simplify the expression . express using positive exponents.​

If p and q vary inversely and p is 5 when q is 4, the value of q when p is equal to 10 is 2.

An inverse variation can be defined as a type of proportionality which shows the relationship that exist between two (2) distinct variables, wherein, as the value of one variable increases, the value of the other variable decreases and vice-versa.

Mathematically, an inverse variation can be modeled or represented by this expression:

p ∝ 1/q

p = k/q

Where:

Next, we would determine the constant of proportionality (k) by substituting the value of the given variable as follows:

k = pq

k = 5(4)

k = 20

Now, we can determine the value of q:

q = k/p

q = 20/10

q = 2.

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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

Answer:

I need more information to solve this.

Step-by-step explanation:

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

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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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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Answer:

1/9

Step-by-step explanation:

-1/9  + 2/9

Since the denominator is the same, we can add the numerators

(-1+2)/9 = 1/9

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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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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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: (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:

The average speed of the puck is 110 ft per second.

Step-by-step explanation:

Using the d = st formula to find distance when given the speed and time, you can rewrite it to be s = d/t.

When you substitute the values in, you get s = 66/0.6, which is 110.

Hope this helps.

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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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The answer is given above

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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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:

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

Answer:

KML and LMK

Step-by-step explanation:

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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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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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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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.

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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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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Answer:  21 x=4 ​

Solve the system of equations

Steps:

​ Evaluate

{ 7x−7 x=4 ​

Calculate

{ x=4 21 ​

Solution

{ 21 x=4 ​