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ella [17]
2 years ago
13

1/2(-2x -10) > 3(4 -6x)

Mathematics
2 answers:
allsm [11]2 years ago
6 0

Answer:

10 > -6x

Step-by-step explanation:

1/2(-2 x -10) > 3(4 - 6)

PEMDAS

do the work in the parentheses:

1/2(20) > 3(-2)

multiply (you multiply when a number is next to parentheses fyi):

1/2 x 20 = 10, 3 x -2 = -6

answer: 10 > -6x

mr_godi [17]2 years ago
5 0

Answer:

x>1

Step-by-step explanation:

\frac{1}{2} × (-2x - 10) > 3(4-6x)

-2x - 10 > 6(4-6x)

-2x - 10 > 24 - 36x

-2x + 36x > 24 + 10

34x > 34

x>1

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Express your answer as a polynomial in standard form.
NikAS [45]

Answer:

x² + 16x + 64

Step-by-step explanation:

To find f(g(x)) , substitute x = g(x) into f(x), that is

f(x + 7)

= (x + 7)² + 2(x + 7) + 1 ← expand (x + 7)² using FOIL

= x² + 14x + 49 + 2x + 14 + 1 ← collect like terms

= x² + 16x + 64

3 0
3 years ago
Read 2 more answers
the value of a car when purchased in 2008 was $21,500. It loses 12% of its value every year. What is the value of the car in 201
shusha [124]

Answer: the value of the car in 2019 is $5269

Step-by-step explanation:

It loses 12% of its value every year. This means that the value of the car is decaying exponentially. We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the car after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate of decay.

From the information given,

P = $21500

r = 12% = 12/100 = 0.12

t = 2019 - 2008 = 11 years

Therefore

A = 21500(1 - 0.12)^11

A = 21500(0.88)^11

A = 5269

6 0
3 years ago
Alejandra plans to sew fringe on a scarf. The scarf is shaped rectangle. The length of the scarf is 48 inches. The width is one
aleksandr82 [10.1K]
Ok so you will be finding the perimeter of this rectangle. The formula is P(perimeter)=2L(length) + 2W(width)

so the length is 48 and the width is 1/2 of 48, and we all know that 1/2 of 48 = 24 right? so in the formula is says 2L so we will take 48 and multiply it by 2 and get 96. The same way with the width. 24 times 2 = 48 so then we add them together and get 144. Therefore the perimeter and the length of fringe that she will use (or how ever you say it) will be 144 inches.

Hope this helps!;)
5 0
3 years ago
A common blood test performed on pregnant women to screen for chromosome abnormalities in the fetus measures the human chorionic
goldfiish [28.3K]

Answer:

(a) The proportion of women who are tested, get a negative test result is 0.82.

(b) The proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

Step-by-step explanation:

The Bayes' theorem states that the conditional probability of an event <em>E</em>_{i}, of the sample space <em>S,</em> given that another event <em>A</em> has already occurred is:

P(E_{i}|A)=\frac{P(A|E_{i})P(E_{i})}{\sum\liits^{n}_{i=1}{P(A|E_{i})P(E_{i})}}

The law of total probability states that, if events <em>E</em>₁, <em>E</em>₂, <em>E</em>₃... are parts of a sample space then for any event <em>A</em>,

P(A)=\sum\limits^{n}_{i=1}{P(A|B_{i})P(B_{i})}

Denote the events as follows:

<em>X</em> = fetus have a chromosome abnormality.

<em>Y</em> = the test is positive

The information provided is:

P(X)=0.04\\P(Y|X)=0.90\\P(Y^{c}|X^{c})=0.85

Using the above the probabilities compute the remaining values as follows:

P(X^{c})=1-P(X)=1-0.04=0.96

P(Y^{c}|X)=1-P(Y|X)=1-0.90=0.10

P(Y|X^{c})=1-P(Y^{c}|X^{c})=1-0.85=0.15

(a)

Compute the probability of women who are tested negative as follows:

Use the law of total probability:

P(Y^{c})=P(Y^{c}|X)P(X)+P(Y^{c}|X^{c})P(X^{c})

          =(0.10\times 0.04)+(0.85\times 0.96)\\=0.004+0.816\\=0.82

Thus, the proportion of women who are tested, get a negative test result is 0.82.

(b)

Compute the value of P (X|Y) as follows:

Use the Bayes' theorem:

P(X|Y)=\frac{P(Y|X)P(X)}{P(Y|X)P(X)+P(Y|X^{c})P(X^{c})}

             =\frac{(0.90\times 0.04)}{(0.90\times 0.04)+(0.15\times 0.96)}

             =0.20

Thus, the proportion of women who get a positive test result are actually carrying a fetus with a chromosome abnormality is 0.20.

6 0
3 years ago
The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please
Hitman42 [59]

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx

We let the substitution take place.

Therefore, we let u = 1 + 4x^{2}

Thus, du = 8dx.

So,

xdx = \frac{1}{8}du

Also, the interval of the integration changes to [ 37, 65]

Thus,

S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx

= \frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} }  }

= 156.5 units²

8 0
3 years ago
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