Use your calculator to find the angle, to the nearest hundredth of a degree, whose tangent value is
O 0.35
O 18.43
O 0.32
O 71.57

Answer: The correct answer is 14/7

Step-by-step explanation: This is the correct answer because it's explaining how to do it

check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?

well, it means that if we evaluate f(5) our result should be 0, so

[tex]\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}[/tex]

Answer:

log4 (70)

Step-by-step explanation:

log4(7) + log4(10) = log4(7 * 10 ) = log4(70)

Answer:

127.2 miles

Step-by-step explanation:

using the relationships

speed = [tex]\frac{distance}{time}[/tex] ( time in hours ) = [tex]\frac{159}{2.5}[/tex] = 63.6 mph

constant speed is 63.6 mph

then

distance = speed × time = 63.6 × 2 = 127.2 miles

The dimensions of this rectangular tank that has the minimum surface area are 42 feet and 21 feet.

First of all, we would determine the surface area of this rectangular tank with a square​ base by using this formula:

h = V/s²

Where:

For the surface area of this rectangular tank with a square​ base, we have:

Surface area, A = base area + 4(lateral area)

Surface area, A = s² + 4(s × h)

Surface area, A = s² + 4(s × V/s²)

Surface area, A = s² + 4V/s

Next, we would take the first derivative of the surface area as follows:

A' = 2s - 4V/s²

Substituting the given parameters into the formula, we have;

A' = 2s - 4(37044)/s²

For the minimum surface area dimension, the first derivative of the surface area would be equated to zero:

2s - 148,176/s² = 0

148,176/s² = 2s

148,176 = 2s³

s³ = 74,088

s = ∛74,088

s = 42 feet.

For the height, we have:

Height, h = V/s²

Height, h = 37044/42²

Height, h = 37044/1764

Height, h = 21 feet.

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78 meals are eaten in a restaurant, 58 meals are eaten in a car, 33 meals are eaten at home and the question is solved by using linear equations.

What is the linear equation?

A linear equation is an algebraic equation of the form y =mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are present. The variables in the above equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given that the total number of meals is 169.

Assume that,

a = number of meals eaten in a restaurant

b = number of meals eaten in a car

c = number of meals eaten at home

a + b + c = 169 .....(i)

Since the total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13.

Thus b + c = a + 13 .....(ii)

Again twenty more restaurant-purchased meals will be eaten in a restaurant than at home.

a = 20 + c .....(iii)

Subtract equation (ii) from (i)

a + b + c - b - c = 169 - a - 13

2a = 156

Divide both sides by 2

a = 78

Substitute a = 78 in equation (iii)

78 = 20 +c

c = 58

Putting c =58  and a =78  in equation (ii)

b + 58 = 78 + 13

b = 33

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Question:

The total number of restaurant-purchased meals that the average person will eat in a restaurant, in a car, or at home in a year is 169. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 13. Twenty more restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of​ restaurant-purchased meals eaten in a​ restaurant, the number eaten in a​ car, and the number eaten at home.

These are equivalent. I hope this helps a ton. I had this question on a test. Tell me if its wrong or not. <:

⇒[tex]\frac{d}{dx} (e^{x} )= e^{x} *\frac{d}{dx} (x)\\\frac{d}{dx} (e^{x} )=e^{x}*1\\\frac{d}{dx} (e^{x} )=e^{x}[/tex]

⇒Note this is all applied due to chain rule.

The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;

(a) The dimensions of the tiles are;

Width = 0.3 meters

Length = 0.8 meters

(b) 384 tiles are needed

(c) The fitting cost of the tiles is Kshs 51,000

An equation is a mathematical statement that consists of two expressions connected with an equals sign

Shape of the floor = Square

Shape of the tiles = Rectangular

Perimeter of the tiles = 220 cm = 2.2 m

The number of tiles in each row =  20 + The number of tiles in each column

Length of the floor = 9.6 m

(a) Let w represent the width of the tiles, the length l is found using the equation;

[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]

Let n represent the number of tiles in each row, which gives;

The number of tiles in each column = 20 + n

(20+n)·x = n·(1.1 - x)

Which gives;

[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]

The side length of the square floor, s = 9.6

(20+n)·x = n·(1.1 - x) = 9.6

Which gives;

[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]

Which gives;

0.55·n² - 1.4·n -96 = 0

n = 12 or n ≈ -14.5

The number tiles in each roe, n = 20

Which gives; n·(1.1 - x) = 9.6

20 × (1.1 - x) = 9.6

x = 0.3

The width of each tile, x = 0.3 m

The length of each tiles = 1.1 m - 0.3 m = 0.8 m

(b) The number of tiles in each row, n = 20

The number of tiles in each column = n + 20, which gives;

Number of tiles in each column = 12 + 20 = 32

The number of tiles needed = 12 × 32 = 384

(c) The cost of a dozen tiles = Kshs 1,500

The labour cost = Kshs 3,000

Number of dozens of tiles = 384 ÷ 12 = 32

The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000

The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000

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Answer:

x = √10,-√10

explanation:

5x2 + 1 = 51

you would carry the +1 to the other side making it

5x2=51-1

which is 5x2=50

this equation above can then be turned into

x2=50÷5

which goes on to form the equation

x2=10

this can then be turned into x=the square root of ten

and since it is know that when an equation is x2 whether it is negative or positive it would result in the same answer

but yeah I'm not smart or whatever but I hope this helps

not too sure it's correct though

Answer:

it's decimal value then it is 11.1803399.

The integer close to it is 11

Step-by-step explanation:

let's square this :

4² × 5 = 16 × 5 = 80

the closest squared integer is 81 (9²).

so, the closest integer to 4×sqrt(5) is 9.

wa can rewrite it as 12/1 which is A

The number of items that are missing from the order if She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items is 8.

The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given:

The number of the ordered products, O = 27,

The number of the received order, R = 19,

If m stands for the number of missing items, then,

m = O - R,

m = 27 - 19

m = 8

Therefore, the number of items that are missing from the order if She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items is 8.

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Answer:

4(67 + 22)

Step-by-step explanation:

1. Find the greatest common factor(in this case it is 4)

2. Divide both 268 and 88 by 4 and you get 67 and 22

3. Put it in the requested format and you are left with 4(67 +22)

The meaning of the expression x + 4 as required in the task content is; "four more than the number of questions on test".

It follows from the task content that the word phrase which best represent the algebraic expression; x + 4 is to be determined.

Given; x = the number of questions on test.

It therefore follows that the algebraic expression x + 4 can be interpreted as; "four more than the number of questions on test".

Hence, the meaning of the expression is; "four more than the number of questions on test".

PS: Just like word phrases can be accurately represented by algebraic expressions, the latter can be represented by the former too.

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After using the property of power, the expressions as a power of the number a is [tex](a^3)^{-2} = a^{-6}[/tex] , [tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex] and [tex]((a^2)^{-2})^2=a^{-8}[/tex] .

In the given question we have to solve the given expressions as a power of the number a where a≠0.

The first given expression is [tex](a^3)^{-2}[/tex].

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

Simplifying the expression.

[tex](a^3)^{-2} = a^{3*(-2)}[/tex]

[tex](a^3)^{-2} = a^{-6}[/tex]

The second expression is [tex](a^{-1}\cdot a^{-2})^{-3}[/tex]

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(-1)\times(-3)}\cdot a^{(-2)\times(-3)}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{3}\cdot a^{6}[/tex]

Using the property of sum of power [tex]a^m\cdot a^n=a^{m+n}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{(3+6)}[/tex]

[tex](a^{-1}\cdot a^{-2})^{-3} = a^{9}[/tex]

The third expression is [tex]((a^2)^{-2})^2[/tex].

Using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex]((a^2)^{-2})^2=((a^2)^{(-2)\times2})[/tex]

[tex]((a^2)^{-2})^2=(a^2)^{-4}[/tex]

Again using the property of multiplication of power; [tex](a^m)^n=a^{mn}[/tex].

[tex]((a^2)^{-2})^2=a^{2\times(-4)}[/tex]

[tex]((a^2)^{-2})^2=a^{-8}[/tex]

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lynn got the better deal than Roger.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

lynn bought a new crash cymbal for her drum set. it costs 120$ but she received a 15% student discount.

Convert 15% to decimal form

15%=15/100=0.15

0.15×120=18

So 15% of 120 is 18.

Iynn bought crash cymbal for her drum set is 120-18=102

Roger bought the same crash cymbal from another store for$130

Roger applied coupon of $25.

So 130-25=$105

When we compare both Iynn and Roger, Iynn got the crash cymbal for a better deal.

Hence lynn got the better deal than Roger.

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The percentage of students in the tutor group that have attended at least one tutorial is 71%

The percentage of students who have attended at least a single tutorial in the tutor group can be found by the formula:

= Number of students who attended at least one tutorial / Total number of students in tutor group x 100%

Number of students who attended at least one tutorial = 21 students

Total number of students in tutor group = 15 students

The percentage is therefore:

= 15 / 21 x 100%

= 0.7142857 x 100%

= 71.42%

= 71%

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The function notation when the function was shifted right 6 is f(x-6).

Given that, the function was shifted right 6 units.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Rule: In function notation, to shift a function left, add inside the function's argument: f(x + b) shifts f(x) b units to the left. Shifting to the right works the same way, f(x - b) shifts f(x) b units to the right.

So, the transformation from the original function to new function is

f(x-6)

Therefore, the function notation when the function was shifted right 6 is f(x-6).

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The expression that is equivalent to (f × g²) + 5 - (g² × f) is 5

The expression whose equivalence is to be determined is given as

(f × g²) + 5 - (g² × f)

To start with, we need to remove the brackets in the expression

So, we have the following representation

(f × g²) + 5 - (g² × f) = f × g² + 5 - g² × f

Evaluate the products

This gives

(f × g²) + 5 - (g² × f) = fg² + 5 - fg²

Next, we collect the like terms

So, we have

(f × g²) + 5 - (g² × f) = fg²  - fg² + 5

Lastly, we evaluate the like terms

So, we have

(f × g²) + 5 - (g² × f) = 5

The above expression cannot  be further simplified

Hence, the equivalent expression is 5

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The numeric value of the expression -b + 8x when b = 5 and x = -6 is given as follows:

-53.

To find the numeric value of a function or of an expression, we replace each instance of the variable/variables in the function or in the expression by the value/values at which we want to find the numeric value.

In this problem, the expression is given as follows:

-b + 8x.

The values at which the numeric value is to be found are:

b = 5, x = -6.

Hence:

Thus the numeric value of the expression is obtained as follows:

-5 + 8(-6) = -5 - 48 = -53.

The problem is given by the image at the end of the answer.

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Answer: 1.367

Step-by-step explanation:

csc47° = 1.3673 ≈ 1.367

The value of cosec 47° is 1.367.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

cosec 47°

The value of cosec 47°.

= 1.367334

Rounding to the nearest thousandth.

= 1.367

Thus,

The value of cosec 47° is 1.367.

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The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.

A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.

y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.

y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.

y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.

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If a man is 6 feet 2 inches tall, his z-score is equal to 1.82.

If a woman is 5 feet 10 inches tall, her z-score is equal to 2.92.

The 5 feet 10 inches American woman is relatively taller.

In a normal distribution, the z-score of a given sample score can be calculated by using this formula:

Z-score = (x - μ)/σ

Where:

Next, we would convert the height in feet to inches as follows:

American man = 6 × 12 + 2 = 74 inches.

American woman = 5 × 12 + 10 = 70 inches.

For the American man's z-score, we have:

Z-score = (74 - 69.2)/2.64

Z-score = 4.8/2.64

Z-score = 1.82

For the American woman's z-score, we have:

Z-score = (70 - 64.2)/2.53

Z-score = 5.8/2.53

Z-score = 2.92

Therefore, the 5 feet 10 inches American woman is relatively taller because she has a higher z-score (2.92 > 1.82).

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Complete Question:

The heights of adult men in America are normally distributed, with a mean of 69.2 inches and a standard deviation of 2.64 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.2 inches and a standard deviation of 2.53 inches.

a) If a man is 6 feet 2 inches tall, what is his z-score (to two decimal places)?

b) If a woman is 5 feet 10 inches tall, what is her z-score (to two decimal places)?

c) Who is relatively taller?

The 6 feet 2 inches American man

The 5 feet 10 inches American woman

The value of x is 11° and measure of other two angles are 80° and 117°

A triangle can be defined as a polygon which has three angles and three sides. The interior angles of a triangle sum up to 180°, and the exterior angles sum up to 360°.

Given that, the interior angles of the triangle are 37° and (3x+47)° and an exterior angle measures (5x+ 62)°

We know that the sum of two interior angles equals to the measure of an exterior angle,

Therefore,  37° + (3x+47)° = (5x+ 62)°

x = 11°

Hence, The value of x is 11° and measure of other two angles are 80° and 117°

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Answer:

8×2+8×g

Step-by-step explanation:

Answer:

Infinite solutions

Step-by-step explanation:

The equation is,

→ 8x + 16x - 12 = 24x - 12

Let's solve for the value of x,

→ 8x + 16x - 12 = 24x - 12

→ 24x - 24x = -12 + 12

→ [ 0 = 0 ]

Hence, it has infinite solution. Because, all the real numbers are suitable.

Answer:

infinite number.

Step-by-step explanation:

Comment

There is only the same letter (x) on both sides of the equation. None of the xs are raised to any power. The power is 1 for all of them. That being so, there is only ONE solution.

x^2 + 5x + 6 would give 2 solutions because the x is raised to the second power.

x^3 + x^2 + 4x + 9 would give 3 solutions.

Solution

8x + 16x - 12 = 24x - 12 This equation is a little different. Both sides are exactly the same -- 24x - 12. That means that there is an infinite number of solutions.

For example let x = 10

The right side = 240 - 12 = 228

The left side = 8*10 + 16*10 - 12 = 228

You can't come up with a number that will make the left side unequal to the right side.

Answer:5/9

Step-by-step explanation: