An animal shelter has enough pens for x small dogs and y large dogs, and can hold up to 36 dogs at a time. It costs the shelter $12 a week to keep a large dog and $7 a week to keep a small dog. The shelter must keep its weekly costs under $350. Which system of inequalities can be used to represent this situation?

Answer:

1. [tex]2^{3}[/tex] x [tex]3^{6}[/tex]

ii. 18

b. -12

2. nth = a + (n - 1)d

ii. k = 103

3. [tex]x^{o}[/tex] = [tex]27^{o}[/tex]

4. Volume = 25.025 [tex]m^{3}[/tex]

Step-by-step explanation:

1. Prime factors of 5832 = 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

                                       = [tex]2^{3}[/tex] x [tex]3^{6}[/tex]

ii. [tex]\sqrt[3]{5832}[/tex] = 18

b. 2[tex]a^{2}[/tex] - 3[tex]b^{2}[/tex] + 3abc

a = 3, b = 2, c = -1

Thus,

2[tex](3)^{2}[/tex] - 3[tex](2)^{2}[/tex] + 3(3 x 2 x -1)

= 18 - 12 - 18

= -12

2. The required formula is;

nth = a + (n - 1)d

where: a is the first term, n is the number of terms in the sequence and d is the common difference.

b. kth term = 304, then

304 = -2 + (k - 1) 3

      = -2 + 3k -3

      = 3k - 5

3k = 304 + 5

3k =  309

k = [tex]\frac{309}{3}[/tex]

  = 103

k = 103

3. Comparing <DAB and < EBC;

<DAB ≅ <EBC = [tex]x^{o}[/tex]

<BEC = [tex]90^{o}[/tex] (right angle property)

<C = [tex]63^{o}[/tex]

Thus,

<B + <C + <E = [tex]180^{o}[/tex] (sum of angles in a triangle)

[tex]x^{o}[/tex] + [tex]63^{o}[/tex] + [tex]90^{o}[/tex] = [tex]180^{o}[/tex]

[tex]x^{o}[/tex] + 153 = [tex]180^{o}[/tex]

[tex]x^{o}[/tex] = 180 - 153

   = 27

[tex]x^{o}[/tex] = [tex]27^{o}[/tex]

4. Volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h

where r is the radius and h is the height of the cylinder.

Diameter = 3.5 m, h = 2.6 m

r = [tex]\frac{3.5}{2}[/tex]

r = [tex]\frac{7}{4}[/tex] m

So that,

Volume = [tex]\frac{22}{7}[/tex] x [tex](\frac{7}{4}) ^{2}[/tex] x 2.6

             = [tex]\frac{22}{7}[/tex] x [tex]\frac{49}{16}[/tex] x [tex]\frac{13}{5}[/tex]

             = 25[tex]\frac{1}{40}[/tex]

Volume = 25.025 [tex]m^{3}[/tex]

Answer:

yes it is

Step-by-step explanation:

it is quadrilateral

Answer:

yes

Step-by-step explanation:

just look up rhombus and then look at the pictures

Answer:

hey. pls post the graphs with the question so we may help you. you can add the pictures as an attachment.

Answer:

C:  Square centimeters

Step-by-step explanation:

We are measuring length here, not volume, so recognize that this fact eliminates Answer B.  The area of a rectangle, such as this picture is, is A = Length * Width, measured in (cm)(cm), or C:  Square centimeters.

Answer:

The answers are options d and e

Answer:

does not have a solution because √-0.75 ≠ R

Step-by-step explanation:

x^2 - 5x + (5/2)^2 = -7

x^2 - 5x + 6.25 = -7 + 6.25

(x - 2.5)^2 = -0.75

(x - 2.5) = √-0.75

does not have a solution because √-0.75 ≠ R

Answer:

x = (1/2)(5 ± i√3)

Step-by-step explanation:

x² - 5x + 7 = 0

subtract 7 from both sides

x² - 5x = -7

Use half the x coefficent, -5/2, as the complete the square term

(x - 5/2)² = -7 + (-5/2)²

(x - 5/2)² = -7 + 25/4

(x - 5/2)² = -3/4

Take the square root of both sides

x - 5/2 = ±(√-3) / 2

x - 5/2 = ±(i√3) / 2

Add 5/2 to both sides

x = 5/2 ± (i√3) / 2

factor out 1/2

x = (1/2)(5 ± i√3)

Answer:

78.54inches²

Step-by-step explanation:

Area of a circle=πr²

radius=½ diameter

=5inches

=π×(5inches)²

=π25inches²

=78.539816339744830inches²

rounded to the two decimal places=78.54inches²

Answer:

(0.30, 0.42)

Step-by-step explanation:

Given the sample proportion is = 0.36

Number of trials required for determining the margin of the error = 100

Sample size, n = 50

The point estimate = 0.36

The minimum sample proportion form the simulation = 0.28

The maximum sample proportion from the simulation = 0.40

Also the margin of the error of population proportion is found by using the half of the range.

Therefore, the interval estimate for the true population proportion is = (0.30, 0.42)

Answer:

d.

Step-by-step explanation:

1) just to substitute the value of 'x' into the given equation and check equality:

(9;-2): -2≠ -45-1;

(5;24): 24≠-25-1;

(-1;6): 6≠5-1;

(-4;19): 19=20-1.

Answer:

(f + g)(x) = 5x + 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x - 6

g(x) = 3x + 9

(f + g)(x) is f(x) + g(x)

Step 2: Find

Answer:

[tex] \frac{1}{3} [/tex]

Step-by-step explanation:

Mia used One Third of the felt for her art project. 3/3 would be the whole felt together. Since one part of three sections was used up then this means that 1/3 was used.

Answer:

17) option b

18) option b

19) option d

Step-by-step explanation:

17)

Cost of 25 burgers = $75

Therefore , cost of 1 burger:

                                          [tex]\frac{75}{25} = 3[/tex]

18)

Area of  rectangle = length x breadth

                 [tex]\frac{7}{6} = length \times \frac{5}{6}\\\\\frac{7}{6} \times \frac{6}{5} = length \\\\\frac{7}{5} = length \\\\Length = \frac{7}{5} \ km[/tex]

19)

                   14.25

                 x    6.3

             _________

                   4275

            +    8550              

             __________

                89.775

            ___________

a.

Answer:

240 cm^3

b.

Answer:

208cm^2

Answer:

a. m<B = 100°

b. m<L = 55°

c. Scale factor = 9/11

Step-by-step explanation:

a) Similar triangles have their three corresponding angles congruent to each other, while the ratio of their corresponding sides are proportional to each other.

Since ∆ABC ~ ∆GLJ, therefore,

<A = <G,

<B = <J

<C = <L

m<J = 100° (given)

Therefore,

m<B = m<J = 100°

m<B = 100°

b) m<A = m<G

m<A = 25° (given)

Therefore,

m<A = m<G = 25°

m<G = 25°

m<L = 180° - (m<J + m<G)

Substitute

m<L = 180° - (100° + 25°)

m<L = 55°

c) scale factor of smaller triangle to the larger = side length of smaller triangle / corresponding side length of bigger triangle

Scale factor = AB/GJ

Substitute

Scale factor = 18/22

Simplify

Scale factor = 9/11

Answer:

the quotient of w and 7

is it correct?

Step-by-step explanation:

Answer:

~ 7 years

Step-by-step explanation:

2 = (1 + .1/4)^(4t)

2 = (1.025)^(4t)

Take the log of both sides

log2 = 4t * log1.025

divide both sides by log1.025

log2/log1.025 = 4t

28.07103452593863 = 4t

Divide both sides by 4

7.017758631484657 = t

~ 7 years

Answer:

C)

Step-by-step explanation:

When you see something like 6³) 2, to get both the exponent and the multiplier together, you must multiply 3 x 2. As this problem goes, there is -7 and 5 as our exponents. If we both multiply them by 2, we will get -14 and 10. Its one of the rules in basic algebra. Check the pic I posted below.

Hope this helps!

-kiniwih426

=======================================================

Work Shown:

A = h*(b1+b2)/2  .... area of trapezoid formula

A = 4*(7+3)/2

A = 4*(10)/2

A = 40/2

A = 20 square units

-----------

notes:

Answer:

Not independent

Explanation:

Two events are not independent/dependent if the result of one event affects the outcome of the other. In the case above, numbers are picked without replacement, therefore if one slip is picked then the other slip will be picked(slips are picked only once not twice or more as in independent events). Events would be independent if there was a replacement.

Answer:

a. 81 square inches

b. 108 inches

Step-by-step explanation:

The area of all 5 squares combined is 405 square inches. This is 5 times the area of 1 square. 405/5 = 81. The area of 1 square is 81 square inches.

Since this is a square, the sides are equal. Thankfully the area of 1 square is a perfect square so the length of one side of the square is a full number, which is 9. All of the squares are congruent as shown in the diagram so we simply add every length together (there are 12 sides, each side is 9 inches).

12*9 = 108 and that is the perimeter.

Answer:

area

Step-by-step explanation:

a = 405/5 = 81

a =81 square inches

perimeter

p = √81

= 9

=4×9×5

=180 inches

Answer:

36

Step-by-step explanation:

largest share = 9parts = 108

1 part = 108÷9 = 12

smallest share = 3parts = 12×3 = 36

The two chords are the same length given by the 4 short lines through each section.

Because the chords are the same length they need to be equal distance from the center of the circle

X = 9

Answer:

0.383 (3 d.p.)

Step-by-step explanation:

Probability formula

[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]

Let P(A) = probability that the student owns a credit card

Let P(B) = probability that the student is a freshman

Use the given table to calculate the probability that the student is a freshman and owns a credit card:

[tex]\implies \sf P(B \cap A)=\dfrac{23}{100}=0.23[/tex]

Use the given table to calculate the probability that the student is a freshman:

[tex]\sf \implies P(B) = \dfrac{60}{100}=0.6[/tex]

To find the probability that the student owns a credit card given that they are a freshman, use the conditional probability formula:

Conditional Probability Formula

The probability of A given B is:

[tex]\sf P(A|B)=\dfrac{P(B \cap A)}{P(B)}[/tex]

Substitute the found values into the formula:

[tex]\implies \sf P(A|B)=\dfrac{0.23}{0.6}=0.383333...[/tex]

Therefore, the probability that the student owns a credit card given that they are a freshman is 0.383 (3 d.p.).

P(Freshman credit card holder)

P(Freshman)

P(Freshman credit holder|Freshman)

Answer:

Kindly check explanation

Step-by-step explanation:

Given the regression equation :

y = 31.6 + 10.9x

x = the number of years of study ;

y = the grade on the test.

The predicted is y which is also the same as the response variable, hence, the response variable is grade on the test

The predictor variable is x, which is the independent variable, which is the number of years of study.

From. The regression output given ;

The slope which is the Coefficient of the predictor variable is 10.9 which means that for every unit change in number of years of study, the grade on test increases by 10.9

The intercept which is the constant value, 31.6, means, the least a person can get in the get in grade is 31.6 (at x = 0)

Answer:

2,4,6,8,10,12,14,16,18,20

Answer:

How do you make the number 7 an even number without addition, subtraction or multiplication?

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22 Answers



Yogesh Rana, B.Sc. Mathematics, University of Delhi (2016)

Answered 4 years ago

You can remove alphabet S from SEVEN.

You can change the convention. Whole mathematics works like that. After all it is just a name, ie, call the numbers divisible by 2 odd and not divisible by 2 even. Everything will still work fine. You got to rename some theorems also.

Introduce and derive a new number system from the current number system, name the symbol 6 as seven and the symbol 7 as Six. Just rename the symbols.

Introducing a new number system and interchange position of 7 with an even number.

If we remove one number before 7 ( 1 - 6 ) with its name, we have again a new number system with base 9 and technically no. 7 is still no. 7 with value = 6.

These are some genuine ways rather than dividing.

ANSWERS OF DIVISION ARE TECHNICALLY WRONG AND RIDICULOUS BECAUSE DIVISION BY ‘x’ is MULTIPLICATION BY ‘1/x’ .

Answer:

20$ i think

Step-by-step explanation:

A fraction is a way to describe a part of a whole. If a car is parked in the garage for 5 hours and 30 minutes the charge will be $10.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

Given that for the first hour that a car is parked in the garage, there is no charge. After the first hour, for the next two hours that a car is parked in the garage, there is a $5 charge. After the third hour, the garage charges $2 for each additional hour that the car is parked in the garage.

1.) Since the car is parked for 30 minutes only.

Charge = $0

Hence, No charge will be charged for 30 minutes.

2.) If a car is parked in the garage for 2 hours and 30 minutes.

Charge for 1 hour = $0

Charge for the next 1 hour and 30 minutes = $5

Hence, the charge will be $5.

3.)  If a car is parked in the garage for 5 hours.

Charge for 1 hour = $0

Charge for the next 2 hour = $5

Charge for the next 2 hour = 2×$2 = $4

Charge = $5 + $4 = $9

Hence, the charge will be $9.

4.) If a car is parked in the garage for 5 hours and 30 minutes.

Charge for 1 hour = $0

Charge for the next 2 hour = $5

Charge for the next 2 hour 30 minutes = 2.5 ×$2 = $5

Charge = $5 + $5 = $10

Hence, the charge will be $10.

Learn more about Fraction:

https://brainly.com/question/1301963

#SPJ2

Answer:

.216165788

.582225057

.417774943

Step-by-step explanation:

We need to use a binomial distribution here

A.

10C5*.58⁵*(1-.58)⁵= .216165788

B.

I honestly think the fastest way to solve this is adding the probabiblity of exactly 6,7,8,9,10

which means we write

10C6*.58⁶*(1-.58)⁴+10C7*.58⁷*(1-.58)³+10C8*.58⁸*(1-.58)²+10C9*.58⁹*(1-.58)+10C10*.58¹⁰= .582225057

C.

To solve this just take the compliment of answer B

1-.582225057= .417774943

Reflection across the y-axis composition translation of 6 units x, -5 units y. Then the correct option is D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

On a coordinate plane, 3 triangles are shown.

Triangle B C D has points (1, 4), (1, 2), (5, 3).

Triangle B'C'D' has points (-1, 4), (-1, 2), (-5, 3).

Triangle B"C"D" has points (5, -1), (5, -3), (1, -2).

Reflection across the y-axis composition translation of 6 units x, -5 units y.

The diagram is given below.

More about the transformation of the points link is given below.

https://brainly.com/question/27224339

#SPJ1

Answer:

combination

Step-by-step explanation:

solution :

6C2 + 15C7

=6,450