Graph the following inequality. Then click to show the correct graph.


3x - 2y ≤ 6

Answer:

[tex]F^{-1} (x) = 2x + 12[/tex]

Step-by-step explanation:

Let's assume F(x) = y, then

[tex]y = \frac{1}{2} x - 6[/tex]

Let us solve the equation for x.

[tex]y + 6 = \frac{1}{2} x[/tex]

[tex]2y + 12 = x[/tex]

Next, replace y with x and also replace x with F⁻¹(x)

Answer: [tex]F^{-1} (x) = 2x + 12[/tex]

Answer:

[tex]h(x) = \frac {3}{2}x + 1 \\ { \tt{let \: the \: inverse \: be \: { \bold{m}}}} \\ { \tt{m = \frac{1}{ \frac{3}{2}x + 1 } }} \\ \\ { \tt{m = \frac{2}{3x + 2} }} \\ \\ { \tt{m(3x + 2) = 2}} \\ \\ { \tt{3x + 2 = \frac{2}{m} }} \\ \\ { \tt{x = \frac{2 - 2m}{3m} }} \\ \\ { \tt{x = \frac{2}{3m}(1 - m) }} \\ \\ { \bf{h {}^{ - 1} (x) = \frac{2}{3x}(1 - x) }}[/tex]

The Answer is -0.985

I just took the test.

Answer:

Fraction of money spent on calculator = 2/5

Find the fraction of money left:

1 - 2/5 = 3/5

Find the fraction of money spent on a book:

4/7 x 3/5 = 12/35

Answer: She spent 12/35 of the money on a book

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To find the fraction of saving:

Fraction of money saved = 1 - calculator - book

Fraction of money saved = 1 - 2/5 - 12/35 = 9/35

Fraction of the money saved = 9/35

Step-by-step explanation:

Answer:

0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Defective

Event B: Manufactured by machine A.

Six percent of all the parts are defective.

This means that [tex]P(A) = 0.06[/tex]

Probability that a part is defective and was manufactured on machine A

3% of the parts manufactured on machine A are defective, manufacture A is responsible for 50% of the parts. So

[tex]P(A \cap B) = 0.03*0.5 = 0.015[/tex]

Find the probability that a part was manufactured on machine A, given that the part is defective.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.015}{0.06} = 0.25[/tex]

0.25 = 25% probability that a part was manufactured on machine A, given that the part is defective.

Answer:

42.02 ft

Step-by-step explanation:

60 : 360 = 44 : x

x = 264 ft (length of the circumference)

C = 2 * radius * pi

radius = C / 2 * pi

Radius = 264 / 2 * pi = 42,016905 ft

Answer:

-4 , -1 , -2 , 0 , +1 , +3

Step-by-step explanation:

Answer:

the integers -4,-2,-1,0, +1, +3

Step-by-step explanation:

because when you put them in order  you find which pairs are located between -5 and +5

-8,-4,-2,-1,0,+3,+8,+9

which tells you that

-4,-2,-1,0, +1, +3 are between -5 and +5

Step-by-step explanation:

a + b = 90

a + c = 180

a) If a = x, the. we can write

x + b = 90 and x + c = 180

or

b = 90 - x

c = 180 - x

b) c - b = (180 - x) - (90 - x)

= 180 - x - 90 + x

= 90

Answer:

hypotenuse:15

Step-by-step explanation:

Pythagorean Theorem is a^2 + b^2 = c^2

"a" and "b" are the legs, "c" is the hypotenuse

9^2 + 12^2 = 225

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

hypotenuse = 15

Answer:

0.46017

Step-by-step explanation:

Given :

Mean score = 75

Standard deviation, s = 10

Areum's score = 76

Probability of scoring higher than Areum is given by :

P(x > 76)

The standardized score : (x - mean) / standard deviation

P(x > 76) = P[Z > (76 - 75) / 10]

P[(Z > 0.1)] = 0.46017 (Z probability calculator)

= 0.46017

Step-by-step explanation:

5 1/2% = 5.5% = 5.5/100 = 0.055

0.055 * 68 = 3.74

Answer:

3.74

Step-by-step explanation:

[tex]5\frac{1}{2}%[/tex] of 68

In order to do this you need to convert 5 1/2 into a decimal!

Answer: 5.5

Explanation: 5 is a whole number and half of one unit will be 0.5

5 + 0.5 = 5.5

Then multiply 5.5 and convert 68 into "0.68"

5.5 × 0.68 = 3.74

Answer: 3.74

Answer:

-7

Step-by-step explanation:

We are given the following functions:

[tex]g(x) = x^2 + 4 + 2x[/tex]

[tex]h(x) = -3x + 2[/tex]

(g•h) (1)

The multiplication is:

[tex](g \times h)(1) = g(1) \times h(1)[/tex]

So

[tex]g(x) = 1^2 + 4 + 2(1) = 7[/tex]

[tex]h(1) = -3(1) + 2 = -3 + 2 = -1[/tex]

Then

[tex]g(1) \times h(1) = 7(-1) = -7[/tex]

So -7 is the answer.

Given:

The system of inequalities is:

[tex]y>-\dfrac{1}{3}x+1[/tex]

[tex]y>2x-3[/tex]

To find:

The graph of the given system of inequalities.

Solution:

We have,

[tex]y>-\dfrac{1}{3}x+1[/tex]

[tex]y>2x-3[/tex]

The related equations are:

[tex]y=-\dfrac{1}{3}x+1[/tex]

[tex]y=2x-3[/tex]

Table of values for the given equations is:

    [tex]x[/tex]                   [tex]y=-\dfrac{1}{3}x+1[/tex]             [tex]y=2x-3[/tex]

   0                             1                              -3

   3                             0                              3

Plot (0,1) and (3,0) and connect them by a straight line to get the graph of [tex]y=-\dfrac{1}{3}x+1[/tex].

Similarly, plot (0,-3) and (3,3) and connect them by a straight line to get the graph of [tex]y=2x-3[/tex].

The signs of both inequalities are ">". So, the boundary line is a dotted line and the shaded region or each inequality lie above the boundary line.

Therefore, the graph of the given system of inequalities is shown below.

Answer:

The equation of a line, having inclination 120° with positive direction of x-axis, .of x-axis, which is at a distance of 3 units from the origin is​. 1. See answer ... where α is the angle with the positive X-axis, made by the perpendicular line drawn Now, from equation  the equation of the straight line will be.

Step-by-step explanation:

Answer:

a)

The null hypothesis is [tex]H_0: \mu \leq 10[/tex]

The alternative hypothesis is [tex]H_1: \mu > 10[/tex]

b-1) The value of the test statistic is t = 1.86.

b-2) The p-value is of 0.0348.

Step-by-step explanation:

Question a:

Test if the battery life is more than twice of 5 hours:

Twice of 5 hours = 5*2 = 10 hours.

At the null hypothesis, we test if the battery life is of 10 hours or less, than is:

[tex]H_0: \mu \leq 10[/tex]

At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:

[tex]H_1: \mu > 10[/tex]

b-1. Calculate the value of the test statistic.

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

10 is tested at the null hypothesis:

This means that [tex]\mu = 10[/tex]

In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.

This means that [tex]n = 45, X = 10.5, s = 1.8[/tex]

Then

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}[/tex]

[tex]t = 1.86[/tex]

The value of the test statistic is t = 1.86.

b-2. Find the p-value.

Testing if the mean is more than a value, so a right-tailed test.

Sample of 45, so 45 - 1 = 44 degrees of freedom.

Test statistic t = 1.86.

Using a t-distribution calculator, the p-value is of 0.0348.

Answer:

To convert kilometres to metres, divide the value by 1000.

0.7 ÷ 1000 = 700 metres

Kayli swam 700 meters in the swimming pool

Hope this helps!

Find the perimeter or circumference and area of each figure. Round to the nearest tenth.

The circumference of a circle with radius r is given by C = 2πr. The radius of the circle is 4 in.

Substitute 4 for r.

[tex]\sf{C=2πr}[/tex]

[tex]\sf{ \: \: \: \: =2π(4)}[/tex]

[tex]\sf{ \: \: \: \: ≈{\color{darkviolet}{25.1}}}[/tex]

The circumference of the circle is about 25.1 in.

The area of a circle with radius r is given by A = πr².

Substitute 4 for r.

[tex]\sf{A = πr²}[/tex]

[tex]\sf{ \: \: \: \: = π(4)²}[/tex]

[tex]\sf{ \: \: \: \: ≈{\color{magenta}{50.3}}}[/tex]

The area of the circle is about 50.3 in².

#Hope it helps!

(ノ^_^)ノ

Answer:

0.79

Step-by-step explanation:

Given the probability distribution :

Payment Methd: Cash Credit Cards Debit Cards Proportion : ____0.11 ____ 0.43 _____0.21

The probability that a customer did not pay with debit card can be obtained as :

If customer did not pay with debit card, then he would have paid with any of the other payment methods

This Can best be obtained using the complement method

P(not debit card) = 1 - P(debit card)

P(debit card) = 0.21

P(not debit card) = 1 - 0.21

P(not debit card) = 0.79

Answer:

5 days

Step-by-step explanation:

75 = 10d +25

-25           -25

50 = 10d

/           /

10        10

5 = d

Answer:

The answer in each numeral is:

Step-by-step explanation:

To obtain the result in each case, you must replace the variable (n) by the value that appears in the second case, I'll explain it with the first exercise:

As you can see, in the second doesn't appear f(n), but f(4), that means you must replace the "n" in the equation by 4, if we do this, we obtain:

The first answer is 28, now we'll continue with the next exercises:

In this form, you can prove the answers are: 28, -19, -33, and -9 respectively.

Answer:

There was a profit of ₹750.

Step-by-step explanation:

325 bags of white cement

Profit of 10 for each bag of white cement. So

[tex]P = 325*10 = 3250[/tex]

500 bags of grey cement.

Loss of 5 for each bag of grey cement. So

[tex]L = 5*500 = 2500[/tex]

What is its profit or loss?

3250 - 2500 = 750

Positive, so profit. There was a profit of ₹750.

Answer:

That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average

Step-by-step explanation:

The National average number of runs scored by a LL team is

μ   =  5.7

Sample Information:

size sample   n = 5

sample average   x  =  7.4

sample standard deviation    s  =  2.88

Is required to investigate if  that sample average is statistically different from the National average

We will do a test with 95 % of confidence Interval that means

significance level α = 5 %   or α = 0.05.

The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.

Then  α = 0.05    α/2  =  0.025

df  =  n  -  1     df  =  5  -  1     df  =  4

Then from t-student table we get  t(c)  =  2.132

Hypothesis test:

Null Hypothesis                                  H₀              x  =  μ

Alternative Hypothesis                      Hₐ              x  ≠  μ

To calculate t (s)

t(s)  = ( x  -   μ ) / s/√n

t(s)  = ( 7.4  -  5.7  )* 2.24 / 2.88

t(s)  =  1.7* 2.24 / 2.88

t(s)  = 1.32

Comparing  t(s)  and  t(c)

1.32 < 2.132

That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average

Answer:

x = 6, y = 12

x = 7  y = 14

Step-by-step explanation:

im pretty sure that right, hope this helps!

Answer:

2 7/12

Step-by-step explanation:

You have to get all the fractions to a common denominator. Smallest common denominator would be 12.

5 and 3/4 turns to 5 and 9/12

2/3 turns to 8/12

2 and 1/2 turns to 2 and 6/12

8/12 + 2 6/12 = 3 2/12

5 9/12 - 3 2/12 = 2 7/12

2 7/12 being the remaining amount

Answer:

7% divided by 1050 is basically 73.5 but the fraction of that is 147/2 hope u find my answer reasonable have a great day.

Step-by-step explanation:

The required, solution set to the given equation is {4}. Option A is correct.

A logarithmic function is a mathematical function that represents the logarithm of a number with respect to a given base. In other words, it is a function that relates a number to its logarithm. The general form of a logarithmic function is f(x) = logₐ(x).

Using the product rule of logarithms, we can combine the two logarithms on the left-hand side of the equation:

log2(x - 2) + log2x = log2[(x - 2) * x] = log2(x² - 2x)

So the given equation becomes:

log2(x² - 2x) = 3

2³ = x² - 2x

8 = x² - 2x

x² - 2x - 8 = 0

Factor this quadratic equation as:

(x - 4)(x + 2) = 0

x - 4 = 0, which gives x = 4

x + 2 = 0, which gives x = -2

However, the logarithm function is only defined for positive values of x, so the only possible solution is:

x = 4

Therefore, the solution set to the given equation is {4}.

Learn more about logarithmic function here:

https://brainly.com/question/30284289

#SPJ2

Answer:

x = 10

Step-by-step explanation:

y = 2x + 1

21 = 2x + 1

21 - 1 = 2x

2x = 20

x = 10

Answer:

0.02275

Step-by-step explanation:

Standard deviation is the square root of variance

Standard deviation= Square(0.0025)= 0.05

Because of the normally distributed, the z- score for 0.9 inches is:

(0.9-0.8)/0.05= 2

-> P(x<= 0.9)= P(2) = 0.97725

-> P (x>= 0.9)= 1-0.97725 = 0.02275

Answer:

Step-by-step explanation:

X                  Y                 X²                              Y²                  XY

993              50               986049                 2500              49650

995              60               990025                 3600              59700

994              60               988036                  3600              59640

1006             40               1012036                 1600              40240

942             120               887364                 14400              113040

1002             40               1004004                 1600              40080

[tex]\sum X: 5932[/tex]   [tex]\sum Y : 370[/tex]     [tex]\sum X^2 : 5867514[/tex]    [tex]\sum Y^2 = 27300[/tex]    [tex]\sum XY : 362350[/tex]

To determine the regression:

[tex]Mean \ (X) = \dfrac{\sum X }{n} \\ \\ = \dfrac{5932}{6} \\ \\ = 988.67[/tex]

[tex]Mean \ (Y) = \dfrac{\sum Y}{n} \\ \\ = \dfrac{370}{6} \\ \\ = 61.67[/tex]

Intercept [tex]b_o = \dfrac{\sum YX *\sum X^2 - \sum X \sum Y}{n(\sum X^2) - (\sum X)^2}[/tex]

[tex]=\dfrac{370(5867514) -(5932)(370)}{6(5867514) - (5932)^2}[/tex]

= 131760.9563

Slope [tex]b_1 = \dfrac{n(\sum XY) -(\sum X *\sum Y) }{n(\sum X^2)-(\sum X)^2}[/tex]

[tex]b_1 = \dfrac{6(362350) -(5932*370) }{6(5867514)-(5932)^2}[/tex]

[tex]b_1 = -1.2600[/tex]

The regression line equation [tex]Y = b_o +b_1X[/tex]

[tex]Y = 131760.96 -1.2600 X[/tex]

We then make a comparison of the slope of the equation to y = mx+c

slope of the equation = -1.2600

the y-intercept corresponds to when X = 0, thus:

y-intercept = 131760.9563

Yes, it is reasonable to interpret the y-intercept of the regression line, Using atmospheric pressure as an explanatory variable due to the fact that:

X is the independent variable and Y exists as the dependent variable.

Answer:

ans: ii) 87° and iii) 60°

Step-by-step explanation:

ii)

y° = 180° - ( 56° + 37°)

missing angle on triangle is alternate angle of y° so are equal and sum of angles of triangle is 180°

iii)

x° + 2x° = 180°

sum of co interior angles is 180°