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Part 1

[tex)400+30x=4900[/tex]

Part 2

[tex]30x=4500 \\ \\ x=150[/tex]

So, the answer is 150 ft².

Answer:

82°

Step-by-step explanation:

 The exterior angle of triangle equals the sum of opposite interior angles.

 ∠C + ∠B = 143°

  61+ ∠B  = 143

         ∠B  = 143 - 61

         ∠B = 82°

The resultant matrix after elementary row operation is:

[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]

What is elementary row operation?

In mathematics, the elementary row operation is a method in which the two rows exchanged. In this, the rows are either multiplied, added or division. Sometimes, single row is multiplied by some constant.

According to the question, the given matrix A is written below:

[tex]A = \left[\begin{array}{ccc}-3&5&2\\8&-1&3\end{array}\right][/tex]

Now, performing elementary row operations represented by [tex]-3R_{2} +4R_{1}[/tex]

The given matrix becomes after elementary row operations:

[tex]A = -3R_{2} + 4R_{1} = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]

Hence, the resultant matrix after elementary row operation is::

[tex]A = \left[\begin{array}{ccc}-12&20&8\\-24&3&-9\end{array}\right][/tex]

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By using the method subtraction, Jackson's height is 1.25m.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

Grace's height is 1.45 m.

Jackson is 0.2 m shorter than Grace.

Jackson's height is 1.45 -0.2 = 1.25

Therefore, Jackson's height is 1.25m.

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1. Month for assistance caregivers is 14 months.

Month for senior caregivers will be 14 months.

2. After 2 month, there will be 14 of each types of caregiver.

What is an expression?

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

Given that;

A daycare center in Hillsdale currently has 12 assistant caregivers and 6 senior caregivers.

On high demand the owner is going to be hiring 1 assistant caregiver per month and 4 senior caregivers per month.

Let m is number of months.

Then, Each month has 12+ m for assistant caregivers and 6 + 4m for senior caregivers.

By given condition we formulate;

12 + m = 6 + 4m

12 - 6 = 4m - m

6 = 3m

3m = 6

m = 2

Thus, 12 + m = 12 + 2 = 14

And, 6 + 4m = 6 + 4 x 2 = 14

So, After 2 month, there will be 14 of each types of caregiver.

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Answer: 33.6

Step-by-step explanation:

Answer:

33.6

Step-by-step explanation:
4.20 x 8 = 33.6

The approximate value of x(t), which indicates the location of coordinate the ladder's foot at time t seconds, is 6.85. 7

Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.

The location in the cartesian plane will be determined by the coordinate points. A point's distance from the y axis is known as the x-coordinate, also known as the abscissa, and its distance from the x-axis is known as the y-coordinate, also known as the ordinate.

based on the information provided,

x = the distance between the wall and the bottom of the ladder

y = distance of the top of the ladder from the ground

x² + y² = 25²

x² + 7² = 25²

x² = 625 -49 = 429

y = √576

Differentiating the equation with respect to time t gives

2x dx/dt + 2y dy/dt = 0

dx/dt = -y dy/dt / x

 = -√576 * (2) / 7

= 6.85 feet per second approximately.

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The value of d after addition or subtraction is 7.5

The area of mathematics known as algebra aids in the representation of circumstances or problems as mathematical expressions. To create a meaningful mathematical expression, it takes variables like x, y, and z together with mathematical operations like addition, subtraction, multiplication, and division. Algebra is used in every discipline of mathematics, including trigonometry, calculus, and coordinate geometry.

Given that : the equation is 5.5 = −2+d

5.5 = −2+d

5.5 + 2 = d

7.5 = d

The value of d after addition or subtraction is 7.5

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The principal of account A is $20.83 and the principal of account B is $58.33. Account 2 earned the most interest rate in the first​ month.

The formula to calculate Simple interest, Simple interest = Principal × rate of interest × time.

The principle for Account A would be,

2 = Principal × 3.2% × 3

So, the principal is $20.83

The principle for account B would be,

38.50 = Principal × 2.2% × 30

So, the principal is $58.33,

The interest rate for both accounts is now as follows:

For account 1

= $20.83 × 3.2%

= $0.67

And, for account 2

= $58.33 × 2.2%

= $1.28

Account 2 has the greatest interest rate, thus it is taken into account.

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Answer:2479

Step-by-step explanation: subtract 2,994 and 515 and you would get 2479

Answer: 3509 treats

Step-by-step explanation:

If I'm understanding correctly, we need to add the desserts together right?

[tex]2994+515\\=3509[/tex]treats in total

Answer:

0.3,1/2,26%

Step-by-step explanation:

ascending order if arranging from smallest to highest .In this case, 0.3 Is the smallest followed by 1/2 and then 26%.

Answer:

subtract 2x from 3x thats x so 50=x

Step-by-step explanation:

Answer:x=50

Step-by-step explanation:bring 3x over on one side with 2x and bring 50 over on the other side by itself.

The equation becomes 2x-3x=-50

2x-3x is -x

so the equation is -x=-50

there are two negatives in the equation so you make the equation positive because a negative and a negative equals a positive

Therefore the answer is x=50

Answer:

4⅜ or 4.375 inches.

Step-by-step explanation:

35 ribbon into 8 pieces is:

35/8 = 4⅜ or 4.375 inches.

The cost of the polishing, £C, is given by C = 6πr² + 300/r​.

The volume of the solid cylinder is 75 m³.

Formula for volume of cylinder = πr²h.

Where R is rhe radius of cylinder and h is the height of the cylinder.

So we can write,

πr²h = 75

h = 75/πr².

So the height of the cylinder is 75/πr² centimeters.

Curved surface area of the cylinder is 2πrh m².

Cost of polishing the curved surface area is £2/cm².

Total cost of polishing the curved surface area = £2×2πrh

Area of the base and the top is 2(πr²).

Cost of polishing base and top is £3/cm².

Cost of polishing 1m² of the base and top,

Cost of area of base and top = £3/cm².

Total Cost of polishing base and top area = £3×2(πr²)

The total cost C of polishing the whole glass,

C = 4πrh + 6πr²

Puting the value of h = 75/πr²

C = 4πr(75/πr²) + 6πr²

C = 6πr² + 300/r.

Hence it is proved that the total cost of polishing is,

C = 6πr² + 300/r.

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In 13 days they will travel 1904 miles altogether.

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.

Multiplication in action or in progress. The multiplication of 8 and 3 is the same as the sum of 8+8+8, which is a mathematical operation that takes two numbers and returns an answer that is equal to the sum of a column in which one of the numbers is repeated the amount of times of the other number.

Given Data

they travel 238 miles a day for 13 days

1 day = 238 miles

13 days = 238 (13)

13 days = 1904

In 13 days they will travel 1904 miles altogether.

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The total terms that in the following sequence 7, 10, 13,..., 391, 394 is 130

The formula for the nth term of an arithmetic sequence is expressed as;

Tn = a + (n-1)d

Where;

a = 7

Tn = 394

d = 3

Substitute the value in the formula, we have;

394 = 7 + ( n -1) 3

expand the bracket

394 = 7 + 3n - 3

collect like terms

394 - 4 = 3n

find the difference

390 = 3n

Make 'n' the subject of formula

n = 390/3

n = 130

Hence, the number is 130

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there are no restrictions other than 2 x + 1 > 81 on the radical inequality.

We are given the radical inequality as:

⁴√ 2 x + 1 > 3

We need to find the restriction on this inequality.

For this we will first put x on one side and other constant on the other side.

So, we get that:

2 x + 1 > 3⁴

2 x + 1 > 81

So, the restriction is not from the given options.

But, the value of 2 x + 1 should be greater than 81 for the inequality to be true.

Therefore, we get that, there are no restrictions other than 2 x + 1 > 81 on the radical inequality.

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The equation of the circle with the centre (5,7) and containing the point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

The equation for a circle in standard form is [tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex]  = [tex]r{2}[/tex], where (x, y) denotes arbitrary coordinates on the circle's perimeter, r denotes the circle's radius, and (x1, y1) denotes the coordinates of the circle's centre.

The equation of a circle with centre (x1,y1)

[tex](x-x1){2}[/tex]+ [tex](y-y1){2}[/tex]  = [tex]r{2}[/tex]

we know the centre , which is (5,7) so the equation changes to:

[tex](x-5){2}[/tex]+ [tex](y-7){2}[/tex]  = [tex]r{2}[/tex]

putting the values of the point p we get

[tex](1-5){2}[/tex] [tex]+ (9-7){2}[/tex][tex]= r{2}[/tex]

r=[tex]\sqrt{20}[/tex]

so the equation of the circle will be:

[tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

Therefore the equation that satisfies the given condition of a circle with centre (5,7) and containing point p (1,9) is [tex]\sqrt{20} =(x-5){2}+(y-7){2}[/tex]

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Step-by-step explanation:

Splitting the middle term

8a^2 +16a + 2a+4 =0

8a (a+2) +2(a+2) = 0

(8a+2) (a+2)

8a=-2 , a = -2

a= -2/8

a= -1/4

a ( -1/4 , -2)

The most appropriate choice for similarity of figures will be given by

Volume of cylinder B is 720 [tex]cm^2[/tex]

What is similarity of figures?

Two figures are said to be similar if they have same shape but different sizes.

Actually sides of similar figures are proportional

Ratio of heights of cylinder A and B = 5 : 10

                                                            = 1 : 2

Ratio of areas of cylinder A and  cylinder B = [tex]1 ^2 : 2^2[/tex]

                                          = 1 : 4

Area of cylinder A = [tex]18[/tex] [tex]cm^2[/tex]

Area of  cylinder B = [tex]18 \times 4\\[/tex]

                                = [tex]72[/tex] [tex]c[/tex][tex]m^2[/tex]

Height of  cylinder B = [tex]10 cm^2[/tex]

Volume of cylinder B = Area of cylinder B [tex]\times[/tex] Height ofcylinder B

                     = [tex]72 \times 10[/tex]

                     = [tex]720[/tex] [tex]cm^2[/tex]

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Complete Question

The image of the question has been attached with this question.

If each digit can be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9, giving a total of 10 possible numbers for each digit. if a pin is 4 digits, each digit can be any one of the 10 possible numbers, The different possible combinations are there is : 10,000.

Given :

Digit = 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9

Possible number  = 10

Pin = 4 digits

Now let determine the different possible number

Possible number combination = 10 x 10 x 10 x 10

Possible number combination = 10,000

Therefore the combination is 10,000.

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If Caleb worked his 40 regular hours last week, plus 6 overtime hours at the time-and-a-half rate. His gross pay was $1,063. His hourly rate is : $21.69.

Hourly rate can simply be defined as the wages earn per hour.

Given data :

Regular hours = 40

Over time = 6 ( 1.5 ) = 9

Gross pay = $1,063

Hence,

let h represent the hourly rate

So,

1.5h = overtime rate

Now let determine the hourly rate

40h + 6(1.5h) = 1,063

40h + 9h = 1,063

49h = 1,063

Divide both side by 49h

h = 1,063/ 49

h = $21.69

Therefore the hourly rate is the amount of $21.69.

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In a case whereby the area of a trapezoid is given by the formula A=12(b1+b2)h then the equation for b2 is b2= (A - 12hb1)/12h.

The formula for the  trapezoidis given as A=12(b1+b2)h , where the value of term b2 is been exdpected to be found.

firstly, we need to open the bracket as :

A=12(b1+b2)h

A= 12hb1 + 12hb2

Then this can be simplified as  12hb2= (A - 12hb1)

Then we can try to make the b2 the subject of the formula as

b2= (A - 12hb1)/12h.

Therefore, the value of the term b2 can be written as b2= (A - 12hb1)/12h.

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The circumference of the given circle will be 18.84cm and its area will be 28.26cm²

the center of the given circle is A with coordinates (2,3)

we are given that each block on the graph represents 1cm,

on observing the graph we can conclude that the radius of the circle is 3cm.

circumference of the circle is given by  the formula,

2πr

taking pi as 3.14 and substituting r=3 in the above formula we get,

2*3.14*3

=18.84cm

thus the circumference of the circle will be 18.84 units.

Similarly, area of a circle can be calculated using the formula,

πr²

taking π as 3.14 and substituting r=3 in the above formula,

3.14*3²

=28.26cm²

What is the difference between area and perimeter?

Perimeter is - "distance around the outside of a shape" while area is - "measures of the space inside a shape."

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The number of pipes that are made of chrome according to the prediction by Patty are 120.

It is given in the question that :-

Number of pipes in stock at Patty's hardware store = 600

Number if pipes randomly selected by Patty = 40

Number of pipes of chrome = 8

Hence, we can write,

Probability of chrome pipes = 8/40 = 1/5

Therefore, we can write,

Number of pipes that are made of chrome according to the prediction by Patty = (1/5)*600 = 120

Probability

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

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The probability that at least five spots will be showing up on the die is 1/3.

It is given that a professor rolls a fair, six-sided die.

We need to find the probability that at least five spots will be showing up on the die.

Total possible outcomes = {1,2,3,4,5,6}

Number of total outcomes = 6

At least five spots will be showing up on the die. So,

Favorable outcomes = {5,6}

Number of favorable outcomes = 2

Formula for probability:

Probability = [tex]\frac{Number of Favorable Outcomes}{Number of Total Outcomes}[/tex]

On substituting Number of favorable outcomes and Number of total outcomes in the formula of Probability, we get

Probability = 2/6

Probability = 1/3

Therefore, the required probability is 1/3.

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hope this helps. . .....

We would find the percentage of those knowing neither Hindi nor English in the population using set theory,

Percentage of population knowing English (A) = 46%

Percentage of  population knowing Hindi (B) = 34%

Percentage of population who know both languages (A U B) = 23%

therefore,

Applying set theory,

A U B = A + B - (A ∩ B)

23% = 36% + 46% - ( A ∩ B)

A ∩ B = 80% - 23% = 57% population knows either Hindi OR English.

So, Population who neither know Hindi or English = 100% - 57% = 43%

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Answer:25.8184143223

1+1+278*67/782

1+1+18626/782

2+23.8184143223

25.8184143223