the square root of $x$ is greater than 3 and less than 4. how many integer values of $x$ satisfy this condition?

Answer: A

Step-by-step explanation:

The solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

The equation of a straight line in point slope form can be also written as-

[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]

We have the following set of equations -

x+3y+z=-8       ..[1]

2x+y-6z=20     ..[2]

x-2y+z=-13        ..[3]

We can write eq [3] as -

z = - 13 - x + 2y

So, eq [1] and [2], will become -

x + 3y + (-13 - x + 2y) = -8

x + 3y - 13 - x + 2y = -8

5y = - 8 + 13

5y = 5

y = 1       ..Eq[4]

AND

2x + y - 6z = 20

2x + y - 6(- 13 - x + 2y) = 20

2x + y + 78 + 6x - 12y = 20

2x + 1 + 78 + 6x - 12 = 20

8x = 47

x = 5.875      ..Eq[5]

Now -

x - 2y + z = -13

5.875 - 2 + z = - 13

z = 16.875

Therefore, the solution for the system of equations -

x+3y+z=-8      

2x+y-6z=20    

x-2y+z=-13    

is x = 5.875, y = 1, z = 16.875.

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We have to prove (cosA−sinA+1)/(cosA-sinA-) = cotA+cosecA using Trigonometric Functions

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

L.H.S=(cosA−sinA+1)/(cosA-sinA-)

dividing by sinA

=cotA+1−cosecA/cotA−1+cosecA

​=(cotA−1+cosecA)(cotA+1+cosecA)/(cotA+1)²-cosec²A

=(cotA+cosec)²-1/2cotA

=cotA+cosecA(R.H.S)

​Hence the above trigonometric function is proved.

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Answer:

[tex]\frac{73}{8}[/tex]

If u mean that x^y+y^x then the above answer is correct. You can more simplify it in decimals if you want.

Norman will measure the light pole to be 12 feet tall

Information from the question

Norman uses his sextant to measure the angle of elevation to be 36

5 feet from the ground. if he is 10 feet away from the light pole

how tall is the light pole = ?

The height of the light pole is calculated using SOH CAH TOA

The direction of movements describes a right angle triangle of

opposite = height of the light pole

adjacent = 10 feet away from the light pole

The height is is calculated using tan, TOA let the angle be x = 36

tan x = Opposite / Adjacent

tan 36 = opposite  / 10

opposite = tans 35 * 10

opposite = 7 feet

this is height 5 feet from the ground, so total height is calculated to be

5 + 7 = 12 feet

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Answer:

[tex]\dfrac{4}{35}[/tex]

Step-by-step explanation:

Dividing a number is the same thing as multiplying by its reciprocal. So:

[tex]\dfrac{4}{7} \div 5 = \dfrac{4}{7} \cdot \dfrac{1}{5}[/tex]

Finally, simplify by multiplying out the numerators and the denominators.

[tex]\dfrac{4}{7} \cdot \dfrac{1}{5} = \dfrac{4 \cdot 1}{7 \cdot 5} = \dfrac{4}{35}[/tex]

Answer:

4/7 divided by 5 is 4/35

Step-by-step explanation:

Step 1: Convert 5 into an improper fraction

    A. 5 = 5/1

Step 2: Divide 4/7 by the reciprocal of 5/1

    B. 4/7 ÷ 1/5 = 4/35

Using a proportional relationship, it is found that:

A. The slope of the line is of 4.

B. The slope is the same over both segments.

A proportional relationship is modeled as follows:

y = kx.

Hence a proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0.

For the presented case, the two variables x and y are direct proportional, and thus the output variable y is obtained as the multiplication of the input variable x by the constant of proportionality k.

In this problem, the relationship has two points presented as follows:

(3, 12) and (4, 16).

Hence the slope, which is the constant of the relation, is given as follows:

k = 12/3 = 16/4 = 4.

Given two points, the slope is given by the change in y divided by the change in x. Hence, over each segment, the slopes are given as follows:

Which are the same slopes.

The problem is given by the image at the end of the answer.

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The exchange rate if each souvenir costs 200 Jamaican dollars, 38 might be purchased.

The exchange rate refers to the value of one country currency about's currency. It is determined by the foreign currency market, often known as the FOREX market.

Amount needed for vacation = $50 USD = $7,740 JMD

Each souvenir is priced at 200 Jamaican dollars.

One US dollar = 154.8 Jamaican dollars when converted to Jamaican currencies.

50 US dollars = 154.8 × 50

= 7,740 Jamaican dollars

Number of souvenirs you can buy = Amount of money with you for vacation ÷ Cost of each souvenir

= 7,740 Jamaican dollars ÷ 200 Jamaican dollars

= 38.7 souvenirs.

As a result, for 200 Jamaican dollars for each souvenir, about 38 souvenirs may be obtained with 50 US dollars.

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Answer:

Step-by-step explanation:

1.
4,000 mm to km = 0.004

4,000 mm to m = 4
4,000 mm to cm = 400

2.

12,000 km to m = 12000000
12,000 km to cm = 1.2e+9
12,000 km to mm = 1.2e+10

3.
5,800 m to km = 5.8
5,800 m to cm = 580000
5,800 m to mm = 5800000

4.
2 mm to km = 2e-6
2 mm to m = 0.002
2 mm to cm = 0.2

5.
40,108 to m = 40108000
40,108 to cm = 4010800000
40,108 to mm = 40108000000

Using the elimination method, the solution to the system of linear equations is: x = 4.5 and y = -5.

Solving a system of linear equations by elimination involves eliminating one of the variables, then solve to find the other variable.

Given the equations:

6x + 5y = 2 --> eqn. 1

4x + 2y = 8 --> eqn. 2

Multiply eqn. 1 by 2 and eqn. 2 by 5:

12x + 10y = 4 --> eqn. 3

20x + 10y = 40 --> eqn. 4

Subtract

-8x = -36

x = 4.5

Substitute x = 4.5 into eqn. 2

4(4.5) + 2y = 8

18 + 2y = 8

2y = 8 - 18

2y = -10

y = -5

The solution is: x = 4.5 and y = -5.

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Answer:

L=12, W=6

Step-by-step explanation:

L=2W

(L+2L)=36

3L=36

2L=12

L=6

The table of solutions for this quadratic equation (y = -2x²) include the following:

x                    y_

-2                  -8

-1                   -2

0                   -0

1                    -2

2                   -8

A graph of the solution of the given quadratic equation has been plotted in the image attached below.

In Mathematics, the graph of any quadratic equation or function always forms a parabola, which simply means a u-shaped curve. In order to determine the correct solutions to the given quadratic equation, we would have to substitute the x-values contained in the table into the quadratic equation.

At point x = -2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(-2)²

y = -2 × 4

y = -8

At point x = -1, the y-value for this quadratic equation is given by:

y = -2x²

y = -2(-1)²

y = -2 × 1

y = -2

At point x = 0, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(0)²

y = -2 × 0

y = 0

At point x = 1, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(1)²

y = -2 × 1

y = -2

At point x = 2, the y-value of this quadratic equation is given by:

y = -2x²

y = -2(2)²

y = -2 × 4

y = -8

In conclusion, we can logically deduce that the graph of this quadratic equation forms a downward parabola.

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Answer:

730 hours = 43800 minutes

Step-by-step explanation:

Formula = multiply the time value by 60

Answer:

43,800 minutes

Step-by-step explanation:

convert 730 hours into minutes​

there are 60 minutes in 1 hour so:

730 * 60 = 43,800 minutes

The mean will be the middle number or 12.1.

According to our question-

The median is the middle number  in the data set when the data set is written from least to greatest.

least to greatest 4.8, 6.9, 12.1, 14.8, 16.2

Hence, The mean will be the middle number or 12.1.

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Answer:f(10) or the power generated by the wind turbine at the wind speed of 10 m/s is 190.26 kW

41/5

Step-by-step explanation:

14/5=9+2+q

14/5=11+q

14=55+5q

14-55=5q

-41=5q

q=-41/5

The value of the expression b(x) = x + 4 is -6.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, b(x) = x + 4.

When x = -10, the value of b will be:

b(x) = x + 4.

b(-10) = - 10 + 4

b= -6

The value is -6.

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The domain of the inequality is from zero to negative infinity

The domain refers to the values in the input of a function, these values are in the x direction.

The domain says the extents the values of the input is therefore no all the input values must be in the domain

Examining the graph shows that the graph reached the point x = 0 and returned with an arrow.

The arrow means that the values continued limitlessly, such limitless values are represented by infinity with symbol ∞.

The infinity is in the negative direction

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Answer:

Step-by-step explanation:

A=lw

= 21/4 in * 1/3in= 21/12 in.^2= 7/4in^2 or 7/4 inch squared

Answer:

I+P=A

Step-by-step explanation:

isolate a on 1 side

I=A—P

+P. +P

I+P=A

Hopes this helps please mark brainliest

Answer:

A=P+I

Step-by-step explanation:

make A the subject of formula

giving A= P+I

9% of the volume of the original volume is removed.

Given that the dimensions of solid box is 15 cm by 10 cm by 8 cm.

So the volume of solid box = 15*10*8 cubic cm = 1200 cubic centimeter

The volume of the cube with side 3 cm = 3*3*3 = 27 cubic centimeter

For each corner one cube so the number of cube is 4

So total volume removed = 4*27 = 108 cubic centimeters

The percent of volume is removed = (108/1200)*100% = 9%

Hence the percentage of volume removed is 9%.

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The measures, using the normal distribution, are given as follow:

a) Probability that a wedding costs less than $20,000: 0.257 = 25.70%.

b) Probability that a wedding costs between $20,000 and $32,000: 0.659 = 65.90%.

c) Minimum cost of the most expensive 5% of weddings:  $33,564

Normal Probability Distribution

The z-score of a measure X of a variable that has to mean symbolized by  and standard deviation symbolized by  is given by the rule presented as follows:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

The z-score represents how many standard deviations measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.

Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of measure X in the distribution.

The mean and the standard deviation for the wedding prices are given as follows:

μ = 23858, σ = 5900

a) The probability that a wedding costs less than $20,000 is the p-value of Z when X = 20000, hence:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z = (20000 - 23858)/5900

Z = -0.65

Z = -0.65 has a p-value of 0.257.

The probability that it costs between $20,000 and $32,000 is the p-value of Z when X = 32000 subtracted by the p-value of Z when X = 20000, found above, hence:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z = (32000 - 23858)/5900

Z = 1.38

Z = 1.38 has a p-value of 0.816.

0.916 - 0.257 = 0.659.

The minimum cost for a wedding to be in the most expensive 5% of weddings is the 95th percentile, which is X when Z = 1.645, hence:

1.645 = (X - 23858)/5900

X - 23858 = 1.645 x 5900

X = $33,564.

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The total number of athletes, the football club has is 180.

Given, In the football club, 36 footballers are Latvian, while there are 4 times the footballers of other nationalities.

as, footballers that are Latvian = 36

now, footballers of other nationalities = 4×36

footballers of other nationalities = 144

so the total number of footballers = 144 + 36 = 180

Therefore, the total number of athletes, the football club has is 180.

Hence, the total number of athletes, the football club has is 180.

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The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

Both t tests and F tests (also known as analyses of variance, or ANOVAs) are based on the premise that the population variances (i.e., the distribution, or "spread," of scores around the mean) of two or more samples are identical. The independent samples t-test and ANOVA employ the t and F statistics, which, provided that group sizes are equal, are often resistant to breaches of the assumption. A ratio of less than 1.5 between the largest and smallest group can be used to identify equal group sizes.

The independent samples t-test and ANOVA make the assumption of homogeneity of variance, which states that all comparison groups have the same variance. The homogeneity of variance is an assumption for the one-way between-subjects anova means each population from which the samples are drawn has the same level of variation.

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Answer:

  a. 3/2 meters

  b. 15/4 times as great

Step-by-step explanation:

You want the width of a rectangle that is 3/5 m² in area and 2/5 m long. You also want to know the factor by which the length is greater than the width.

The formula for the area of a rectangle is ...

  A = LW

Filling in the known values, we can solve for the length:

  3/5 m² = (2/5 m)·L

  L = (3/5)/(2/5) m = 3/2 m . . . . . . divide by the coefficient of L

The length of the rectangle is 3/2 meters.

The ratio of length to width is ...

  length/width = (3/2 m)/(2/5 m) = (15/10)/(4/10) = 15/4

The length is 15/4 times greater than the width.

Formula of parabola for given values is F(x) = 7.5(x^2-15.7x+61.32)

The general equation of a parabola in math is: y = a(x-h)^2 + k ,where (h,k) denotes the vertex. The standard equation of a the parabola is y^2 = 4ax.

We have, horizontal intercepts x=8.4 and x=7.3, passes through point(0, 8.2)

As we parabola is quadratic function,

f(x) = a(x-8.4)(x-7.3)

It is passing through the point (0, 8.2)

8.2 = a(-8.4)(-7.3)

a = 8.2/61.32 =7.5 (approx)

Now, equation of parabola is

F(x) = 7.5(x-8.4)(x-7.3)

f(x) = 7.5(x^2-7.3x-8.4x+61.32)

F(x) = 7.5(x^2-15.7x+61.32)

Thus, required equation of parabola is F(x) = 7.5(x^2-15.7x+61.32).

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There is a 0.091125 probability that all three randomly chosen houses have dogs.

In light of this, imagine that a recent survey of American homes regarding pet ownership revealed that 45% of households with pets were dog-owning, 34% were cat-owning, and 10% were bird-owning households.

• Three families are chosen at random, replaced, and with mutually exclusive ownership.

The calculation of probability is as follows based on the facts above:

=0.43^3

= 0.091125

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The inequality describing oil and tyre change within 180 minutes is 3x + 4y > 60.

Taking each information seperately followed by summing them for a complete equation.

1 oil change taken amount of time = 9 minutes

So, x oil change will take amount of time = 9x

Similarly, y number of tire changes will take amount of time = 12y

Adding these values to form the equation -

Number of oil and tyre changes in less than 180 minutes

Keep the value of each and symbol for 'less than'

9x + 12y > 180

Dividing the inequality by 3

3x + 4y > 60

Hence, the required inequality is 3x + 4y > 60.

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Answer:

24

Step-by-step explanation:

lets set up the equation

x=25-(0.05x20) this is

x=25-1

x=24