Solve the proportion for x.

A x=2
B x=3
C x=5
D x= 10​

Answer:

4.7

Step-by-step explanation:

Given :

initial mean length =4.1  minutes.

Final mean length =5.3 minutes

The mid point of the given interval can be determined by the

[tex]Midpoint \ = \frac{Initial\ Mean\ length\ +Final\ Mean\ length }{2} \\Midpoint \ = \frac{4.1\ +\ 5.3\ }{2} \\Midpoint \ = \frac{9.4 }{2} \\Midpoint \ =4.7\\[/tex]

Therefore 4.7 is the midpoint

Answer:

Step-by-step explanation:

Hello,

We just need to apply the formula using the discriminant

[tex]-6x^2-2x+1=0\\\\\Delta = b^2-4ac = (-2)^2-*4(-6)*1=4+24=28[/tex]

so we have two distinct real solutions

[tex]x_1=\dfrac{2+\sqrt{28}}{2*(-6)}=\dfrac{2+2\sqrt{7}}{2*(-6)}=-\dfrac{\sqrt{7}+1}{6} \\\\ and \\\\x_2=\dfrac{\sqrt{7}-1}{6}[/tex]

Hope this helps

Answer:

The x-values of the inflection points of the curve are x = -52 and x = 52.

Step-by-step explanation:

Suppose we have a normal curve with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex]

The x-values of the inflection points of the curve are [tex]x = \mu - \sigma[/tex] and [tex]x = \mu + \sigma[/tex]

x ~ N(0, 52)

This means that [tex]\mu = 0, \sigma = 52[/tex]

So

[tex]x = 0 - 52 = -52[/tex]

[tex]x = 0 + 52 = 52[/tex]

The x-values of the inflection points of the curve are x = -52 and x = 52.

The statement; the area of a rectangle is 6 if and only if its length and width are 3 and 2 is true

Area of a rectangle = length × width

= 3 × 2

= 6

Therefore, the area of a rectangle is 6 if and only if its length and width are 3 and 2 is true

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Answer:

a. ans=1

b. ans=2/5

c. ans=4

hope u understood...

Answer:  see below

Step-by-step explanation:

Inverse is when you swap the x's and y's.

The Slope-Intercept form is [tex]y=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]    which isn't convenient to graph.

So take the points from the original equation (-1, -2) & (0, 3) and switch the x's and y's to get the points (-2, -1) & (3, 0).

Draw a line through points (-2, -1) and (3, 0) to sketch the graph of the inverse.

Answer:

D

Step-by-step explanation:

Sample space = {H1,H2, H3, H4, H5, H6 , T1, T2, T3, T4, T5, T6}

So, (H, 6) is an element in the sample space

Answer:

(7, 5.25) lies on the graph.

Step-by-step explanation:

We are given the following values

x = 4,   6,  8, 12 and corresponding y values are:

y = 3, 4.5, 6, 9

Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.

Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:

[tex]y=mx+c[/tex]

where m is the slope.

(x,y) are the coordinates from where the line passes.

c is the y intercept.

Here,

[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]

Formula for slope is:

[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]

Now, the equation of line becomes:

[tex]y=\dfrac{3}{4}x+c[/tex]

Putting the point (4,3) in the above equation to find c:

[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]

So, final equation of given function is:

[tex]y=\dfrac{3}{4}x[/tex]

OR

[tex]4y=3x[/tex]

As per the given options, the point (7, 5.25) satisfies the equation.

So correct answer is [tex](7, 5.25)[/tex].

Step-by-step explanation:

n = 61,647, p = 0.26, q = 0.74

μ = p = 0.26

σ = √(pq/n) = 0.00177

At 0.05 significance, z = 1.96.

0.26 ± 1.96 × 0.00177

(0.257, 0.263)

0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.

Behold the quotient of F and the product of r,s, and T:  F / (r·s·T)

The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).

The number which is being divided is the dividend.

The number with which we are dividing is the divisor.

The result when a dividend is divided by the divisor is the quotient.

A remainder is the extra portion of a number when it isn't completely divisible.

Given, Are some variables F, r, s, and t.

Now, The product of r,s, and T is,

= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,

F/(r×s×T).

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Answer:

105.6 miles

Step-by-step explanation:

In the diagram

The angle at B = 59.7°-29°=30.7°

The angle at A =180°-(78.9°+59.7°)=41.4°

Using the sum of angles in a triangle, Angle C = 107.9°

Applying the Law of Sines

[tex]\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\\b=\dfrac{c}{\sin C} \times \sin B\\\\=\dfrac{456.2}{\sin 107.9^\circ} \times \sin 30.7^\circ\\\\AC=b=244.76$ miles[/tex]

Similarly

[tex]\dfrac{a}{\sin A}=\dfrac{c}{\sin C}\\a=\dfrac{c}{\sin C} \times \sin A\\\\=\dfrac{456.2}{\sin 107.9^\circ} \times \sin 41.4^\circ\\\\BC=a=317.04$ miles[/tex]

Therefore:

AC+BC=244.76+317.04 =561.8 miles

Difference

561.8 - 456.2 =105.6 miles

Therefore, Adam would receive 105.6 miles more frequent flyer miles.

Answer:

30 dimes and 20 quarters

30×.10=$3.00

20×.25=$5.00

30+20=50

$3+$5=$8

Answer:

The answer is given below

Step-by-step explanation:

a) Let u and v be real numbers. The sum of u and v = u + v and the difference between u and v = u - v.

u + v < u - v means the sum of two real numbers is less than the difference between the two numbers.

There exist two real numbers such that their sum is less than the difference between them

This is true when atleast one of the numbers is negative, for example u = 2 and v = -2

u + v = 2 + (-2) = 0 , u - v = 2 - (-2) = 4

u + v < u - v.

b) Let x be a real number and x² be the square of the real number

x² < x means that the square of a real number is less than the real number

We can rewrite the statement as: There exist a real number such that its square is smaller than itself.

The statement is true for x is between 0 and ±1

E.g. for x = 1/2, x² = (1/2)² = 1/4

1/4 < 1/2

c) Let n represent all positive integers. n² is the square of n.

n²≥n means that the square of n is greater or equal to n.

We can rewrite the statement as: For all positive integer numbers, the square of the number is greater than or equal to the number itself

The statement is true.

1² ≥ 1, 2² ≥ 2 e.t.c

d)  Let a and b be real numbers. The sum of a and b = a + b. |a| is the absolute value of a and |b| is the absolute value of b

|a+b|≤|a|+|b| means the absolute value of the sum of two real numbers is less than or equal to the sum of their individual absolute value.

We can rewrite the statement as: For two real numbers, the absolute value of their sum is less than or equal to their individual absolute value sum.

This statement is true for all real numbers.

Evaluating the expressions given using appropriate illustrations, all the statements are True.

Statement 1 :

Real numbers ar both rational and irrational values and hence can be tweaked using arithmetic operators such as addition. Hence, the Statement is True

Statement 2 :

Real numbers can be expressed or raised to the power of another number such as being squared.

Statement 3 :

The squared Value of all positive integers is always greater than or equal the value.

Statement 4 :

The absolute value of a sum is always less than or equal to the sum of the absolute values two numbers

a = 3 ; b = - 4

|a + b | = |3-4| ≤ |-3|+|4|

|-1| ≤ 3 + 4

-1 ≤ 7

Therefore, all the statements are true.

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Answer:

Step-by-step explanation:

The answer is 2,4,3 and -9

The range is the y value

Answer:

The answer is option B.

√5

Hope this helps you

Answer:

B. [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Irrational numbers cannot be expressed as simple fractions.

3/5 is a fraction.

[tex]\sqrt{5}[/tex] cannot be expressed as a fraction.

-3.5 can be written as -7/2.

3.555... can be written as 32/9.

Step-by-step explanation:

Volume is = 4ft × 4ft × 8ft

= 128 cubic feet

Answer:

The answer is "As the number of files increases, the storage space used decreases."

Step-by-step explanation:

When the music files are put into storage they take up space, this causes the storage space to decrease.

Answer:

As the number of files increases, the storage space used increases.

Answer:

7x-1

Step-by-step explanation:

The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of  (f+g)(x) is : 7x-1.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

given that,

If f(x) = 5x – 2 and g(x) = 2x + 1,

now, we have to find (f+g)(x).

so, we have,

f(x) = 5x – 2

and g(x) = 2x + 1

now,

(f+g)(x)

=f(x)+g(x)

=5x-2+(2x+1)

=5x-2+2x+1

=7x-1

Hence, The solution is : If f(x) = 5x – 2 and g(x) = 2x + 1, then the value of  (f+g)(x) is : 7x-1.

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Answer: 14/11

Step-by-step explanation:

When 14/11 is multiplied by 1/4, you get a repeating decimal.  All repeating decimals are rational.

Hope it helps <3

Answer:

<MAX = 93

Step-by-step explanation:

Since <MAX is technically <1 + <5, we know that <1 is 28 and <5 is 65. We can add both of these angles up to solve for <MAX, which is 28 + 65 = 93.

The angle of MAX is 93 degrees.

The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.

Since m∠MAX = m∠1 + m∠5,

we know that m∠1 = 28 and m∠5 = 65.

To solve for m∠MAX, which is 28 + 65 = 93.

Thus, the angle of MAX is 93 degrees.

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Answer:

The correct answer to the following question will be "60 students".

Step-by-step explanation:

Marta will be taking a sampling frame from some kind of 600 student group.

Mean,

N = 60  

Although the sampling method could perhaps consist of the following components 10% of the population,

⇒  [tex]600\times 10 \ percent[/tex]

⇒  [tex]60[/tex]

In order to view these findings as autonomous, 60 students would then have to analyze Marta lacking replacements.

Marta have to sample 60 students without replacement to treat the observations as independent.  

Given,

Marta is going to take a sample from a population of 600 students.

We have to find the no. of students Marta have to sample without replacement.

The 10% condition states that sample sizes should be no more than 10% of the population. Normally, Bernoulli trials are independent, but it's okay to violate that rule as long as the sample size is less than 10% of the population.

So,

[tex]N=10\% \ of \ 600[/tex]

[tex]N=\frac{10}{100} \times600[/tex]

[tex]N=60[/tex]

Hence, Marta have to sample 60 students without replacement to treat the observations as independent.

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Answer: 132

Step-by-step explanation: To solve this equation we know that x is greater than 81 unless the equation would not make sense. 81 + 51 = 132

Answer: x=132

Step-by-step explanation: Add 51 to 81, as positive 51 is the inverse of -51. You need to get the x alone. Therefore, 51+81=132 and x=132.

Answer:

[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-2.162)=0.0306[/tex]  

Step-by-step explanation:

Information given

n=100 represent the random sample taken

[tex]\hat p=0.21[/tex] estimated proportion of the readers owned a particular make of car

[tex]p_o=0.31[/tex] is the value that we want to test

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We need to conduct a hypothesis in order to test if the true proportion is 0.31 or no.:  

Null hypothesis:[tex]p=0.31[/tex]  

Alternative hypothesis:[tex]p \neq 0.31[/tex]  

The statistic is given by:

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

And replacing we got:

[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-2.162)=0.0306[/tex]  

Answer:

0.41

Step-by-step explanation:

Given;

5.6, 5.2, 4.6, 4.9, 5.7, 6.4

To calculate the variance of a given set of ungrouped data, follow the following steps;

(i). First calculate the mean (average) of the data as follows;

[tex]\frac{5.6 +5.2 +4.6+ 4.9 +5.7 +6.4}{6}[/tex] = [tex]\frac{32.4}{6}[/tex] = 5.4

(ii) Secondly, find the deviation of each point data from the mean as follows;

5.6 - 5.4 = 0.2

5.2 - 5.4 = -0.2

4.6 - 5.4 = -0.8

4.9 - 5.4 = -0.5

5.7 - 5.4 = 0.3

6.4 - 5.4 = 1.0

(iii) Thirdly, find the square of each of the results in step ii.

(0.2)² = 0.04

(-0.2)² = 0.04

(-0.8)² = 0.64

(-0.5)² = 0.25

(0.3)² = 0.09

(1.0)² = 1.0

(iv) Fourthly, find the sum of the results in step iii.

0.04 + 0.04 + 0.64 + 0.25 + 0.09 + 1.0 = 2.06

(v) The variance, v, is now the quotient of the result in step (iv) and n-1. i.e

v = [tex]\frac{2.06}{n-1}[/tex]

Where;

n = number of data in the set

n = 6 in this case

Therefore,

v = [tex]\frac{2.06}{6-1}[/tex]

v = [tex]\frac{2.06}{5}[/tex]

v = 0.412

Therefore, the variance is 0.41 to the nearest hundredth

Answer:

.34

Step-by-step explanation:

god this is so boring

Answer:

245 might be the answer

Step-by-step explanation:

(7*7*10)/2

Answer:

A. y=-1/4x

Step-by-step explanation:

We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.

Answer:

An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.

See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?

July 10 book Science up55 down8

AA BB

CC DD

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{7}[/tex]

Step-by-step explanation:

There are 7 days in a week.

For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.

Let Event A be the event that the first person was born on a day of the week.

Therefore:

[tex]P(A)=\dfrac{7}{7}=1[/tex]

The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.

Let Event B be the event that the second person was born.

Therefore, the probability that the second person was born on the same day as the first person:

[tex]P(B|A)=\dfrac{1}{7}[/tex]

By the definition of Conditional Probability

[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]

The probability that both were born on the same day is:

[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]

Answer:

  A.)  The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.

Step-by-step explanation:

For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...

  g(x) = k·f(x)

For translation up by k units, f(x) is transformed to ...

  g(x) = f(x) +k

___

Comparing the following ...

  f(x) = log(x)

  g(x) = 2·log(x) +6

We see that a multiplication factor and an addition factor have been applied. That means ...

  g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.

Answer:

A.)  The graph of g(x) is the graph of f(x) expanded vertically by a factor of 2, and translated 6 unit(s) up.

Step-by-step explanation:

For vertical expansion by a scale factor of k, the graph of f(x) is transformed to ...

 g(x) = k·f(x)

For translation up by k units, f(x) is transformed to ...

 g(x) = f(x) +k

___

Comparing the following ...

 f(x) = log(x)

 g(x) = 2·log(x) +6

We see that a multiplication factor and an addition factor have been applied. That means ...

 g(x) is f(x) expanded vertically by a factor of 2, and translated up 6 units.

Step-by-step explanation:

I just used this and I got it correct

Answer:

[tex]sec\ y = \frac{6}{b}[/tex]

Step-by-step explanation:

Given

[tex]sin\ y = \frac{a}{6}[/tex]

[tex]tan\ y = \frac{a}{b}[/tex]

Required

sec y

From trigonometry;

[tex]sec\ \theta = tan\ \theta\ /\ sin\ \theta[/tex]

Substitute y for θ

[tex]sec\ y= tan\ y\ /\ sin\ y[/tex]

Substitute values for tan y and sin y

sec y = a/b ÷ a/6

[tex]sec\ y= \frac{a}{b} /\ \frac{a}{6}[/tex]

[tex]sec\ y= \frac{a}{b} *\ \frac{6}{a}[/tex]

[tex]sec\ y= \frac{6 * a}{a *b}[/tex]

[tex]sec\ y= \frac{6 a}{ab}[/tex]

Divide numerator and denominator by a

[tex]sec\ y= \frac{6}{b}[/tex]

Hence, the value of sec y is

[tex]sec\ y= \frac{6}{b}[/tex]