Simplify:6 to the power of 5/6to the power of 2.
A.1/6 to the power of 3
B.6 ttpo 7
C.6ttpo 2
D.6ttpo 3

Answer:

X = 12

<B = 45°

Explanation:

From the diagram above:

Alternate exterior angles are equal. Therefore,

[tex]5x - 15 = 2x + 21 \\ collecting \: liketerms \\ 5x - 2x = 21 \: + 15 \\ 3x = 36 \\ dividing \: bothsides \: by \: 3 \\ \frac{3x}{3} = \frac{36}{3} \\ x = 12 [/tex]

For the measure of angle B

2x + 21°

2(12) + 21 = 24 + 21 = 45

Measure of angle B = 45°

The equations have the same solution are 2.3p – 6.5p + 0.01p =– 4  + 10.1 and -4.19p = 6.1

This are equations that has a leading degree of 1. GIven the expression as shown below

2.3p – 10.1 = 6.5p – 4 – 0.01p

Collect the like terms

2.3p – 6.5p + 0.01p =– 4  + 10.1

Simplify

-4.19p = 6.1

Hence the equations have the same solution are 2.3p – 6.5p + 0.01p =– 4  + 10.1 and -4.19p = 6.1

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Each van carries 13 students and each bus carries 25 students.

Given that the senior class at High School A and the senior class at High School B both planned trips to Yellowstone, and the senior class at High School A rented and filled 5 vans and 2 buses with 115 students, while High School B rented and filled 1 van and 6 buses with 163 students, and each van carried the same number of students and each bus carried the same number of students, to determine the number of students in each van and in each bus, the following calculation must be made:

Therefore, each van carries 13 students and each bus carries 25 students.

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Answer:

Each van carries 13 students and each bus carries 25 students.

Step-by-step explanation:

Answer:

Jim is 5

Step-by-step explanation:

word problems can be sort of like translation questions

'times' means multiply

'as old as' means equal or =

'will be' means equal or =

'more than' means plus or +

when I saw

"Dad is 4 times as old as his son Jim is now"

I knew needed to make

Jim = x &

Dad = 4x

when I saw

"In 10 years, Dad's age will be 20 years more than twice Jim's age"

I knew

'Dad's age' means 4x

'In 10 years' means 10 +

'will be' means equal sign or =

'20 years more than' means 20 +

'twice Jim's age' means 2x

sentence can be re written

4x+10=20+2x

'if D = dad's age now' means 4x=D (Dad)

'J = Jim's age now' means x = J (Jim)

I solved for x

4x+10=20+2x

2x=10

x=5

then I checked the math

today

x = Jim = J = 5

4x = Dad = D = 20

'in 10 years'

Dad is 20 + 10 = 30

means

does 30 = 20 years more than twice Jim's age?

does 30 = 20 + 2x ?

does 30 = 20 + 2(5)?

does 30 = 20 + 10?

does 30 = 30?

yes!

it checks out!

Based on the information provided in the first table, we have the following angle and trigonometric function:

Based on the information provided in the first table, we have the following trigonometric function:

tanθ = √3

θ = tan⁻¹(√3)

θ = 60°.

In radians, we have:

θ = 60 × π/180

θ = 1.0472 radian.

sin60 = √3/2

cos60 = 1/2

csc60 = 2/√3

sec60 = 2

cot60 = 1/√3

Based on the information provided in the second table, we have the following trigonometric function:

θ = 30 × π/180

θ = 0.5236 radian.

sin30 = 1/2

cos30 = √3/2

tan30 = 1/√3

csc30 = 2

sec30 = 2/√3

cot30 = √3

Based on the information provided in the third table, we have the following trigonometric functions:

sinθ = √2/2                                   tanθ = 1

θ = sin⁻¹(√2/2)                               θ = tan⁻¹(1)

θ = 45°.                                          θ = 45°.

In radians, we have:

θ = 45 × π/180

θ = 0.7854 radian.

cos45 = √2/2

csc45 = √2

sec45 = √2

cot45 = 1

Based on the information provided in the fourth table, we have the following trigonometric function:

sinθ = 1                                

θ = sin⁻¹(1)                      

θ = 90°.

θ = 90 × π/180

θ = 1.5708 radian.

cos90 = 0

tan90 = not defined

csc90 = 1

sec90 = not defined

cot90 = 0

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(a) The median mark is 44

(b) The number of students who scored 54 marks or less is 120

(c) The number of students who scored 60 marks or more is 20

From the question, we are to determine the median mark

The median mark for a cumulative frequency curve corresponds to the second quartile (Q₂)

Q₂ = 1/2(n+1)th mark

Where n is the total frequency

In the graph,

n = 160

∴ Q₂ = 1/2(160+1)th mark

Q₂ = 80.5th mark

The 80.5th mark is 44

∴ The median mark is 44

(b)

The number of students who scored 54 marks or less = 120 - 0

The number of students who scored 54 marks or less = 120

(c)

The number of students who scored 60 marks or more = 160 - 140

The number of students who scored 60 marks or more = 20

Hence, (a) The median mark is 44

(b) The number of students who scored 54 marks or less is 120

(c) The number of students who scored 60 marks or more is 20

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The z value for the probability in the standard normal table is 1.29.

In this question,

Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.

The value of probability is 0.80

A standard normal random variable is between -z and +z, So

P(-z < 0 < z) = 0.80

⇒ 2P(0 < z) = 0.80

⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]

⇒ P(0 < z) = 0.40

From the standard normal table, z value for the probability 0.40 is

⇒ z = 1.29

Thus P(0 < 1.29) = 0.40

Hence we can conclude that the z value for the probability in the standard normal table is 1.29.

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A quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0.

The Factor of the equation from Part B is (x - 13)(x + 5)  and the possible solutions to the equation is x = 13 or -5.

The value for the second number is 5

The general formula for quadratic equation in a in standard form is

a[tex]x^{2}[/tex] + bx + c = 0

Given that the  difference between two integers is 8

Let the two integers = x and y,

and their product is 65. If the larger of the two numbers is x. Then,

x - y = 8 and xy = 65

Since we are looking for the value of x, make y the subject of formula in the first equation.

y = x - 8

Substitute y in the second equation.

x(x - 8) = 65

[tex]x^{2}[/tex] - 8x - 65 = 0

[tex]x^{2}[/tex] - 13x + 5x - 65 = 0

(x - 13)(x + 5) = 0

x = 13 or -5

We will ignore -5 since x is the larger number.

To get y Substitute x in the second equation.

xy = 65

13y = 65

y = 65/13

y = 5

Therefore, a quadratic equation in standard form that can be used to determine the value of x is [tex]x^{2}[/tex] - 8x - 65 = 0. The Factor of the equation from Part B is (x - 13)(x + 5)  and the possible solutions to the equation is x = 13 or -5. The value for the second number is 5

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Answer:

y =2

Step-by-step explanation:

Substitute -10 for x:

2(-10)-9y = -38

-20-9y = -38

-9y = -18

9y = 18

y = 2

The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

The volume of a cylinder is calculated using the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

The expression used by Aiden to calculate the volume of a cylinder is π(16)(12), or, π(4²)(12).

Comparing this expression with the general formula of the volume of a cylinder, V = πr²h, where V is its volume, r is its radius, and h is its height, we can say that the radius can be 4 units and the height can be 12 units.

Assuming the units to be cm, we can say that:

The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

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The complete question is:

Aiden evaluated the expression π(16)(12) to find the volume of a cylinder. What could be the dimensions of the cylinder?

The height is 12 cm, and the diameter of the base is 8 cm.

The height is 12 cm, and the area of the base is 16 cm².

The height is 16 cm, and the diameter of the base is 6 cm.

The height is 16 cm, and the area of the base is 12 cm².

Answer:

C. 21°C

Step-by-step explanation:

Substitute 69.8 for F in the equation, [tex]69.8=\frac{9}{5}C+32[/tex]. This becomes [tex]37.8=\frac{9}{5} C[/tex]. Divide both sides by [tex]\frac{9}{5}[/tex] to get [tex]21=C[/tex].

Answer:

21

Step-by-step explanation:

hfjajxnzjaiidnsnjaoaoaoa

Answer: 37.92

Step-by-step explanation: We know that 3202 / 5 = 640.4.

We subtract that by 830 to get (830 - 640.4  =) 189.6. Then we do / by five again to get 37.92. That is the answer.

Answer:

(7,3)

Step-by-step explanation:

you can add the equations together to eliminate y and first solve for x

(x-3y = -2) + (x+3y=16) = (2x = 14)

x = 7

then plug x into one of the equations to solve for y

(7) - 3y = -2

9 = 3y

y = 3

the solution is (7,3)

Answer: (7, 3)

Step-by-step explanation:

x - 3y = -2

x + 3y = 16

Here we can add the two equations together to cancel out the y

2x = 14

divide by 2 on both sides to get

x = 7

Now that we have the X value, plug in x value into an equation to get the Y

x - 3y = -2

7 - 3y = -2

-3y = -9

y = 3

So the solution is (7, 3)

Answer:

2×sqrt(2) = 2.828427125...

Step-by-step explanation:

x = "a positive number"

x + 56/x = x³

x² + 56 = x⁴

x⁴ - x² - 56 = 0

(x² + 7)(x² - 8) = 0

this is true only for

x² = -7

or

x² = 8

x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.

x² = 8 means

x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...

46.5 is higher than 5.2

Note that:

The larger the magnitude(value) of the heights given the larger the heights

Units are not added to the values representing each height

By carefully considering the heights given:

5.2 is a lesser value than 46.5

Since 46.6 > 5.2, we can conclude that 46.5 is higher than 5.2

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Her answer should look like y = x + 2, x ≤ 2

The complete question is added as an attachment

From the attached graph, we have the following points

(x, y) = (2, 4) and (0, 2)

See that the difference between the y and x values is 2 where y > x

So, we have

y - x = 2

Add x to both sides

y = x + 2

The highest value of x in the graph is 2.

So, we have

x ≤ 2

Hence, her answer should look like y = x + 2, x ≤ 2

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The length of the radius of the circle is 4.9cm.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point.

The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Calculation for the length of the radius of the circle-

In order to overcome this issue, we must first translate the angle from radians to degrees.

The central angle of circle is 7/6π rads = 210 degrees.

Length of the arc is 18 cm.

The formula of length of an arc is given as-

[tex]l_{a r c}=\frac{\theta}{360} * 2 \pi r[/tex]

Let's change the values and find the solution.

[tex]\begin{aligned}&18=\frac{210}{360} * 2 \pi r \\&18=3.663 r \\&r=\frac{18}{3.663} \\&r=4.9 \mathrm{~cm}\end{aligned}[/tex]

Therefore, the length of the radius of the circle is 4.9 cm.

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Answer:

C.) [tex]x^{\frac{3}{2} } y^{\frac{19}{2} }[/tex]

Step-by-step explanation:

To simplify the expression, you need to:

1.) Rewrite [tex]\sqrt{xy^{3} }[/tex]

    -----> [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]

2.) Distribute the exponents

    -----> When an exponent is raised to another exponent, they should be multiplied

3.) Create common denominators

4.) Combine the variables

    -----> When two variables with exponents are being multiplied, the exponents should be added

Answer:

[tex]y = \frac{1}{4} x + 9[/tex]

Step-by-step explanation:

All lines take the form

[tex]y = mx + c[/tex]

Where m is the gradient (or slope), and c is the y-intercept. To find the gradient if a line perpendicular to another, we must find the negative reciprocal of the other line. The gradient of the line given is -4, so our negative reciprocal is 1/4.

To find our y-intercept, we must find the point where the line crosses the y-axis (in other words, when the X coordinate is 0). Helpfully, the coordinate given is already at this point, so we can simply take the y coordinate from here, and we know our y-intercept is 9. Putting this altogether, our equation is:

[tex]y = \frac{1}{4} x + 9[/tex]

The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the width, hence:

length = x + 2

The area of a rectangle is the product of its length and its width.

Area = length * width

Area = x(x + 2)

120 = x² + 2x

x² + 2x - 120 = 0

x = 10, length = 10 + 2 = 12

The length and width of the rectangle with an area of 120 units² are 12 units and 10 units respectively.

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The nth term of a sequence exists 2n2² - 4n+4 is 36.

The order of operations exists as a rule that describes the right sequence of measures for estimating a math expression. We can recognize the order utilizing PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition, and Subtraction (from left to right).

[tex]$2*8*2^{2} - 4*8+4[/tex]

Follow the PEMDAS order of operations

Calculating the exponents, we get 2² = 4

[tex]= 2*8*4 - 4*8+4[/tex]

= 64-32 +4

= 36

Therefore, the nth term of a sequence that exists 2n2² - 4n+4 is 36.

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Answer:

6y^2 + 18y

Step-by-step explanation:

2y (3y + 9)=

6y^2 + 18y

[2y (3y becomes 6y^2]

[2x(      + 9) becomes 18y]

Add them to obtain 6y^2 + 18y

Answer:

60 kilograms

Step-by-step explanation:

Answer:

- 11 < x < 8

Step-by-step explanation:

inequalities of the type | x | < a have solutions of the form

- a < x < a

then

| 2x + 3 | < 19

- 19 < 2x + 3 < 19 ( subtract 3 from each interval )

- 22 < 2x < 16 ( divide each interval by 2 )

- 11 < x < 8

The independent variable that caused a change in the dependent variable is called cofounding variable.

Given the Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called _____ variables.

These are variables in statistics other than the dependent and independent variables which can also be important to a researcher because it affects the dependent variable.

Confounding variables can also be called influences, external factors or third variables because they mostly affect the outcome of a research and prevent a researcher from achieving its objectives.

Hence, Factors that are unequal across groups and can prevent a researcher from concluding that it was the independent variable that caused a change in the dependent variable are called cofounding variables.

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Answer: 30 degrees

Step-by-step explanation:

Let [tex]P[/tex] be the number of plain cakes sold, and [tex]D[/tex] the number of decorated cakes sold.

Each plain cake sells for $7, so [tex]P[/tex] cakes sells for [tex]\$7P[/tex].

Similarly, each decorated cakes goes for $11, so [tex]D[/tex] cakes are worth [tex]\$11D[/tex].

The baker sells all but 3 cakes, so

[tex]P + D = 117[/tex]

After the sale, the baker earns a total of $991, so

[tex]7P + 11D = 991[/tex]

Now just solve the system of equations for [tex]P[/tex] and [tex]D[/tex]. This is easily done by substitution or elimination.

(The selected answer is actually the correct one.)

Step-by-step explanation:

I assume the question really looks like

-4b² + 4b - 4 is to be subtracted from 3b² + 2b - 5.

so,

3b² + 2b - 5 - (-4b² + 4b - 4) =

= 3b² + 2b - 5 + 4b² - 4b + 4 =

= 7b² - 2b - 1

The function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)

The equation is given as:

f(x) = 2(0.35)^x

The reflection of a function over the y-axis is :

f'(x) = f(-x)

So, we have:

f(-x) = 2(0.35)^(-x)

From the list of options, we have

h(x) = 2(0.35)^(-x)

Hence, the function that is a reflection of f(x) over the y-axis is h(x) = 2(0.35)^(-x)

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