Simplify the following expression. (75x - 67y) - (47x + 15y)

Answer: Choice B

[tex](f * g)(x) = \frac{x^2+6x+8}{x^2+2x-15}, \ \text{ for } x \ne -5 \text{ and } x \ne 3\\\\[/tex]

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Work Shown:

[tex]h(x) = (f * g)(x)\\\\h(x) = f(x) * g(x)\\\\h(x) = \frac{x^2-16}{x^2+3x-10}*\frac{x^2-4}{x^2-7x+12}\\\\h(x) = \frac{(x-4)(x+4)}{(x+5)(x-2)}*\frac{(x-2)(x+2)}{(x-3)(x-4)}\\\\h(x) = \frac{x+4}{(x+5)(x-2)}*\frac{(x-2)(x+2)}{x-3} \ \ \text{ ... see note 1}\\\\h(x) = \frac{x+4}{x+5}*\frac{x+2}{x-3} \ \ \text{ ... see note 2}\\\\h(x) = \frac{(x+4)(x+2)}{(x+5)(x-3)}\\\\h(x) = \frac{x^2+6x+8}{x^2+2x-15}\\\\[/tex]

note 1: A pair of (x-4) terms canceled

note 2: A pair of (x-2) terms canceled

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Extra info (optional section):

The fact that [tex]x \ne -5 \text{ and } x \ne 3[/tex] is to avoid a division by zero error in the simplified version of h(x).

I would argue that [tex]x \ne 2 \text{ and } x \ne 4[/tex] should be thrown in as well simply so that the domains match up perfectly with the original f(x) and g(x) functions.  

So I think the full domain should be that x is any real number but

[tex]x \ne -5 \text{ and } x \ne 2\\x \ne 3 \text{ and } x \ne 4[/tex]

Put another way: if x = 2 is allowed in h(x), then that clashes with the fact that it's not allowed in f(x). The same idea happens with x = 4 but with g(x) this time. It's possible your teacher glossed this fact over, or ran out of room.

Answer:

b. The solution is a non empty set.

Step-by-step explanation:

There are no common elements.

Step-by-step explanation:

Exterior angle BOA = 250°

Interior angle BOA = 360°- 250° = 110°

Now,

(A) BDA = interior angle BOA / 2 = 55°( Property of circles)

(B) From the figure, we observe that AOBC is a cyclic quadrilateral (i.e. sum of opposite angles is 180°).

Therefore, BCA + BOA = 180°

BCA = 180° - 110° = 70°

Answer:

46

Step-by-step explanation:

See attached for reference

The points given:

They form a rectangle as seen in the picture.

We can notice that this is a parallelogram, as respective lines have same difference of coordinates.

So calculating only the two of the sides will be sufficient to get its perimeter:

So, the perimeter:

Answer:

(-25)+(-12)+(-34) = -71

so when you add negative numbers you simply add them such as -2+-2 -4

so same conditions

so it will be -25+-12+-34 and it will simply be 25+12+34 so -71

Answer:

the probability that out of these 75 people, 14 or more drink coffee is 0.6133

Step-by-step explanation:

Given that:

sample size n = 75

proportion of high school students that drink coffee p = 20% = 0.20

The proportion of the students that did not drink coffee = 1 - p

Let X be the random variable that follows a normal distribution

X [tex]\sim[/tex] N (n, p)

X  [tex]\sim[/tex] N (75, 0.20)

[tex]\mu = np[/tex] = 75 × 0.20

[tex]\mu =[/tex] 15

[tex]\sigma = \sqrt{p (1-p) n}[/tex]

[tex]\sigma = \sqrt{0.20(1-0.20) 75}[/tex]

[tex]\sigma = \sqrt{0.20*0.80* 75}[/tex]

[tex]\sigma = \sqrt{12}[/tex]

[tex]\sigma = 3.464[/tex]

Now ; if 14 or more people drank coffee ; then

[tex]P(X \geq 14) = P(\dfrac{X-\mu }{\sigma} \leq \dfrac{X-\mu}{\sigma})[/tex]

[tex]P(X \geq 14) =P(\dfrac{14-\mu }{\sigma} \leq \dfrac{14-15}{3.464})[/tex]

[tex]P(X \geq 14) = P(Z \leq \dfrac{-1}{3.464})[/tex]

[tex]P(X \geq 14) = P(Z \leq -0.28868)[/tex]

From the standard normal z tables; (-0.288)

[tex]P(X \geq 14) = P(Z \leq 0.38667)[/tex]

[tex]P(X \geq 14) = 1 - 0.38667[/tex]

[tex]P(X \geq 14) = 0.61333[/tex]

the probability that out of these 75 people, 14 or more drink coffee is 0.6133

Answer:

12

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

PC * PA = PB^2

(PA+AC) * PA = PB^2

(4+32) * 4 = PB^2

36*4 = PB^2

144 = PB^2

Taking the square root of each side

sqrt(144) = sqrt(PB^2)

12= PB

Answer:

a

Step-by-step explanation:

Given a tangent and a secant to a circle from an external point, then

The square of the tangent is equal to the product of the external part and the whole of the secant , that is

PB² = PA × PC = 4(4 + 32) = 4 × 36 = 144 ( take square root of both sides )

PB = [tex]\sqrt{144}[/tex] = 12 → a

Answer:

let length be x

b = x - 3

perimeter = 2( l + b)

54 = 2(x+x-3)

27 = 2x - 3

30 = 2x

x = 15

l = 15

b = 15 - 3

b = 12

Answer:

c.) in the correct answer

Answer:

4th multiple = 24

Step-by-step explanation:

Given

Let the two numbers be represented by m and n

Required

Find the 4th common multiple of the numbers.

From the question, we understand that the first common multiple of m and n is 6.

This can be represented as:

m * n * 1 = 6

mn = 6

Their fourth common multiple can be represented as: m * n * 4

4th multiple = m * n * 4

4th multiple = 4 * mn

Substitute 6 for mn

4th multiple = 4 * 6

4th multiple = 24

Hence, the 4th multiple of both numbers is 24.

Answer:

A. There is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag.

D. Fail to reject H0.

Step-by-step explanation:

From the summary of the given test statistics.

The null and the alternative hypothesis are:

[tex]H_0:\mu_1=\mu_2 \\ \\ Ha:\mu_1 \neq \mu_2[/tex]

This test is also a two tailed test.

Similarly, the t value for the test statistics = 1.44

The p- value - 0.167

The level of significance ∝ = 0.05

The objective we are meant to achieve here is to determine which of the following from the given options are appropriate conclusions for this hypothesis test.

From what we have above:

Decision Rule: We fail to reject the null hypothesis since the p-value is greater than the level of significance at 0.05

CONCLUSION: Therefore, we can conclude that  there is insufficient evidence at the 0.05 level of significance to conclude that Regular and Salt & Vinegar chips have different amounts of chips per bag as we fail to reject H0.

Answer:

I'm confused by this. What do they mean by prove?

Step-by-step explanation:

Answer:

hello bro

Step-by-step explanation:

can you translate it on english so i can help you

Answer: [tex]1\dfrac{11}{12}\text{ pounds}[/tex]

Step-by-step explanation:

The complete question is provided in the attachment.

Given, Amount blueberry jelly beans= [tex]1\dfrac{1}{4}[/tex] pounds

[tex]=\dfrac{5}{4}[/tex] pounds.

Amount lemon jelly beans = [tex]2\dfrac{1}{3}[/tex]pounds

[tex]=\dfrac{7}{2}[/tex] pounds

Total jelly beans she bought = Amount blueberry jelly beans + Amount lemon jelly beans

[tex]=(\dfrac{5}{4}+\dfrac{7}{3})[/tex] pounds

[tex]=\frac{15+28}{12}\text{ pounds}\\\\=\dfrac{43}{12}\text{ pounds}[/tex]

Amount of jelly beans she gave away = [tex]1\dfrac{2}{3}=\dfrac{5}{3}\text{ pounds}[/tex]

Amount of jelly beans she has left= Total jelly beans - Amount of jelly beans she gave away

=[tex]\dfrac{43}{12}-\dfrac{5}{3}\\\\=\dfrac{43-20}{12}\\\\=\dfrac{23}{12}\\\\=1\dfrac{11}{12}\text{ pounds}[/tex]

She has left [tex]1\dfrac{11}{12}\text{ pounds}[/tex] of jelly beans.

Answer:

2x-1=3

2x=3+1

2x=4

x=2

[tex]\huge\boxed{\underline{\bf \: Answer}}[/tex]

(a) Let's try with x = - 1

[tex] \sf \: 2x - 1 = 3 \\\sf 2( - 1) - 1 = 3 \\ \sf- 2 - 1 = 3 \\ \\ \boxed{\bf- 3 \: \bcancel= \: 3}[/tex]

So, x = - 1 is not the solution to the given equation.

______________

(b) Now, try with x = 2

[tex]\sf2x - 1 = 3 \\ \sf2(2) - 1 = 3 \\ \sf4 - 1 = 3 \\ \\ \boxed{\bf3 = 3}[/tex]

Yes, we can see that x = 2 is the correct solution for the equation.

______________

Hope it helps.

RainbowSalt2222

Answer:

1) akram : shazia

20-4 : 15-4

16 : 11

2) akram : shazia

20 + 5 : 15 + 5

25 : 20

5 : 4

3) ratios are not always constant

The midpoint is the point that divide a segment into two equal halves, while the distance between points is the number of units between both points.

The distance between

The coordinate of midpoint of:

The distance in a coordinate geometry is calculated using: [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex].

The distance between points is calculated as follows:

(1,-4.6) and (3,7)

[tex]d = \sqrt{(1 - 3)^2 + (-4.6 - 7)^2}[/tex]

[tex]d = \sqrt{138.56}[/tex]

[tex]d = 11.77[/tex]

(-6,-5) and (2,0)

[tex]d = \sqrt{(-6 - 2)^2 + (-5 - 0)^2}[/tex]

[tex]d = \sqrt{89}[/tex]

[tex]d = 9.43[/tex]

(-1, 4) and (1-1)

[tex]d = \sqrt{(-1 - 1)^2 + (4 - -1)^2}[/tex]

[tex]d = \sqrt{29}[/tex]

[tex]d = 5.39[/tex]

(0.-8) and (3,2)

[tex]d = \sqrt{(0 - 3)^2 + (-8 -2)^2}[/tex]

[tex]d = \sqrt{109}[/tex]

[tex]d = 10.44[/tex]

The midpoint (M) is calculated using: [tex]M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]

The coordinate of midpoint is calculated as follows:

(5, 8) and (-1,-4)

[tex]M = (\frac{5-1}{2},\frac{8-4}{2})[/tex]

[tex]M = (\frac{4}{2},\frac{4}{2})[/tex]

[tex]M = (2,2)[/tex]

(-5,9) and (-2,7)

[tex]M = (\frac{-5-2}{2},\frac{9+7}{2})[/tex]

[tex]M = (\frac{-7}{2},\frac{16}{2})[/tex]

[tex]M = (-3.5,9)[/tex]

(-3,-7) and (13.-5)

[tex]M = (\frac{-3+13}{2},\frac{-7-5}{2})[/tex]

[tex]M = (\frac{10}{2},\frac{-12}{2})[/tex]

[tex]M = (5,-6)[/tex]

(12,-6) and (-8,5)

[tex]M = (\frac{12-8}{2},\frac{-6+5}{2})[/tex]

[tex]M = (\frac{4}{2},\frac{-1}{2})[/tex]

[tex]M = (2,-0.5)[/tex]

Read more about distance and midpoints in coordinate geometry at:

https://brainly.com/question/3715220

Answer:hope it helps

Step-by-step explanation:

Result:

0.6

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Plain Text

Number line:

Number line

Rational form:

3/5

[tex]5(2x + 4) = 15\\10x+20=15\\10x=-5\\x=-\dfrac{5}{10}=-0,5[/tex]

Answer:

[tex]\huge\boxed{x=-0.5}[/tex]

Step-by-step explanation:

[tex]5(2x+4)=15\qquad\text{divide both sides by 5}\\\\\dfrac{5\!\!\!\!\diagup(2x+4)}{5\!\!\!\!\diagup}=\dfrac{15\!\!\!\!\!\diagup}{5\!\!\!\!\diagup}\\\\2x+4=3\qquad\text{subtract 4 from both sides}\\\\2x+4-4=3-4\\\\2x=-1\qquad\text{divide both sides by 2}\\\\\dfrac{2x}{2}=\dfrac{-1}{2}\\\\\boxed{x=-0.5}[/tex]

Answer:

b = 10.5

Step-by-step explanation:

2(b-9) = 3

then:

2*b + 2*-9 = 3

2b - 18 = 3

2b = 3 + 18

2b = 21

b = 21/2

b = 10.5

check:

2(10.5 - 9) = 3

2*1.5 = 3

Answer:

C. Line chart

Step-by-step explanation:

Answer:

B. Histogram

Step-by-step explanation:

Histogram uses time.

Answer:

8 home games and 10 away games

Step-by-step explanation:

Total home goals

= 8+5+9+8

= 30

Number of home games

= 30/3.75

= 8

Total away game goals

= 7+8+4+5

= 24

Number of away games

= 24/2.4

= 10

Answer:

i think it is 8 home and 10 away matches

Step-by-step explanation:

Answer:

3/11

Step-by-step explanation:

In the above question, we have the following information

Total number of balls = 12

White balls = 4

Blue balls = 3

Red balls = 5

We are to find the chance of probability that if we select 3 balls, all the three are selected.

Hence,

Probability ( all the three balls are selected) = P(White ball) × P(Blue ball) × P( Red ball)

Probability ( all the three balls are selected) = 4/12 × 3/11 × 5/10

= 60/1320

= 1/22

The number of ways by which we can selected all the three balls is a total of 6 ways:

WBR = White, Blue, Red

WRB = White, Red, Blue

RBW = Red, Blue, White

RWB = Red, White, Blue

BRW = Blue, Red, White

BWR = Blue, White, Red

Therefore, the chance that all three are selected :

1/22 × 6 ways = 6/22 = 3/11

Answer:

Step-by-step explanation:

Given that:

[tex]T(x,y) = \dfrac{100}{1+x^2+y^2}[/tex]

This implies that the level curves of a function(f) of two variables relates with the curves with equation f(x,y) = c

here c is the constant.

[tex]c = \dfrac{100}{1+x^2+2y^2} \ \ \--- (1)[/tex]

By cross multiply

[tex]c({1+x^2+2y^2}) = 100[/tex]

[tex]1+x^2+2y^2 = \dfrac{100}{c}[/tex]

[tex]x^2+2y^2 = \dfrac{100}{c} - 1 \ \ -- (2)[/tex]

From (2); let assume that the values of c > 0 likewise c < 100, then the interval can be expressed as 0 < c <100.

Now,

[tex]\dfrac{(x)^2}{\dfrac{100}{c}-1 } + \dfrac{(y)^2}{\dfrac{50}{c}-\dfrac{1}{2} }=1[/tex]

This is the equation for the  family of the eclipses centred at (0,0) is :

[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]

[tex]a^2 = \dfrac{100}{c} -1 \ \ and \ \ b^2 = \dfrac{50}{c}- \dfrac{1}{2}[/tex]

Therefore; the level of the curves are all the eclipses with the major axis:

[tex]a = \sqrt{\dfrac{100 }{c}-1}[/tex]  and a minor axis [tex]b = \sqrt{\dfrac{50 }{c}-\dfrac{1}{2}}[/tex]  which satisfies the values for which 0< c < 100.

The sketch of the level curves can be see in the attached image below.

Answer:

x= (2+ √ 34) /5 , (2- √ 34) /5

decimal form= 1.566

Step-by-step explanation:

Answer: surface area

Step-by-step explanation:

Answer:

Rebecca does not have a return yet because the stock was not sold since there was a limit order at $33.

However, the value of her investment can be put around $2,400 (100 x $24 average price).

Step-by-step explanation:

Price of Havad Stock bought a year ago = $20

No. of shares = 100

Limit order selling price = $33

Stock prices during the limit order day = $23, $26, and $22

The stock cannot be sold, since its price did not reach $33.

Rebecca's limit order is an order to buy or sell her stock in Havad at $33 or better. Since her order is a sell limit order, it can only be executed at the limit price of $33 or higher.  Unfortunately, the price of the stock did not reach the limit order on that particular day.  This implies that her limit order is not guaranteed to execute.

Step-by-step explanation:

mean add upp all the numbers and divide by how many they are