Plz help me with the problem

Answer:

Step-by-step explanation:

Cross multiply on both sides

= (x + 1) (21) = 15(x + 3)

= 21x + 21 = 15x + 45

Bringing like terms on one side

21x - 15x = 45 - 21

= 6x = 24

x = 24/6 = 4

Option A is the correct answer

[tex] =\tt (a) \: 4[/tex]

[tex] = \frac{x + 1}{x + 3} = \frac{15}{21} [/tex]

[tex] =( x + 1 )\times 21 = (x + 3 )\times 15[/tex]

[tex] = 21x + 21 = 15x + 45[/tex]

[tex] = 21x + 21 - 15x = 45[/tex]

[tex] = 6x + 21 = 45[/tex]

[tex] = 6x = 45 - 21[/tex]

[tex] = 6x = 24[/tex]

[tex] = x = \frac{24}{6} [/tex]

[tex] =\color{plum} \bold{x = 4}[/tex]

Let us now place 4 in the place of x and see if the substitution is equivalent to [tex] \frac{15}{21} [/tex] :

[tex] = \frac{4 + 1}{4 + 3} = \frac{15}{21} [/tex]

[tex] = \frac{5}{7} = \frac{15}{21} [/tex]

[tex] = \frac{5}{7} = \frac{15÷3}{21÷3} [/tex]

[tex] = \frac{5}{7} = \frac{5}{7} [/tex]

Therefore, the value of x in this proportion = 4

Answer:

15 cars

Step-by-step explanation:

If there are 7 trucks for every 5 cars, the ratio is 7:5. So if there are 21 trucks, that's 7 x 3, which means we also multiply 5 by 3 = 15

Answer:

[tex]Y=$24+0.09X[/tex]

Step-by-step explanation:

From the question we are told that

February Heat [tex]H_1=1900\textdegree[/tex]

February Gas [tex]G_1 =\$195[/tex]

April Heat [tex]H_2=600\textdegree[/tex]

April Gas [tex]G_2=\$78[/tex]

Generally equation for heating degree-days X is mathematically given by

 [tex]X=\frac{\triangle gas\ bills}{\triangle Heating\ days}[/tex]

 [tex]X=\frac{195-78}{1900-600}[/tex]

 [tex]X=\$ 0.09[/tex]

Generally the equation for gas bill Y is mathematically represented by

 [tex]Y=78-(600*0.09)\\Y=\$24[/tex]

The equation representing the relationship between the gas bill (Y) and heating degree-days (X) is

 [tex]Y=$24+0.09X[/tex]

Answer: it’s C

Step-by-step explanation:

d,

hope this helps! May I have brainliest please? :D

Answer:

13.433333333

Step-by-step explanation:

Answer:

He needs to sell 200 ribbons to break even.

Step-by-step explanation:

The break even point is where the expenses are equal to the earnings, so you can write an expression that indicates that Lucas' expenses are equal to his earnings:

46+0.02x=0.25x

Now, you can solve for x to find the answer:

46=0.25x-0.02x

46=0.23x

x=46/0.23

x=200

According to this, the answer is that he needs to sell 200 ribbons to break even.

Answer:

6 tables

Step-by-step explanation:

8 multiply by 6 gives you 48

Answer:

$16

Step-by-step explanation:

[tex]0.75x = 12\\3x = 48\\x = 16[/tex]

9514 1404 393

Answer:

  -12

Step-by-step explanation:

The average rate of change of a function f(x) on an interval [a, b] is defined as ...

  average rate of change = ((f(b) -f(a))/(b -a)

For the given function and interval, this is ...

  average rate of change = (f(1.25) -f(0.75))/(1.25 -0.75)

  = (4 -10)/(0.5) = -12

The average rate of change is -12 on the interval.

__

The calculator results for f(1.25) and f(0.75) are shown in the attachment, along with the computation of the average rate of change.

Answer:

3/8

Step-by-step explanation:

We want the probability of getting a tail in three trials.

We will use binomial distribution, given by the formula:

[tex]\displaystyle P(x)={n\choose x}p^xq^{n-x}[/tex]

We want one success out of three trials. So, n = 3 and x = 1.

The probability for success in one trial is 1/2. So, p = 1/2.

And the probability for failure in one trial is 1/2. q = 1/2.

Therefore, the probability of getting a tail is:

[tex]\displaystyle P(1)={3\choose 1}\Big(\frac{1}{2}\Big)\Big(\frac{1}{2}\Big)^2[/tex]

Evaluate:

[tex]\displaystyle P(1)=3\Big(\frac{1}{8}\Big)=\frac{3}{8}[/tex]

The probability of getting a tail by tossing a coin thrice is 3/8.

Edit:

My apologies. If you haven't learned the binomial distribution yet, below is another method.

Using the fundamental counting principle, we have a total of 2 times 2 times 2 or 8 total outcomes.

We want only one tail. This can be the first toss, the second toss, or the third toss.

So, out of 8 total outcomes, only 3 are favorable.

Hence, the probability of getting one tail by tossing a coin thrice is 3/8.

Answer:

133/10

Step-by-step explanation:

first turn into proper fraction

19/5 * 7/2 = 133/10

Answer:

a) P (A)= 88/102= 0.8627

(b) P (B)=  89/102= 0.8725

c) P (A`) =  14/102 = 0.1372

(d) P (A∩B) = 84/102 =0.8235

(e) P(AUB)= 93/102 = 0.9117

(f)P (A`UB) = 98/102= 0.96078

Step-by-step explanation:

                                                                   edge                  

                                                  finish excellent       good           Total

(A )surface finish excellent            84                      4                  88

good                                    ( B) ⇵    5                       9                  14

Total                                               89                      13                102

a) Upper P left-parenthesis Upper A right-parenthesis equals

P (A)= 88/102= 0.8627

All the elements of set A = 84+4= 88

(b) Upper P left-parenthesis Upper B right-parenthesis equals

P (B)=  89/102= 0.8725

All the elements of set B = 84+5= 89

c) Upper P left-parenthesis Upper A prime right-parenthesis equal

P (A`) =  14/102 = 0.1372

All the elements of Universal set U which are not elements of set A = 102- 88= 14

(d) Upper P left-parenthesis Upper A intersection Upper B right-parenthesis equals

P (A∩B) = 84/102 =0.8235

Only those elements of set A and set B which are common

(e) Upper P left-parenthesis Upper A union Upper B right-parenthesis equals

P(AUB)= 93/102 = 0.9117

Totalling elements of set A and B= 88+5= 93

(f) Upper P left-parenthesis Upper A prime union Upper B right-parenthesis equals

P (A`UB) = 98/102= 0.96078

All the elements of Universal set U which are not elements of set A and the elements of Set B = 5+9+ 84= 98

Answer:

6:4:9 Yw❤️

Step-by-step explanation:

Step-by-step explanation:

11x² + 33x + 22

= 11(x² + 3x + 2)

= 11(x + 1)(x + 2).

Answer:

c

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

one tin of cheese $23

one tin of caramel $27

Step-by-step explanation:

let 'x' = cost of cheese tin

let 'y' = cost of caramel tin

10x + 8y = 446

22x + 11y = 803

i multiplied the first equation by -11 and the second by 8 to eliminate the 'y' terms

  -110x - 88y = -4906

+  176x + 88y = 6424

    66x = 1518

     x = 1518 / 66

     x = 23

find 'y':  10(23) + 8y = 446

             230 + 8y = 446

              8y = 216

               y = 27

Answer:

Restaurant A: 31 grams of fat

Restaurant B: 25 grams of fat

Step-by-step explanation:

[tex]x + (x + 6) = 56\\2x + 6 = 56\\2x = 50\\x = 25[/tex]

Answer:

20 weeks

Step-by-step explanation:

30/15=2

300/15=20

20 weeks

Answer:

(8 × 20) ÷ 4

40

Step-by-step explanation:

8 × 20 = 160

160/4 = 40

The fraction is defined as a number in the form of a/b where a nd b are integers and b is not equal to zero. Sarah has left with 120 balloons.

A fraction is used to represent a portion or part of anything. It consists of two parts a numerator and a denominator. For example 1/4 is a fraction where numerator is 1 and denominator is 4.

The total number of packages = 8

Number of balloons in each package = 20.

The portion of balloons use to decorate hall = 1/4.

Suppose the remaining balloons are x.

Thus the expression for remaining balloons can be written as,

x = 20 × 8 - 1/4×(20 × 8)

x = 160 - 40

  = 120.

Hence, Sarah has left with 120 balloons and the expression for left balloons is x = 20 × 8 - 1/4×(20 × 8).

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Answer:

Step-by-step explanation:

Given

Without using a synthetic division, we can use easier method to find the quotient.

We know the formula:

Rewrite the given as:

This expression, when divided by (x - 1) leave the quotient (x² + x + 1) and a remainder of 2

The quotient of the equation is A = x³ + x + 1 + ( 2/x + 1 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the first equation be p = x³ + 1

Let the second equation be q = x - 1

A = p / q

On simplifying , we get

A = x³ + 1 / ( x - 1 )

On dividing , we get the quotient as

A = x² + ( x² + 1 ) / ( x - 1 )

A = x³ + x + 1 + ( 2/x + 1 )

Hence , the quotient is A = x³ + x + 1 + ( 2/x + 1 )

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Answer:

3

Step-by-step explanation:

ndnsjsjwnanaksodbsjcif

Answer:

5x=5x-20 or -20=5x-20

Step-by-step explanation: