy's tube will be,

f(x) = 7.5x

Another company Fred's float charges a base fee $2 plus $6.25 per hours.

For 'x' hours Fred's float will charge = 6.25x + 2

And the function that defines the charges will be,

g(x) = 6.25x + 2

1). If x = 1.5 hours,

Rental charged by Timmy's tube,

f(1.5) = 7.5(1.5)

        = $11.25

Rental charged by Fred's float,

g(1.5) = 6.25(1.5) + 2

         = $11.375

2). If Terri has $12 to spend,

For f(x) = 12,

12 = 7.5x

x = 1.6 hours

For g(x) = 12

12 = 6.25x + 2

10 = 6.25x

x = 1.6 hours

Therefore, both the companies charge the same for 1.6 hors.

Terri can opt any company to spend $12.

Answer:

Left 2 units

Step-by-step explanation:

Without knowing what f(x), it is impossible to answer this question. I'll answer assuming a parent function of [tex]f(x)=x^2[/tex].

In the function [tex]y=(x-c)^2[/tex], [tex]c[/tex] represents the phase shift from parent function [tex]f(x)=x^2[/tex]. If [tex]c[/tex] is positive (e.g. [tex](x-3)^2[/tex]), then the function shifts to the right however many units [tex]c[/tex] is. If [tex]c[/tex] is negative (e.g. [tex](x+5)^2[/tex]), the function shifts to the left however many units the absolute value of [tex]c[/tex] is.

In the function [tex]g(x)=(x+2)^2[/tex], let's find out the value of [tex]c[/tex]:

Format: [tex]y=(x-c)^2[/tex]

[tex]g(x)=(x+2)^2=(x-(-2))^2[/tex]

Therefore, [tex]c=-2[/tex].

Since [tex]c[/tex] is negative, the function must shift to the left. To find out how many units it shifts to the left, take the absolute value of [tex]c[/tex]:

[tex]|-2|=\boxed{2\text{ units to the left}}[/tex].

Thus, the graph of [tex]g(x)=(x+2)^2[/tex] is a translation of the graph [tex]f(x)=x^2[/tex] by 2 units to the left.

*Note: Once again, this answer is assuming [tex]f(x)=x^2[/tex] as it is not clarified in the question. If [tex]f(x)\neq x^2[/tex] and is already shifted, you will need to account for shift. If you believe this is the case, feel free to let me know in the comments.

Answer:

c. y = ¼x - 2

Step-by-step explanation:

Find the slope (m) and y-intercept (b) then substitute the values into y = mx + b (slope-intercept form)

Slope = change in y/change in x

Using two points on the graph, (0, -2) and (4, -1):

Slope (m) = (-1 - (-2))/(4 - 0) = 1/4

m = ¼

y-intercept = the point where the line intercepts the y-axis = -2

b = -2

✔️To write the equation, substitute m = ¼ and b = -2 into y = mx + b:

y = ¼x - 2