Rewrite 4^-3 x 4 using a single positive exponent.

In linear equation ,The mean  number that the test positive for the HIV virus is 2.1 .

What in mathematics is a linear equation?

Let x be the number of blood samples test positive for the HIV virus in a sample of 70 blood test.

Here X ~ Binom( n = 70, p = 0.03)

Using binomial distribution property , the mean of X is

μ = ηp

    = 70 * 0.03  = 2.1

The mean  number that the test positive for the HIV virus is 2.1 .

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The constant of proportionality of y = 9x is 9.

i.e  y ∝ x and y = 9x

Option B is the correct answer.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

y = 9x

y = liters of water the baseball team drinks each practice

x = number of practice

We have an equation that after four practices, the team will have consumed 36 liters of water.

y = 36

9x = 38

x = 4

The equation can be written with a constant of proportionality as:

y ∝ x

y = 9x

So,

9 is the constant of proportionality.

Thus,

The constant of proportionality of y = 9x is 9.

i.e

y ∝ x

y = 9x

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Answer: The constant of proportionality of y = 9x is 9

Given the attached graph, the statement that is NOT true about scarlet's dive is that "She hits the water at 3 seconds." (Option D) See the explanation below.

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In this scenario, the relationship represented is between Scarlet's descent from a 10-foot platform and the time it takes her to complete the trajectory from point of dive to point of reaching the water.

Hence, it is clear from the graph attached that Scarlet hits the water at 3.25 seconds.

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Answer:

  10.97 seconds

Step-by-step explanation:

You want to know when a rocket will hit the ground if its height is given by y = -16x² +170x +61, where x is seconds after launch.

The formula for the solutions of a quadratic equation is ...

  [tex]\text{for }ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

When we apply this to the equation y=0, we have ...

  [tex]x=\dfrac{-170\pm\sqrt{170^2-4(-16)(61)}}{2(-16)}=\dfrac{170\pm\sqrt{32804}}{32}\\\\x\approx 10.97\quad\text{seconds}[/tex]

The rocket will hit the ground after about 10.97 seconds.

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The width of the living room on the new blueprint is 15 feet.

Based on the information, the scale of the original blueprint will be:

= 2 in / 5 ft

The width of the original blueprint is 6 inches, the actual width of the living room will be:

2/5 = 6/x

where x = width of living room

Cross multiply

x = 5 × 6 / 2

x = 15 feet.

The width is 15 feet.

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Answer:

t = 19.99h + 30

Step-by-step explanation:

t is the total cost and h is the hourly charge.  The 30 is a one time fee.

The customer can select the meal in 2016 ways.

There are four different methods to choose an appetizer, eight different ways to choose a salad, nine different ways to choose an entree, and seven different ways to choose a dessert. Customers can choose a meal in the range of 4*8*7*9 if, according to the multiplication rule, a meal includes an appetizer, a salad, an entree, and a dessert.

x = 4 * 8 * 7 * 9 =  2016 ways.

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First, we must find the total of females, it will be

Now we must look at the table how many females prefer suspense movies, it's

Now we do the quotient between the females that prefer suspense by the total of females:

Rounding it, we can say that approximately,

Or 20% of the females prefer suspense movies

I hope this was helpful.

The original number is 0.8.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the number be x.

A certain number was multiplied by 5, then decreased by 3, then halved. The result was 0.3 less than the original number.

So, the mathematical expression is

1/2( 5x- 3) = x- 0.3

Now, solving for x

Multiply both side by 2

5x-3 = 2x- 0.6

5x- 2x= -0.6 + 3

3x= 2.4

Divide both side by 3

3x/3 = 2.4/3

x= 0.8

Hence, the original number is 0.8.

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Answer:

Third option

Step-by-step explanation:

The intercept x-intercept of f¹(x) is 1 and y-intercept of f(x) is also 1.

To determine the value of v that makes the equation true, we have to solve the equation and obtain the value of v

The value of v that makes the equation true is v=8

Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right

The given equation is 3x-6y²+6y=0.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Right

Vertex: (-1/2, 1/2)

Focus: (-3/8, 1/2)

Axis of symmetry: y=1/2

Directrix: x=-5/8

The coordinate points to plot (-1/2, 1/2), (0.5, 1.21), (0.5, -1.21), (1.5, 1.5) and (1.5, -0.5).

Therefore, Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right.

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Answer:

150

Explanation:

Alright so basically, 150 x 40 = 6000, right? So you want to find out how to find it using the division process. It is a whole number with no fractional part. As division with remainder the result of 6000 ÷ 40 = 150 R 0.

6000 divided by 40 ⇒ 150.

Here given that,

6000 is divisible by 40

since we know that,

Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.

6000 is divisible by 40 we get,

⇒ 6000/40

⇒ 150

So, the quotient is 150

Hence,

After dividing 6000 by 40 we get 150.

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Step-by-step explanation:

a) angles that share 1 side and are next to each other

<DBA, <ABE

<ABE, <EBC

b) two angles whose measures add to 180°

<ABE, <EBC

<ABD, <DBC

c) two adjacent angles whose noncommon sides lie on a line

<ABE, <EBC

<ABD, <DBC

The equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6

The equation of the line that parallel to the line

y = 3.2x+7.3

Slope intercept form of the line

y = mx+b

y is the y coordinate

x is the x coordinate

m is the slope of the line

b is the y intercept

Compare it with the equation

The slope of the line m = 3.2

Point slope form of the line passing through the points (-3,0) with the slope of the line 3.2

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

Substitute the values in the equation

y-0 = 3.2(x-(-3)

y = 3.2(x+3)

y = 3.2x+9.6

Hence, the equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6

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The pay for the given weekly time is, $102.

What is the pay wage?

The key distinction between a salary and wages is that wage earners are compensated by the hour, whereas salaried employees receive set payments every pay period.

In the given example the total time for the morning and the afternoon is given.

The total time for the morning is 4 hours and the total time for the afternoon is 4.5 hours.

So, the total number of hours are 4 + 4.5 = 8.5 hours.

The wage of each hour is $12.

So, the wage of 8.5 hours is,

8.5 x $12 = $102.

Therefore, the pay for the given day of a weekly time card given a wage of $12/hr is $102.

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The equivalent ratio of longboard  3 : 10

What is Ratio ?

A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

Given:

Long-boards        A           30

Skateboards        50        100

Find:

An equivalent ratio where the number of skateboards is 50.

Now,

⇒ Equivalent ratio = Long-boards / Skateboards

⇒ Equivalent ratio = 30 / 100

⇒ Equivalent ratio = 3 / 10

Now,  Equivalent value of Long-boards = Equivalent ratio × Number of skateboards

Equivalent value of Long-boards = [3 / 10] × 50

Equivalent value of Long-boards = 15

Then the ratio will be :

15 / 50 = 3 / 10

or, 3:10

Hence, equivalent ratio where the number of skateboards is 50. will be 3:10

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Answer: It would be D. 22.5°

Have a nice day!

Answer:

I need more information to solve this.

Step-by-step explanation:

a) The confidence interval is (0.13, 0.35) for the males who have this blood disorder.

b) The number of African males or the sample size is 88 for the value of P to be 0.20

It is mentioned that a geneticist is interested in the proportion of the African males who have a certain minor blood disorder. In a random sample of 100 males, 24 were found to be afflicted.

So we have,

n (total males) = 100

X (afflicted males)= 24

Let P be the sample porportion,

P = X/ n

∴ P = 24 / 100 = 0.24

a) Here it is given to find the confidence interval if the proportion of males is 99% who have this blood disorder so,

c = 99 % = 0.99

∴ α = [tex]1 -[/tex] c = 1 - 0.99 = 0.01

⇒ α/2 = 0.01/2 = 0.005

Using Z table,

Z of α/2 = [tex]Z_{0.005}[/tex] = 2.576

Margin of error E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]

                            = 2.576 x [tex]\sqrt{\frac{0.24(1-0.24)}{100} }[/tex]

                            = 0.11

Now, 99 % confidence interval is P ± E

P-E < P < P +E

0.24 - 0.11 < P' < 0.24 + 0.11

P' = (0.13, 0.35) is the required confidence interval.

b) It is given to find the the number of African males when

P = 0.20

Z = 2.576

E = 0.11

Now E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]

⇒ 0.11 = 2.576 x [tex]\sqrt[2]{\frac{0.20(1-0.20)}{n} }[/tex]

⇒ 0.0427 = [tex]\frac{0.4}{\sqrt{n} }[/tex]

⇒ [tex]\sqrt{n}[/tex] = 9.37

⇒ n = [tex](9.37)^{2}[/tex]

⇒ n = 87.7969

Hence the approximate number of males is 88 for the proportion of males with this blood disorder to be 0.20

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Answer:

To convert the degrees to radians

we know that,

Radian is equivalent to the angle subtended at the centre of a circle by an arc equal in length to the radius.

we get that,

That is,

we get that,

Answer is: 0.8

In the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.

So, there are no x-intercepts on the graph of a particular quadratic function.

Discriminant= D

For imaginary zeros, D must be negative.

The given option (A) and (C) which are -4 and -18 are negative and hence are the Discriminant with no x-intercepts.

Therefore, in the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.

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If we solve for the value of x we find that x is any value which is greater than -36/11.

What are inequalities ?

When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.

It is given in question that a required number divided by 3 decreased by 7 is less than 4 times the number increased by 5.

Let's assume the number be x.

So , x divided by 3 is x / 3 and if we subtract it by 7 , we get :

x/ 3 - 7  

Also , this value is less than 4 times the number added with 5.

i.e.,

4x + 5

So , the inequality can be written as :

[tex]\frac{x}{3}[/tex] - 7 < 4x + 5

or

x - 21  <  12x + 15

-36 < 11x

or

-36 /11 < x

or

x > -36/11

or

x is greater than -36/11.

Therefore , if we solve for the value of x we find that x is any value which is greater than -36/11.

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On the graph that is included with the solution, the temperature fluctuations are depicted.

A graph is a representation of the relationship between two variables, often measured along one of two right-angled axes each.

It is 56° at 6 a.m.

It rises to 61° for the next 5 hours because it is increasing by 1° per hour, and after another 4 hours it will rise to 69° because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it fell for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.

It is 56° at 6 a.m. The temperature rises to 61° for the next 5 hours because it is increasing by 1° per hour, and then after 4 hours it will rise to 69° again because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it dropped for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.

The final graph is shown in the below attached figure.

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Answer: (4, 2)

Step-by-step explanation:

1) Identify the values of a, b, and c.

a = -1

b = 8

c = -14

2) Use the vertex formula to find the x-value of the vertex.

[tex]{\displaystyle x={\frac {-b}{2a}}}[/tex]

[tex]{\displaystyle x={\frac {-8}{2(-1)}}}[/tex]

[tex]{\displaystyle x={\frac {-8}{-2}}}[/tex]

[tex]{\displaystyle x=4[/tex]

3) Plug the value into the original equation to get the y value.

f(x) = -x² + 8x - 14

f(x) = -(4)² + 8(4) - 14

f(x) = -(16) + 32 - 14

f(x) = 2

3) Put it in an ordered pair

(4, 2)

Answer:  21 x=4 ​

Solve the system of equations

Steps:

​ Evaluate

{ 7x−7 x=4 ​

Calculate

{ x=4 21 ​

Solution

{ 21 x=4 ​

The answer is given above