What is the solution? X/12+3< or = 7

Answer:

A.

Step-by-step explanation:

Density = Mass / Volume

D = 3/0.2

D = 15 kg/m³

Answer:

density=mass/volume

d=3kg/0.2m3

=15kgm-3

Answer:

b. external validity

Step-by-step explanation:

External Validity is the applicability of the results of an experiment to the real world. Most times, there are threats to the validity of an experiment which could result in little or no effect on the general population. For example, if the method of selection reflects a measure of bias, then this could affect the result. Also if the participants are taking different aspects of the same test, it could also affect its validity as they may not be able to make a correct conclusion. If the sample size is not reflective of the entire population, it could also pose a threat to the validity of the experiment.

John's experiment is weak in its external validity because it cannot be generalized to the entire population of customers. He has to identify the threats to the validity of his experiment and correct them. For example, the sample selection may be biased.

Answer:

B. 4x² - 20x  + 26

Step-by-step explanation:

→Set it up, like so:

(2x - 5)² + 1

4x² - 20x + 25 + 1

→Add like terms (25 and 1):

4x² - 20x + 26

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

The given equation is x²+24x=33.

We need to factorise the equation using completing the square method.

Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.

Now, x²+24x-33=0

Add and subtract (b/2)²=144 to the equation.

x²+24x-33+144-144=0

⇒x²+24x+144-33-144=0

⇒(x+12)²-177=0

⇒(x+12)²=177

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

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Answer:

SD = 5.987, Var(X) = 35.85

Step-by-step explanation:

Apply the standard deviation formula, remembering that n represents the sample size. Then, just take the square of the standard deviation to obtain the variance.

Hope this helps!

Answer:

46/ 67

Step-by-step explanation:

The numbers of students irrespective of grades is;

The sum of the last roll of numbers:

10+24+ 33+ 67 = 134

The number of males irrespective of grades is the sum of the numbers in the male row ;

7 +20+ 14 +41= 82

The numbers of students with grade A is the first column at the last row and is 10;

Hence;

the probability that the student was male OR got an 'A' is

the probability that the student was male plus the probability that he/she got an 'A'.

The probability that it's a male is ;

Number of males/ total number of students

=82/134

The probability that he got an A is;

The number of students that got A/ the total number of students;

10/134

Hence

the probability that the student was male OR got an 'A' is;

82/ 134 + 10/134 = 92/134 = 46/ 67

Answer:

x < 11

Step-by-step explanation:

[tex]5(x+4)<75 \\ open \: the \: bracket \: using \: 5 \\ 5x + 20 < 75 \\ subtract \: - 20 \: from \: both \: sides \: [/tex]

[tex]5x + 20 - 20 < 75 - 20 \\ 5x < 55 \\ divide \: both \: sides \: of \: the \: equation \: \\ by \: 5[/tex]

[tex] \frac{5x}{5} < \frac{55}{5} \\ x < 11[/tex]

The required solution of inequality is,

⇒ x < 11

We have to simplify the expression,

⇒ 5 (x + 4) < 75

We can simplify it by definition of inequality as,

⇒ 5 (x + 4) < 75

⇒ 5x + 20 < 75

Subtract 20 both side,

⇒ 5x + 20 - 20 < 75 - 20

⇒ 5x < 55

⇒ 5x - 55 < 0

⇒ 5 (x - 11) < 0

⇒ x - 11 < 0

⇒ x < 11

Therefore, The required solution of inequality is,

⇒ x < 11

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Answer:

350 miles long.

Step-by-step explanation:

First, we analyze the breakdown of the journey

Let the total distance of the journey =x

Therefore:

10% of the total distance of the journey =35 miles

10% of x=35

0.1x=35

Divide both sides by 0.1

x-350 miles

Therefore, the journey was 350 miles long.

Answer:

The journey was 350 miles long

Step-by-step explanation:

The parameters given are;

Distance traveled by Abena alone = 40% and the last half

∴  Distance traveled by Abena alone = 40% + 50% = 90%

Distance Abena traveled with Saralyn = 35 miles = 100% - 90% = 10%

Hence 10% of Abena's journey = 35 miles

The total distance of Abena's journey therefore, is given as follows

10% = 35 miles

Total distance of Abena's journey = 100% of Abena's journey = 10 × 10%

10 × 10% = 10 × 35 miles = 350 miles

The total distance of Abena's journey = 350 miles.

Answer:

B.

Step-by-step explanation:

Since two diameters are intersecting eachother, the angles inside them would be vertical angles so they'll be congruent.

So

m<LYM = m<JYM

Also their arcs would be equal to their angles measures so,

Arc JK = 52°

Answer:

The geometric mean growth rate of sales is 1.4422.

Step-by-step explanation:

We have two sales values, one from 6 years ago and the other from now.

We have to calculate the geometric growth rate of sales.

We have:

[tex]y(-6)=1,000,000\\\\y(0)=9,000,000[/tex]

We can write the relation between these two values as:

[tex]y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422[/tex]

The geometric mean growth rate of sales is 1.4422.

Answer:

The rooms should be rented at $75 per day for a maximum income of $11250 per day.

Step-by-step explanation:

If the daily rental is increased by $ x

then

Rental:  R (x )=( 40 + x )  dollars per room-day

Number of rooms rented:  N ( x ) = ( 220 − 2 x )  and

Income:  I ( x ) = ( 40 + x ) ( 220 − 2 x ) =8800+140x-2x²  dollars/day

The maximum will be achieved when the derivative of  I ( x )  is zero.

[tex]\frac{dI(x)}{dx} =140-4x=0[/tex]

x=35

so, ($40+$35)=75$per day

 I ( x35) =8800+140(35)-2(35)²= 11250

Answer:

Donde didn't multiply 4(1+3i)

Answer: it’s A he did not apply distributive property yo

Step-by-step explanation:

Answer:

f(g(x))=12x+1

Step-by-step explanation:

f(g(x)) = -2(-6x+3)+7

f(g(x))= 12x-6+7

f(g(x))=12x+1

Domain: All real numbers

Answer:

Option D

Step-by-step explanation:

This question is based on the " Partition Postulate. " You might be familiar with it, it states that a whole is composed of several parts. In this case you could say that this " whole " is ∠ ABC, and the " parts " are ∠1 and ∠2. By this Theorem you could also state the following;

[tex]m< ABC = m< 1 + m< 2,\\\\Substitute,\\110 = 4x + ( 5x + 10 ),\\110 = 4x + 5x + 10,\\4x + 5x + 10 = 110 - Option D\\\\Solution - Option D[/tex]

Hope that helps!

Answer:

175

Step-by-step explanation:

+ × - = -

thus 199+(-24)

199-24

175

Answer: 199 + -24 = 175

Step-by-step explanation: 199 is a positive number and -24 is a negative number. If the positive number is bigger than the negative number you subtract. So forget that the - sign is there and subtract it.  

Answer:

D.

Step-by-step explanation:

Since opposite angles of a quadrilateral inscribes in a circle add up to 180°

So,

<P + <N = 180°

2x+2x-12 = 180°

4x = 180+12

4x = 192

Dividing both sides by 4

x = 48

Now

<P = 2(48)

<P = 96

Now

<N = 2(48)-12

<N = 96-12

<N = 84

Answer:

The mass of the grains = 120 ± 1 g

Step-by-step explanation:

we are given the following:

Total mass of container + grains = 185 grams

Mass of container = 65 grams

Therefore, mass of grains is calculated as follows:

Mass of grains = ( Mass of container + grains) - mass of container

= 185 - 65 = 120 grams.

since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g

Answer:

  cos(20°)

Step-by-step explanation:

The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.

The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.

  sin(70°) = cos(20°)

Answer:

[tex]\frac{8}{49}[/tex]

Step-by-step explanation:

Orange: [tex]\frac{4}{7}[/tex]

Red: [tex]\frac{2}{7}[/tex]

[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]

Answer:

(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.

(b) Roughly 16% of vehicle speeds exceeded 57 mph.

Step-by-step explanation:

We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.

For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.

Let X = vehicle speed at impact

SO, X ~ Normal([tex](\mu=42,\sigma^{2} = 15^{2}[/tex])

Here, [tex]\mu[/tex] = population average speed = 42 mph

         [tex]\sigma[/tex] = standard deviation = 15 mph

Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;

(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;

68% data values will lie between [ [tex]\mu-\sigma , \mu+\sigma[/tex] ] , i.e;

        [ [tex]\mu-\sigma , \mu+\sigma[/tex] ]  =  [42 + 15 , 42 - 15]

                                 =  [57 , 27]

So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.

(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.

It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.

This means that roughly 16% of vehicle speeds exceeded 57 mph.

Answer:

= ( $72.756, $110.804)

Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)

Critical value at 90% confidence = 1.645

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $91.78

Standard deviation r = $23.13

Number of samples n = 4

Confidence interval = 90%

Using the z table;

z(α=0.05) = 1.645

Critical value at 90% confidence = 1.645

Substituting the values we have;

$91.78+/-1.645($23.13/√4)

$91.78+/-1.645($11.565)

$91.78+/-$19.024425

$91.78+/-$19.024

= ( $72.756, $110.804)

Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)

Answer:

For ease of writing, θ [tex]=x[/tex]

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]

Step-by-step explanation:

Our angle is [tex]x=\frac{3\pi }{4}[/tex]

To find our answers for [tex]sin(\frac{3\pi}{4} )[/tex] and [tex]cos(\frac{3\pi}{4} )[/tex], we will need to use a unit circle. (I have attached the image of one).

Recall that the [tex]sin[/tex] of an angle is equal to the y-value of the corresponding ordered pair.

And the [tex]cos[/tex] of an angle is equal to the x-value of the corresponding ordered pair.

For the angle [tex]x=\frac{3\pi }{4}[/tex], the ordered pair is [tex](-\frac{1}{\sqrt{2}} }, \frac{1}{\sqrt{2} } )[/tex]

This means that

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]

Answer:

all reals

Step-by-step explanation:

all reals as |x| >= 0 for every x real

so |x| > -9 is always true

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of guesses made for the sat questions.

Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2

Probability of failure, q = 1 - p = 1 - 0.2 = 0.8

the probability that the number x of correct answers is fewer than 4 is expressed as

P(x < 4)

From the binomial distribution calculator,

P(x < 4) = 0.97

Answer:

Step-by-step explanation:

Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/σ

Where

x = sample mean

µ = population mean

σ = standard deviation

From the information given,

µ = 0

σ = 1

the probability that a given score is less than negative 1.15 is expressed as

P(x < - 1.15)

z = (- 1.15 - 0)/1 = - 1.15

Looking at the normal distribution table, the probability corresponding to the z score is 0.13

P(x < - 1.15) = 0.13

The sketch of the region is shown in the attached photo

Answer:

[tex]x=15^\circ[/tex]

Step-by-step explanation:

Please refer to the attached figure for labeling of given diagram:

We are given the following angles:

[tex]\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ[/tex]

Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.

Using property of vertically opposite angles:

[tex]\angle EOF = \angle AOB = 7x^\circ[/tex]

Line CD is a straight line, so [tex]\angle COD = 180^\circ[/tex]

Also,

[tex]\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ[/tex]

Hence, answer is [tex]x = 15^\circ[/tex].

Answer:

b

Step-by-step explanation:

add the three numbers together then minus from the main total

Answer:

B. $899.15

Step-by-step explanation:

Answer:

-26

Step-by-step explanation:

2(x-4)=3(x+6)

2x-8=3x+18

2x-2x -8 = 3x-2x +18

-8 =X+18

-8-18=x+18-18

-26 = x

The value of the unknown number is -26.

Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the unknown number x.

Twice the difference of a number and 4 = 2(x-4)

Three times the sum of the number and 6 = 3(x+6)

So, equation is 2(x-4)=3(x+6)

⇒ 2x-8=3x+18

⇒ 3x-2x=-8-18

⇒ x=-26

Therefore, the value of the unknown number is -26.

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Answer:

(0,34)

Step-by-step explanation:

I graphed the coordinates of the table on the graph below to find the y-intercept.