Are both 7 and -1/2 rational numbers? Why or why not?

Answer:

Substitute the value of 7 into the variable x. Then solve the equation.

f(7) = 10 - 2(7)

f(7) = 10 - 14

Answer:

115° and 245°

Step-by-step explanation:

Given

cos x = - 0.4226

Since cos x < 0 then x is an angle in the second / third quadrants, thus

x =  (0.4226) = 65° ← related acute angle , thus

x = 180° - 65° = 115° ← angle in second quadrant

x = 180° + 65° = 245° ← angle in third quadrant

Answer:

[tex]x=\{44\º, 317\º\}[/tex]

Step-by-step explanation:

The interval given is [tex](0, 360\º) \text{ or } (0, 2\pi)[/tex]

In exercises of this kind I usually use

[tex]\cos \left(x\right)=a\quad \Rightarrow \quad \:x=\arccos \left(a\right)+360\º n, n \in \mathbb{Z}[/tex]

[tex]\quad \:x=\arccos \left( 0.7252\right)+360\º n, n \in \mathbb{Z}[/tex]

And [tex]\arccos \left( 0.7252\right) \approx 43.5^{\circ \:}[/tex]

But once we have the solution for cos in two different quadrants, I mean, Quadrant I and Quadrant IV angle.

To the nearest degree, we have

[tex]x=\{44\º, 317\º\}[/tex]

[tex]\left(3,\,\frac{\big\pi}3\right)[/tex]

Answer:

lower quartile: 80.5 upper quartile: 93

Step-by-step explanation:

Fro the above question, we are given the following values for the number of cars 8 dealerships sold.

GMC = 84

Chevrolet = 81

Nissan = 92

Toyota = 92

Ford = 95

Honda = 94

Hyundai = 80

Acura = 72

We are told to find the lower and upper quartile of this set of data.

The lower quartile of a data set can be defined as the median( middle number) of the lower half of the data set. The lower quartile is also known or referred to as (Q1).

The lower quartile is also calculated using the formula

Q1 = 1/4(n + 1) th value

Where n is the number of values in the the date set.

The upper quartile of a data set can be defined as the median( middle number) of the upper half of the data set. The lower quartile is also known or referred to as (Q3).

The upper quartile is also calculated using the formula

Q3 = 3/4(n + 1) th value

Where n is the number of values in the the date set.

Step 1

Arrange the data set from the lowest to the highest number

72, 80, 81, 84, 92, 92, 94, 95

Step 2

Calculate the lower Quartile

Q1 = 1/4(n + 1)th value

n = number of values in the data set = 8 values

Q1 = 1/4(8 + 1)th value

Q1 = 1/4(9)th value

Q1 = 2.25th value

This means it is between the 2nd and 3rd value

2nd value = 80

3rd value = 81

(80 + 81) ÷ 2 = 161 ÷ 2 = 80.5

The Lower Quartile (Q1) = 80.5

Step 3

Calculate the lower Quartile

Q3 = 3/4(n + 1)th value

n = number of values in the data set = 8 values

Q3 = 3/4(8 + 1)th value

Q3 = 3/4(9)th value

Q3 = (27/4)th value

Q3 = 6.75th value

This means it is between the 6th and 7th value

6th value = 92

7th value = 94

(92 + 94) ÷ 2 = 186 ÷ 2 = 93

The Upper Quartile (Q3) = 93

Therefore, the Lower Quartile: 80.5 and Upper Quartile: 93

Answer:

A

Step-by-step explanation:

good luck on the test ,have a nice day :)

edg 2022

Answer:

Slope = 32+5/-21+55

= 37 / 34

Hope this helps

Answer:

Brainleist!

Step-by-step explanation:

10^x = 0.1

x =log(0.1)

Decimal Form:  x=−1

Answer:

Step-by-step explanation:

[tex]a_{n}=1+(n-1)(4)[/tex]

Answer:

B) Acute triangle

Step-by-step explanation:

In acute triangles, all of the angles are less than 90°. This is true for this triangle :)

I hope this helps!!

Answer:

B) Acute triangle

Step-by-step explanation:

All the angles are less than 90 degrees so all the angles are acute

Answer:

Volume of cuboid = length × width × height

length = 20cm

width = 8cm

height = 15cm

Volume = 20cm × 8cm × 15cm

= 2400cm³

Volume of the cuboid is 2400cm²

Hope this helps.

Answer:

2,400cm³

Step-by-step explanation:

FORMULA FOR VOLUME OF A CUBOID= L×B×H

WHERE L IS LENGTH = 20cm

B IS BREADTH = 15cm

H IS HEIGHT=8cm

:• VOLUME= 20cm ×15cm × 8cm

= 2,400cm³

Answer:

[tex]\frac{9}{20}[/tex]

Step-by-step explanation:

Step 1: Multiply 2 together

1/3(3/5) = 3/15

Step 2: Multiply again

3/15(9/4) = 27/40

Step 3: Simplify

(Divide both top/bottom by 2)

27/2 = 9

40/2 = 20

9/20

Answer: w^6 z^4

Step-by-step explanation:

w^6z^4

w^3^2 z^2^2

w^6 z^4

Answer:

[tex]w^6z^4[/tex]

Step-by-step explanation:

[tex]\text{Apply rule: }(a*b)^n=a^nb^n\\\\(w^3z^2)^2=\left(w^3\right)^2\left(z^2\right)^2\\\\\text{Apply rule: }(a^n)^m=a^{nm}\\\\(w^3)^2=w^{3*2}=\boxed{w^6}\\\\w^6(z^2)^2\\\\(z^2)^2=z^{2*2}=z^4\\\\\boxed{w^6z^4}[/tex]

Answer:

x=6

Step-by-step explanation:

x+y=48

x=y-6

substitute "y-6" instead of x

x+y=48

(y+6)+y=48

y+y is equal to y

6+y=48

-6     -6

y= 42

x= 48-y

x=48-42

x=6

I hope this helped

Answer:

Step-by-step explanation:

x  - the small number

x+6  - the big number

x + x + 6 = 48

2x + 6 = 48

  - 6       - 6

  2x  =  42

  ÷2       ÷2

    x = 21

Verifying:

x+6 = 21 + 6 = 27

21 + 27 = 48

Answer:

A. cos α = – 3/5

B. Sin β = √3/2

Step-by-step explanation:

A. To find the exact value of cos α , we must obtain the Hypothenus for the triangle.

Please attach photo for explanation.

B. To find the value of sin β, we must determine the opposite in the triangle. Please see attached photo for further details.

Answer:

[tex]\frac{3(\sqrt{3} -\sqrt{x})}{3-x}[/tex] or [tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{9} }{\sqrt{3} +\sqrt{x} }[/tex]

[tex]\frac{3}{\sqrt{3}+\sqrt{x} }[/tex]

Multiply by the opposite by using the difference of squares converse formula.

[tex]\frac{3}{\sqrt{3} +\sqrt{x} } *\frac{\sqrt{3} -\sqrt{x}}{\sqrt{3} -\sqrt{x}}[/tex]

[tex]\frac{3(\sqrt{3} -\sqrt{x})}{3-x}[/tex]

[tex]\frac{3\sqrt{3}-3\sqrt{x} }{3-x}[/tex]

Answer:

3 sqrt(3) - 3 sqrt(x)

---------------------------

3  - x

Step-by-step explanation:

sqrt(9) = 3

so writing the expression as

3

--------------------

sqrt(3) + sqrt(x)

Multiply by the conjugate, sqrt(3) - sqrt(x) in the numerator and denominator

3                            sqrt(3) - sqrt(x)

-------------------- * ------------------

sqrt(3) + sqrt(x)    sqrt(3) - sqrt(x)

Foil the denominator

3 sqrt(3) - 3 sqrt(x)

---------------------------

sqrt(3) sqrt(3) + sqrt(3x) - sqrt(3x) - sqrt(x^2)

Simplify

3 sqrt(3) - 3 sqrt(x)

---------------------------

3  - x

Answer:

x= -132

Step-by-step explanation:

Answer:

[tex]x=-132[/tex]

Step-by-step explanation:

[tex]\frac{x}{11}=-12\\ \\x=-12*11\\\\x=-132[/tex]

Answer:

e/4 = 2.5

e/ 4 × 4 = 2.5 × 4

e = 10

His mistake was in step 2 since

2.5 × 4 = 10

Hope this helps

Answer:

C 2:1

Step-by-step explanation:

10 is double 5

and 2 is double 1

Answer:

C 2:1

Step-by-step explanation:

this is the answer

Answer:

Option D is true. ( graph of a vertical line through the point (negative 4,0)

Step-by-step explanation:

Answer:

∠ ABC = 90°

Step-by-step explanation:

∠ ABC is the angle in a semi circle and is right, that is

∠ ABC = 90°

The angle of ABC is 90 degrees.

Using circle theorem,

The angle subtended by an arc at the centre is twice the angle subtended

at the circumference.

Therefore,

1 / 2 ∠O = ∠ABC

∠O = 180 (angle on a straight line)

Therefore,

∠ABC = 1 / 2 × 180

∠ABC = 180 / 2

∠ABC = 90°

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Answer:

y° = 110°

z° = 26°

Step-by-step explanation:

Looking at the above geometry, we have two parallel lines , m and m

We have been asked to solve for y° and z°

Step 1

We solve for y°

On line n , we have can see that 70° and y° are CONSECUTIVE INTERIOR ANGLES

It is important to note that THE SUM OF TWO CONSECUTIVE INTERIOR ANGLES = 180°

Hence,

70° + y° = 180°

y° = 180° - 70°

y° = 110°

Step 2

Solve for z°

Looking at the geometric diagram we can see that

y° and (6z - 46) ° are ALTERNATE INTERIOR ANGLES

This means

y° = (6z - 46) °

In step 1 , we have already solved for y°

y° = 110°

Hence,

110° = (6z - 46) °

110° = 6z° - 46°

collect like terms

110° + 46° = 6z°

156° = 6z°

Divide both sides by 6

156°/6 = z°

z° = 26°

Therefore, the value y = 110° and the value of z = 26°

Answer:

[tex](x-2)^2+(y+4)^2=34[/tex]

Step-by-step explanation:

The standard form for the equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], where h is the x coordinate of the center of the circle, k is the y coordinate, and r is the radius. Since you already know the coordinates of the center of the circle, all you need to do is find the radius. Using the distance formula:

[tex]r=\sqrt{(7-2)^2+(-1-(-4))^2}=\sqrt{5^2+3^2}=\sqrt{25+9}=\sqrt{34}[/tex]

The equation of the circle is therefore:

[tex](x-2)^2+(y+4)^2=34[/tex]

Hope this helps!

Answer:

[tex]3y + x = -6[/tex]

Step-by-step explanation:

Given

y = 3x + 1

Required

Equation of line that passes through (12,-6) and is perpendicular to y = 3x + 1

First, the slope of the line has to be calculated;

Th slope of a line is the coefficient of x in its linear equation;

This implies that the slope of y = 3x + 1 is 3

Having calculated the slope of the first line;

The relationship between both lines are perpendicularity; this implies that [tex]m_1 * m_2 = -1[/tex]

Where m_1 = 3 and m_2 is the slope of the secodnd line

[tex]m_1 * m_2 = -1[/tex] becomes

[tex]3 * m_2 = -1[/tex]

Divide both sides by 3

[tex]\frac{3 *m_2}{m_2} = \frac{-1}{3}[/tex]

[tex]m_2 = \frac{-1}{3}[/tex]

The equation of the line can be calculated using the folloing formula

[tex]m = \frac{y - y_1}{x - x_1}[/tex]

Where [tex](x_1, y_1) = (12,-6)[/tex] and [tex]m_2 = \frac{-1}{3}[/tex]

The equation becomes

[tex]\frac{-1}{3} = \frac{y -- 6}{x - 12}[/tex]

[tex]\frac{-1}{3} = \frac{y + 6}{x - 12}[/tex]

Cross multiply

[tex]-(x - 12)= 3(y + 6)[/tex]

[tex]-x + 12=3y + 18[/tex]

Collect like terms

[tex]12 - 18 = 3y +x[/tex]

[tex]-6 = 3y + x[/tex]

[tex]3y + x = -6[/tex]

Answer:

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage

Step-by-step explanation:

Step(i):-

Given data the researcher has obtained data that states that 45% of citizens are in favor of the president

probability of success  'p' = 45% or 0.45

                                       q = 1-0.45 = 0.55

Given random sample size 'n' = 8

Let 'X' be the random variable

let 'X' = 6

[tex]P(X=r) = n_{C_{r} } (p)^{r} (q)^{n-r}[/tex]

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

[tex]P(X=6) = 8_{C_{6} } (0.45)^{6} (0.55)^{8-6}[/tex]

[tex]8_{C_{6} } = \frac{8!}{(8-6)!6!} = \frac{8 X 7 X 6!}{2 X 1 X 6!} =\frac{8 X 7}{2 x1} = 28[/tex]

P( X=6) = 28 × 0.00830 ×0.3025

P( X=6) = 0.070

Conclusion:-

The probability that 6 out of the next 8 individuals in his community are in favor of the president.

P( X=6) = 0.070 or 7 percentage

Answer:

28

Step-by-step explanation:

Answer:

Choice D

Step-by-step explanation:

After writing the data down seperate the values according to the x-axis on the graphs. You will find that 6 people chose between 0 to 3, 4 people chose between 4 to 7, 3 people chose between 8 to 11 and 2 people chose between 12 to 15.

The rational expression that has a value of 1 when x =-1 would be; D 2x²/ (x + 3).

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol.

We need to determine the expression that has a value of 1 when x =-1

Let's consider the rational expression of the option D;

2x²/ (x + 3)

Now substitute the value x = -1 in the given expression

2x²/ (x + 3)

2(-1)²/ (-1 + 3)

= 2/ 2

= 1

Hence, the required rational expression is D 2x²/ (x + 3).

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Answer:

y = -1/2x + 1

Step-by-step explanation:

Step 1: Find slope

m = (2-4)/(-2+6) = 1/2

Step 2: Find y-intercept

y = -1/2x + b

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

2 = 1 + b

b = 1

Step 3: Write it all together

y = -1/2x + 1

And we have our final answer!

Answer:

The answer would be just about 61% or 9/14

Step-by-step explanation:

So, it would be a 71% chance to get 1 green out of the bag, but then you have to keep that green out, which then lowers the chances of getting another green out of the bag, then you have to combine the percentages, and then that is the final percentage.

The probability of getting 2 greens is 5/31

Probability is the likelihood or chance that an event will occur. It is expressed as:

Probability = Expected outcome/Total outcome

Given that a bag is filled with 4 blue, 3 red and 5 green marbles, the total outcome is expressed as:

If green is picked at first, the probability of selecting a green is  5/12

The probability of getting 2 greens = 5/12 × 4/11

The probability of getting 2 greens = 20/132

The probability of getting 2 greens = 5/31

Hence the probability of getting 2 greens is 5/31

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