ABC is a triangle.
work out angle x. give your answer to 3 significant figures.

Answer:

the correct answer is -16

Step-by-step explanation:

I took the test

The solution for the expression 4x³y² at x = -1 and y =2 will be -16.

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

Given that the expression is 4x³y². The values of x and y are -1 and 2.

The expression at the values of x and y will be solved as:-

E = 4x³y²

Substitute the values of x = -1 and y = 2.

E = 4x³y²

E = 4 x ( -1)³ x ( 2 )²

E = 4 x -1 x 4

E = -16

The value of the expression at x =-2 and y = 2 will be -16.

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Steps to solve:

8j - k + 14; j = 0.25 and k = 1

~Substitute

8(0.25) - (1) + 14

~Simplify

2 - 1 + 14

~Subtract

1 + 14

~Add

15

Best of Luck!

Answer:

[tex]8j - k + 14 \\ 8 \times0 .25 - 1 + 14 \\ 2 - 1 + 14 \\ 1 + 14 = 15[/tex]

hope this helps you...

Answer:

504

Step-by-step explanation:

The sum of the odd numbers between 30 and 54 will be 504.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols. In several numeral systems, the same set of symbols may represent various numbers.

Given numbers are  30 and 54. The sum of the odd integers will be calculated by using the formula below:-

Sn = ( n / 2 ) [ a1 + a2 ]

The total numbers between 30 and 54 will be 12.

Sn = ( 12 / 2 ) [ 31 + 53 )

Sn = 6 x ( 84 )

Sn = 504

Therefore, the sum of the odd numbers between 30 and 54 will be 504.

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Answer:

37.5

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation:

Answer:

No, at alpha equals 0.10​, we do not have enough evidence to support the​ county's claim.

Step-by-step explanation:

We are given that a county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 30 miles per hour.

A random sample of 15 vehicles has a mean speed of 31 miles per hour and a standard deviation of 4.7 miles per hour.

Let [tex]\mu[/tex] = true mean speed of the vehicles.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex]  30 miles per hour   {means that the mean speed of vehicles is lesser than or equal to 30 miles per hour}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 30 miles per hour   {means that the mean speed of vehicles is greater than 30 miles per hour}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

                        T.S.  = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean speed of 15 vehicles = 31 mph

             s = sample standard deviation = 4.7 mph

             n = sample of vehicles = 15

So, test statistics  =   [tex]\frac{31-30}{\frac{4.7}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                               =  0.824

Hence, the value of test statistics is 0.824.

Now at 0.10 significance level, the t table gives critical value of 1.345 at 14 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 0.824 < 1.345, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Therefore, we conclude that the mean speed of vehicles is lesser than or equal to 30 miles per hour which means that the county's claim is not supported.

Answer: The length of the dotted line is 3.75 inches.

Please refer to the picture attached for the missing part of the question

Step-by-step explanation: From the information given we have a regular hexagon, that is a six-sided polygon (all sides equal) with the perimeter given as 7.5 inches. The perimeter is the distance all around the figure, hence to determine the length of one side,

Length = 7.5/6

Length = 1.25

Also, the interior angles of a hexagon can be derived with the formula;

Angles = 180 (n - 2)

Where n is the number of sides of the polygon

Interior Angles = 180 (6 - 2)

Interior Angles = 180 x 4

Interior Angles = 720

If the total of the interior angles equals 720, then each angle can be calculated as;

Each Angle = 720/6

Each Angle = 120

Please refer to attached picture tagged SOLUTION Diagram)

Taking triangle GED as shown in the picture, angle E and angle D measure 60 degrees each. This is because angle E in the entire hexagon ABCDEF measures 120 degrees. The line from point G in the center of the hexagon divides the angle into two equal halves. Same applies to all other five angles in the hexagon. Having angle E and D equal to 120 (that is 60 + 60) angle G would be equal to 180 - 120 {sum of angles in a triangle equals 180) which gives us 60. In effect we have an equilateral triangle, with all angles equal. This also means all sides are equal, hence if line ED equals 1.25, it simply means line GE and line GD equals 1.25 as well.

From this result we can now conclude that the line that runs across the hexagon from point F to point C is 1.25 plus 1.25 which equals 2.50.

The dotted line as indicated in the question runs across one side of the hexagon and all through another hexagon, hence the total length of the dotted line equals;

Dotted line = 1.25 + 2.50

Dotted line = 3.75

Therefore the length of the dotted line is 3.75 inches

Please find attached to this answer a well labelled diagram of the triangle

Answer:

Approximately 176.6 feet

Step-by-step explanation:

From the question, we are to find the height at which the baseball fan was sitting.

From the attached diagram the height at which the fan was sitting is equivalent to the opposite side of the triangle.

Hence , the appropriate trigonometric function to use to solve this question is the sine function.

Sine = Opposite / Hypotenuse

Opposite is unknown so we refer to it as Y

Hypotenuse = 200feet

While the Angle of depression = 62°

Therefore,

Sine 62° = Y/ 200 feet

Cross multiply

Sine 62° × 200 feet = Y

Y = 176.58951857 feet

Approximately 176.6 feet

Therefore , the height at which the fan is sitting is 176.6 feet

Answer:

$40,500  I took a test and this was the answer to the question.

Answer:

$40500

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Because to divde to fractions you multiply the first fraction by the second’s reciprocal. The reciprocal is when you switch the numerator and the denominator.In this case 1/5 times 10/1 which is 2.

Answer:

think ab = 4

Step-by-step explanation:

Answer:

[tex]5.3044992\times 10^{10}[/tex]

Step-by-step explanation:

We are given that a license plate consist of 5 digits and 5 uppercase letters

Digits used=0,1,2,..9

Total number of letters=26

Repetition is not allowed

Total number of odd digits=(1,3,5,7,9)=5

The first place filled by 5

Second place filled by 4

Third place filled by 8

Fourth place filled by 7

Fifth place filled by 6

Sixth place filled by 26

Seventh place filled by 25

Eighth place filled by 24

Ninth place filled by 23

Tenth place filled by 22

Total number of possible  different license plates =[tex]5\times 4\times 8\times 7\times 6\times 26\times 25\times 24\times 23\times 22[/tex]=[tex]5.3044992\times 10^{10}[/tex]

The number of possible license plates, considering the restrictions on the first and second odd digits and no repetition, is 53,144,832,000. This was determined by systematically calculating the choices for each digit and letter and then multiplying them together.

Calculating the Number of Different License Plates

To determine the number of different license plates possible, we need to consider two sections: the digits and the letters. The first and second digits must be odd, and repetition of digits and letters is not permitted.

Step-by-Step Calculation:

→ First digit: Since it must be odd (1, 3, 5, 7, 9), there are 5 choices.

→ Second digit: Also must be odd but different from the first, so there are 4 remaining choices.

→ Third digit: Any digit except the first two, leaving 8 choices.

→ Fourth digit: Any remaining digit, leaving 7 choices.

→ Fifth digit: Any remaining digit, leaving 6 choices.

→ First letter: Any uppercase letter, 26 choices.

→ Second letter: Any remaining uppercase letter, 25 choices.

→ Third letter: Any remaining uppercase letter, 24 choices.

→ Fourth letter: Any remaining uppercase letter, 23 choices.

→ Fifth letter: Any remaining uppercase letter, 22 choices.

→ Multiply these choices together:

5 × 4 × 8 × 7 × 6 × 26 × 25 × 24 × 23 × 22

→ Calculate the total:

5 × 4 × 8 × 7 × 6 = 6720

26 × 25 × 24 × 23 × 22 = 7893600

6720 × 7893600 = 53,144,832,000

Therefore, the number of different license plates possible is 53,144,832,000.

Answer:

950 people

Step-by-step explanation:

95% of people attending supported the home team.

1000 people attended the game.

That means that 95% of 1000 people supported the home team.

We need to find 95% of 1000.

To find a percent of a number, multiply the percent by the number. First, change the percent into a decimal by by moving the decimal point two places to the left. Then multiply the percent written as a decimal by the number.

95% of 1000 =

= 95% * 1000

= 0.95 * 1000

= 950

Answer: 950 people

Answer:

J=10

S=6

Step-by-step explanation:

20j+25s=350

j=s+4

are the equations in the system of equations.

If you substitute them into each other they give you your answer.

Answer:

10 ; 6

Step-by-step explanation:

Ironed by Sydney:

25t

Ironed bu Jordan:

20(t+4) = 20t+80

25t + 20t + 80 = 350

45t = 270

t = 6

Jordan: 6 + 4 = 10

Answer:

9

Step-by-step explanation:

√16=4

5*1=5

4+5=9

hope this helps

Answer:

The dot will be closed, and to the right from -6

Step-by-step explanation:

We can rearrange [tex]m+5>-1 = -6 < m[/tex]

As it is only a < we close the dots. It must go to the left as m is greater than -6 - all numbers greater than a value will be to the right on the number line.

Answer:

Each girl has 60 cents.

Step-by-step explanation:

Since they have between 50 cents and 1 dollar, then Alice should have a 50 cent coin and 1 coin of less value (because if she had 2 coins that are worth 25 cents or less, she would have only 50 cents at most).

On the other hand, Both betty and carol need to have a coin that is at least 25 cents worth (because otherwise they would have 30 cents at most), but since they cant have the same coins, then one of them should have one 50 cent coin (and 2 small cent coins) and the other should have at least two twenty five cent coins.

Lets assume that Betty has a 50 cent coin and Carol has two 25 cent coins. Since Alice also has a 50 cent coin, then the remaining coin of Alice should have the same value than the sum of the remaining 2 coins that Betty has.

The values of the coins are 5,10, 25, 50, and 100. Since they cant have 1 dollar coins, then the only possibility for a coin to have the sum of the values of 2 coins is to have a value of 10 (10 = 5+5). Thus:

Each girl has 50+10 = 50+5+5=25+25+10 = 60 cents

Answer:

527.52 in2 of paper.

Step-by-step explanation:

The area of the water bottle label can be calculated by the product of its circunference length and its height.

The length of its circunference is calculated as:

C = 2 * pi * r

C = 2 * 3.14 * 2 = 12.56 inches

Now, to find the area of the label, we just multiply the length by the height:

Area = C * h = 12.56 * 3.5 = 43.96 in2

As we want to know the amount of paper for 12 water bottles, we multiply the area of one label by 12:

Total Paper = 12 * 43.96 = 527.52 in2

It will be needed 527.52 in2 of paper.

Answer:

18,152 Gallons

Step-by-step explanation:

First, you'll want to put this into an equation. We'll use x as the amount of water in gallons that will remain in the pool.

18,968 - 12 (68) = x

First, we'll multiply - 12 and 68.

We'd end up with this:

18,968 - 816 = x

From here, we can just subtract 816  from 18,968.

18,152 = x

Now we can see that there will be 18,152 gallons of water left in the pool after 68 days.

Answer:

(A)Quotient Identity

Step-by-step explanation:

To Prove: [tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\tan \left(\alpha +\beta \right)[/tex]

Rewrite the numerator on the left side of the identity using the sum and difference formulas.

[tex]\dfrac{\sin \left(\alpha +\beta \right)}{\cos \left(\alpha +\beta \right)}=\dfrac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta -\sin \alpha \sin \beta }[/tex]

Next, Divide the numerator and denominator by[tex]cos\alpha \text{cos}\beta[/tex]

[tex]=\dfrac{\frac{\sin \alpha \cos \beta +\cos \alpha \sin \beta }{\cos \alpha \cos \beta }}{\frac{\cos \alpha \cos \beta -\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]

Rewrite the fraction from the previous step such that it is a sum or difference of two expressions as shown below

[tex]=\dfrac{\frac{\sin \alpha{\cos \beta }}{\cos \alpha{\cos \beta }}+\frac{{\cos \alpha }\sin \beta }{{\cos \alpha }\cos \beta }}{\frac{{\cos \alpha }{\cos \beta }}{{\cos \alpha }{\cos \beta }}-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]

Divide out any common factors in the expression from the previous step.

[tex]=\dfrac{\frac{\sin \alpha }{\cos \alpha }+\frac{\sin \beta }{\cos \beta }}{1-\frac{\sin \alpha \sin \beta }{\cos \alpha \cos \beta }}[/tex]

The expression from the previous step then simplifies to [tex]\tan \left(\alpha +\beta \right)[/tex] using​ the Quotient Identity

[tex]=\dfrac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }=\tan \left(\alpha +\beta \right)[/tex]

Answer:

The expression will be x = 30/6 and she'll have 5 buttons in each box.

Step-by-step explanation:

In order to write the expression for the number of buttons in each box we first need to attribute a variable to that value, in this case we will use "x". The number x will be given by the division of all the buttons she has by the number of boxes she wants to organize them in. We have:

x = (number of buttons)/(number of boxes)

x = 30/6 = 5 buttons per box

The expression will be x = 30/6 and she'll have 5 buttons in each box.

Answer:

Are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

Answer:

02a+.03b+.04c=126,

b=a+500,

c=3b

a=300., b=800., c=2400.

Step-by-step explanation:

The amount of each rate of interest given the total simple interest received is

$400, $900 and $2,700 respectively

let

a = 2% investment

= 0.02

b = 3% investment

= 0.03

c = 4% investment

= 0.04

Total interest = (0.02×a) + (0.03×b) + (0.04×c)

143 = 0.02a + 0.03b + 0.04c (1)

b = a + 500 (2)

c = 3b (3)

substitute (3) into (1)

143 = 0.02a + 0.03b + 0.04(3b)

143 = 0.02a + 0.03b + 0.12b

0.02a + 0.15b = 143 (4)

from (2)

b - a = 500 (5)

multiply (5) by 0.02

0.02b - 0.02a = 10

0.02a + 0.15b = 143 (4)

Add

0.02b + 0.15b = 10 + 143

0.17b = 153

b = 900

substitute b into (3)

c = 3b (3)

c = 3(900)

c = 2700

Recall,

b = a + 500 (2)

900 = a + 500

900 - 500 = a

a = 400

Therefore, the amount of each rate of interest given the total simple interest received is $400, $900 and $2,700 respectively

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Answer:

x-25 = 40

Step-by-step explanation:

Let the number of cookies made = x

The employees bake 40 cookies which is 25 less than the number of donuts they make

Number of Cookies is less than Number of Donuts by 25

Therefore the equation that describes the situation is given as:

x-25 = 40 where x is the number of cookies made.

Answer:

The equation is not correct

Step-by-step explanation:

Lets break it down

Cookies = 40

Donuts lets call it x since we dont have a figure

It is said that the 40 cookies is 25 less than the number of donuts

So therefore

x less than 25 = 40

x-25=40

To get x we add 25 to each side

x-25+25=40+25

x=65

Equation should be

x-25=40

That is 65-25 =40

Answer:

5

xD

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Multiply 4, 5 and 5 which gives 100.

Answer:

Correct answer:  x = - 3  and y = - 5

Step-by-step explanation:

Given:

2 x - y = - 1

3 x - 2 y = 1

We will multiply first equation with number (- 2) and get:

- 4 x + 2 y = 2

then we add this equation to another and get:

- 4 x + 3 x = 2 + 1

- x = 3 / · (- 1)

x = - 3

now we replace x = - 3  in the first equation and get:

2 (- 3) - y = - 1  ⇒ - 6 - y = - 1 / ·(- 1)  ⇒ 6 + y = 1  y = 1 - 6 = - 5

y =- 5

God is with you!!!

Answer:

x= -3

y= -5

Step-by-step explanation:

-2 (2x-y= -1) = -4x + 2y = 2

-4x + 2y = 2

3x - 2y = 1

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

-x = 3

x = -3

plug the x= -3 into the equation to find y

Answer:

y=32x-32

Step-by-step explanation:

this time no algorithm or equation was needed i saw that if the equation was y=32x there would be ordered pairs (1,32) and (2,64) so to delay it by 1  on the x side just subtract the slope from the y - intercept sorry if that doesn't make sense

Answer:

The correct answer is 7 : 8.

Step-by-step explanation:

There are 14 girls and 2 boys taking karate lessons.

Total number of students taking the karate class is 16.

The ratio that compares the number of girls taking karate lessons to the total number of students taking karate lessons is given by 14 : 16 = 7 : 8.

This can be interpreted as for every 8 students in the karate lesson, 7 of them are girls.

Answer:

x = 1, y = 1

Step-by-step explanation:

Use system of equations to solve for x and y by using substitution

The solution to the system of equations, though we can solve using substitution, can also be found by graphing these equations. If you graph these equations, look for where they intersect (it should be one point!).

-5x + 6 = 3x - 2

6 = 8x - 2

8x = 8

x = 1

y = 3(1) - 2

y = 3 - 2

y = 1

Hope this helps!! :)

Answer:

the distance

Step-by-step explanation:

More time care travels, more distance it goes. So distance depends of the time.

Step-by-step explanation:

4(5x-2) = 2(9x+3)

20x-8 = 18x+6

20x-18x = 6+8

2x=14

x= 14/2

∴ x= 7 [ANS]