Find the value of x if 3x = 23² – 17²

Answer:

6.6

Step-by-step explanation:

you subtract 6.6 from both sides to cancel it out on one side

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0.08891% percent of people have a blood pressure reading greater than 145.

acc to our question-

Hence, 0.08891% percent of people have a blood pressure reading greater than 145.

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Answer:

59/15

Step-by-step explanation:

8/5 + 7/3                       Multiply the numerator and denominator by the LCF of the denominator

(3/3) 8/5 + 7/3 (5/5)      Multiply

24/15 + 35/15                Add the numerators

59/15

The area of the  triangle to the nearest hundredth of a square meter is 0.217m²

A right triangle has a hypotenuse of 1 meter and a leg of 1/2 meter

Hypotenuse = 1

base = 0.5

We need to calculate the perpendicular

h² = b² + p²

1² = 0.5² + p²

p² = 1 - 0.25

p = √0.75

p = 0.866

area of the triangle = 1/2 base x height

area = 1/2 (0.5 x 0.866)

area = 0.2165m²

Therefore the area of the  triangle to the nearest hundredth of a square meter is 0.217m²

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Answer:

Step-by-step explanation:

(12-5)x4=28

By using the rule of 3 we wills ee that the percentage of students who play the trumpet is 20%

We know that there are 150 students in the marching band, that will be our 100% in this case, and we know that 30 of them play the trumpet.

These 30 students represent a percentage X that we want to find, so we can write a little system of equations and use the rule of 3.

30  = X

150 = 100%

Taking the quotient between the two equations we get:

(30/150) = X/100%

Solving for X we get:

(30/150)*100% = X = 20%

So we can say that 20% of the students play the trumpet.

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1. The linear function .f(2) = 79.4, therefore, test average for maths class after 2 test is: 79.4

2. Using the function table, the test average for science class is after the second test is: 84.

3. f(4) = 79.8

4. g(4) = 80

5. Science class was higher.

The equation of a linear function is given as .f(x) = mx + b, given that m represents the slope/unit rate, and b is the y-intercept or starting value.

The linear function for average test score in maths class is given as, .f(x) = 0.2x + 79

Write the linear function for science class;

Slope (m) = change in y/change in x = (84 - 82)/(2 - 3) = 2/-1

Slope (m) = -2

Substitute m = -2 and (x, y) = (3, 82) into y = mx + b:

82 = -2(3) + b

82 = -6 + b

82 + 6 = b

88 = b

b = 88

Substitute m = -2 and b = 88 into g(x) = mx + b:

g(x) = -2x + 88

Part 1:

Substitute x = 2 into .f(x) = 0.2x + 79

.f(2) = 0.2(2) + 79

.f(2) = 79.4

Test average for maths class after 2 test is: 79.4

Part 2:

Using the function table, when x = 2, the test average for science class is: 84.

Part 3:

Substitute x = 4 into  .f(x) = 0.2x + 79

.f(4) = 0.2(4)+ 79

.f(4) = 79.8

Part 4:

Substitute x = 4 into g(x) = -2x + 88

g(4) = -2(4) + 88

g(x) = 80

Part 5:

Science class had a higher test 4 average of 80.

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Answer:  The correct answer is x=−3 or x=5

Step-by-step explanation:

Solve for x^2−2x=15 using the quadratic equation

Step 1) Subtract 15 from both sides

x2−2x−15=15−15

x2−2x−15=0

For this equation: a=1, b=-2, c=-15

1x2+−2x+−15=0

Step 2) Use quadratic formula with a=1, b=-2, c=-15

x= (−b±√b2−4ac)/2a

x= (−(−2)±√(−2)2−4(1)(−15))/2(1)

x= (2±√64)/2

x=5 or x=−3

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a) The margin of error for an 80% confidence interval in Arkansas is 0.1041

b) if we want to get an 80% confidence interval with a small margin of error, say only 7%. then the sample size must be 53,599,359

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error.

n = 3600

standard deviation = 399.876

Confidence Interval = 80%

a) α = 0.20

The margin of error = Zα/2 (σ / √n)

Zα/2 = 1.4395 --- (From the tabular value)

The margin of Error = 1.4395 + 399.876 / √3600

Therefore, the Margin of Error = 8.1041

b) Margin of Error = 0.07 = 7%

α = 0.20

Critical Value = 1.2816

Sample Size = (Zc²σ² / ME²) = (Zcσ / ME)²

n = [(1.2816 * 399.876) / 0.07]²

n = 53599358.98

Therefore, Sample size, n = 53599359

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Answer:

y = [tex]\sqrt{(k-a)}[/tex]

Step-by-step explanation:

k= y^2 + a

k-a= y^2

y^2 = k-a

y = (k-a)^(1/2)

y = [tex]\sqrt{(k-a)}[/tex]

Answer:

[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]

Step-by-step explanation:

To make y-term as the subject of formula means to solve for y-term. First, subtract both sides by a-term, this’ll at least isolate y².

[tex]\displaystyle{k-a=y^2+a-a}\\\\\displaystyle{k-a=y^2}[/tex]

Everything that you do or add to one of both sides, that side will also be done too. (e.g Suppose we have x + 1 = y. If we add 2 to left then 2 should also be added to right too so we’ll have x + 1 + 2 = y + 2)

Then square root both sides to get rid of the exponents of y-term:

[tex]\displaystyle{\sqrt{k-a}=\sqrt{y^2}}[/tex]

If we substitute y = any numbers, we’ll always get positive result. Therefore, this means that y-term can be any positive or negative values. Hence, write plus-minus to the left side then evaluate the square root of y² to y:

[tex]\displaystyle{\pm \sqrt{k-a}=y}[/tex]

Therefore, the new equation written in term of y is:

[tex]\displaystyle{y=\pm \sqrt{k-a}}[/tex]

Answer:

x = 14

Step-by-step explanation:

the inscribed angle JKL is half the measure of its intercepted arc, that is

83 = [tex]\frac{1}{2}[/tex] arc JL = [tex]\frac{1}{2}[/tex](9x + 40) ← multiply both sides by 2 to clear the fraction

166 = 9x + 40 ( subtract 40 from both sides )

126 = 9x ( divide both sides by 9 )

14 = x

number 9 is 36  12x3 is 36

The solution for the expression is X =87/ 48 or 1.812

To solve  for x in the equation we follow the step below:

Step 1: Open the bracket by multiply 4

= 4x +4x/3 = 9 2/3

= 4x +  4x /3 = 29/3

Step 2: Evaluate for X

= [tex]\frac{12x + 4x}{3}[/tex] = [tex]\frac{29}{3}[/tex]

= [tex]\frac{16x}{3}[/tex] =[tex]\frac{29}{3}[/tex]

Step 3: Cross multiply

: 3 (16x) = 3(29)

48x = 87

Step 3: Divide both sides by 48

=[tex]\frac{48x}{48}[/tex] =[tex]\frac{87}{48}[/tex]

x = [tex]\frac{87}{48}[/tex] = 1.812

Therefore, the solution for the expression is X =87/ 48 or 1.812

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The test statistic is -2.60 as a sample of 380 patients found that 95 were uninsured.

A statistic used in statistical hypothesis testing is known as a test statistic. A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is typically expressed. For instance, the Z-statistic, which has the typical normal distribution under the null hypothesis, is the test statistic for a Z-test. Here,

n=380

x=95

p=95/380

p=0.25

test=(0.25-0.31)/√(0.28(1-0.28)/380)

test=-2.60

The test statistic is -2.60 because 95 out of 380 patients in the sample did not have insurance.

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Answer:

y=5x+1

Step-by-step explanation:

we already know the slope so we can put it in the slope intercept form

y=5x

And now we can put the coordinate points in there to find the y intercept

-4=5(-1)

-4=-5

We need to add 1 to make this equation true so the y intercept is 1

The equation will be

y=5x+1

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Answer:

y=5x+1

Steps are in the picture

Answer:

to find horizontal asymptotes, we simply evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.

Step-by-step explanation:

The slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

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 can be also written as -

Ax + By + C = 0

By = - Ax - C

y = (- A/B)x - (C/A)

Given is a equation of a straight line as -

4x - 1 = 3y + 5

We have the equation as follows -

4x - 1 = 3y + 5

Rearranging the equation -

3y = 4x - 1 - 5

3y = 4x - 6

y = (4/3)x - 2

Refer to the graph attached.

The slope of the line is [m] = 4/3

The [y] intercept is at [c] = -2

Therefore, the slope of the linear function → 4x - 1 = 3y + 5 is [m] = 4/3 and the [y] intercept is at [c] = -2

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Answer:

b & d

Step-by-step explanation:

Answer:

-8

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

Answer:

y+1=-4(x+5)

Step-by-step explanation:

it changed to point slope form so now it’s different

the equation is y-y1=m(X-x1)

y-(-1)=m(x-(-5)

y+1=m(x+5)

Now to find slope y2-y1/x2-x1

-5+1/-4+5

-4/1

-4 is the slope so we just fill it in

y+1=-4(x+5)

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Proportionately, it would take the restaurant 22.75 avocadoes to make 14 orders of guacamole since it takes 6.5 avocados to make 4 orders.

Proportion refers to the quantity of a value or variable contained in another value.

Proportion is a fractional value like a ratio that shows the numerical relationship between two or more values.

Proportions are depicted using fractions, decimals, or percentages.

The number of avocados required for 4 orders of guacamole = 6.5

The total number of orders of guacamole required = 14

The number of avocados to make 1 order = 6.5/4

The number of avocadoes required to fill 14 orders = 22.75 (6.5/4 x 14)

Thus, in proportion, it would take 22.75 avocados to make 14 orders of guacamole.

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The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval  (4, −∞).

What is an increasing and decreasing functions?

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

We have,

[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]

[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]

[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]

[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]

The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.

x = 4, 4i, −4i, 10, 8

∴ f′(x) = 0  

   x = 4,

Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)

In interval (−∞, 4),  f′(x) < 0

Hence, the given function (f) is strictly decreasing in interval (−∞, 4)

​

In interval (4, −∞),  f′(x) > 0

Hence, the given function (f) is strictly increasing in interval  (4, −∞)

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Answer:

 3x + y - 4z = -222x + 3y + 4z = 32x - y + 2z = 16 Write and number each equation. Eq 1 3x+y-4z = 16. Eq 2 -222x+3y+4z = 16. Eq 3 32x-y+2z = 16 

Step-by-step explanation:

Hope it helps you buddy(:

Answer: 16

You already got the answer- But whatever.

The values of [x], [y] and [z] are 2, 0 and 7.

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 can be also written to express proportional relationship as -

y = kx  {k is constant}

We have the following system of equation -

3x+y-4z=-22

2x+3y+4z=32

x-y+2z=16

We can write -

x - y + 2z = 16

x = 16 + y - 2z

So, we can write 3x + y - 4z = -22 as -

3(16 + y - 2z) + y - 4z = -22      ...eq[1]

and we can write 2x + 3y + 4z = 32 as -

2(16 + y - 2z) + 3y + 4z = 32      ...eq[2]

Plot eq[1] and eq[2], and find [y] and [z]. Refer to graph.

We get y = 0 and z = 7

So -

x = 16 + 0 - 14

x = 2

Therefore, the values of [x], [y] and [z] are 2, 0 and 7.

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The runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

In this question, we have been given the data for the distance and amount of time each person ran one Saturday morning.

We need to select all the runners whose speeds are in a proportional relationship with each other.

We find the speed using formula, speed = distance / time

Name         Time (seconds)           Distance (miles)              Speed(mps)

Liam                   306.6                           0.5                      0.5/306.6 = 0.0016    

Taylor                756.36                          1.2                      1.2/756.36 = 0.0016

Sarah                 504.35                         0.7                     0.7/504.35 = 0.0014

Ashley               459.9                          0.75                    0.75/459.9 = 0.0016

Connor              600.5                              1                          1/600.5 = 0.0017

Nathan               942.75                         1.5                     1.5/942.75 = 0.0016

Juan                   827.82                         1.35                  1.35/827.82 = 0.0016

Katie                   429.48                          0.6                   0.6/429.48 = 0.0014

Therefore, the runners whose speeds are in a proportional relationship with each other:

the running speed of Liam, Taylor, Ashley, Nathan, Juan are equal (0.0016) whereas the running speed  of Sarah and Katie are equal.

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The required positive number whose product is 25 and whose sum is minimum is 5, 5

Sum of two numbers means adding two same or different number together

Let two positive numbers xy = 25

Divide both side by x

y  = [tex]\frac{25}{x}[/tex]  ----------Equation (1)

Sum of two positive numbers s = x + y  -------Equation (2)

Substitute equation (1) into equation (2)

S = x + [tex]\frac{25}{x}[/tex]

differentiate with respect to x

[tex]\frac{ds}{dx} = \frac{d}{dx} (x + \frac{25}{x} ) = 1 - \frac{25}{x^{2} }[/tex]

[tex]\frac{ds}{dx} = 1-\frac{25}{x^{2} }[/tex]  ---------- Equation (3)

[tex]\frac{ds}{dx} = 0[/tex]

[tex]1[/tex][tex]- \frac{25}{x^{2} }[/tex] = 0  ⇒ [tex]x^{2}[/tex] = 25

x = 5

Differentiate equation (3) again

[tex]\frac{d^{2}s }{dx^{2} } = 0 + \frac{50}{x^{2} }[/tex]

hence, at point x = 5,   [tex]\frac{d^{2} s}{dx^{2} } = \frac{50}{5^{2} }[/tex]  [tex]= \frac{50}{25} = 2[/tex]

Value of s minimum at point x = 5.

substitute the value of x into equation (1)

[tex]y = \frac{25}{x} = \frac{25}{5} = 5[/tex]

Therefore the required positive numbers are 5, 5.

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The simplified for of the Algebraic expression which is the sum of two terms is 1 + 7x

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms which can either be a variable or a constant .

11 + 5(3x - 2) -8x

multiply out the bracket we have,

11 + 15x - 10 -8x

collect like terms and simplify

11 - 10 + 15x - 8x

1 + 7x

In conclusion, the expression 11 + 5(3x - 2) as a sum of two terms is 1 + 7x

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The percentage of variation in variable can be accounted for by the other variable is 81%.

What is variation in statistic?

The statistical distance between the values of the observations (data points) is what makes up a measure of variance. There are various ways to measure variation.

What is correlation coefficient?

A statistical indicator of the strength of a linear link between two variables is the correlation coefficient.

The formula of percentage of variation is:

(correlation coefficient × correlation coefficient × 100)%.

Given that the correlation coefficient is 0.90.

Thus the percentage of variation is (0.90 × 0.90 × 100)% = 81%

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Answer:

1) 71.83

2) 43

3) 41

4) 755.66

5) 458

6) 1757.12

7) 123 meters