2(x+ 5) = 3x +1 solve

The number of nickels is 173.

The number of dimes is 258.

The number of quarters is 69.

The coins are worth $51.7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

For every 2 nickles, there are 3 dimes.

For every 2 dimes, there are 5 quarters.

This means,

Let,

Nickles = N

Dimes = D

Quarters = Q

2N = 3D

N = 3D/2

2D = 5Q

Q = 2D/5

Now,

N + D + Q = 500

3D/2 + D + 2D/5 = 500

15D + 10D + 4D = 500 x 10

29D = 5000

D = 5000/29

D = 173

Now,

N = 3 x 172 / 2

N = 3 x 86

N = 258

Q = 2 x 172 / 5

Q = 69

Now,

Total coins = 500

173 + 258 + 69 = 500

Now,

20 nickels = $1

10 dimes = $1

4 quarters = $1

So,

173 nickels = $1 x 173 / 20 = $8.65

258 dimes = $1 x 258 / 10 = $25.8

69 quarters = $1 x 69 / 4 = $17.25

The total worth.

= $8.65 + $25.8 + $17.25

= $51.7

Thus,

The number of nickels is 173.

The number of dimes is 258.

The number of quarters is 69.

The coins are worth $51.7.

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A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

We have that to find our  level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.96}{2} =0.02[/tex]

Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex] .

So it is z with a p value of 1-0.02 = 0.98, so z= 2.055

Now, find the margin M as such

[tex]M = Z*\frac{\sigma }{\sqrt{n} }[/tex]

In which [tex]\sigma[/tex]  is the standard deviation of the population and n is the size of the sample.

In this problem, we have that:

[tex]\sigma = 40 , M = 10\\\\M = Z*\frac{\sigma}{\sqrt{n} } \\\\10 = 2.055*\frac{40}{\sqrt{n} } \\\\\sqrt{n} = 8.22\\\\n= 67.6[/tex]

Hence , a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.

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On solving the provided graph question, we got to know that - the area below the line will be taken into account.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph.

Given : equation  2x + 3y ≤ 6

Out of the options provided, we must select the graph that displays the graph of the solution set for the equation 2x + 3y 6.

Consider the given equation   2x + 3y ≤ 6

We first find the points where the equation cut x- axis and y-axis.

Thus,

[tex]For x - axis put y = 0 ,\\We get 2x + 3(0) \leq 6 =2x \leq 6 x \leq 3\\Thus, point (3,0)\\For y - axis put x = 0 ,\\We get 2(0) + 3y \leq 6 = 3y \leq 6 = y \leq 2\\Thus, point (0,2)[/tex]

For each region, we select a test point, determine the values of x and y there, and then determine whether or not the inequality is satisfied.

Take into account the point (0, 0), and inequality becomes,

[tex]2(0) + 3(0) \leq 6 = 0 \leq 6 (true)\\[/tex]

So, the area below the line will be taken into account.

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The expression is vertically stretched by a factor of 7 then the equation for g(x) will be 7x².

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

f(x) = x²

It is stretched vertically by a factor of 7.

So, k = 7

The equation for vertical expansion is,

y = k(f(x))

Then, the equation will be,

g(x) = 7x²

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D. At the end of 20 years, the policy's cash value will equal $100,000 is INCORRECT regarding a $100,000 20-year level term policy.

A $100,000 20-year level term policy is a type of life insurance policy that provides a fixed amount of coverage for a set period of time. The premiums for this policy will remain level for the entire 20 years and, if the insured dies during that time, the beneficiary will receive the full $100,000. However, the policy will expire at the end of the 20-year period and the cash value will not equal the $100,000. As a result, it is untrue to say that $100,000 will be the policy's cash value after 20 years.

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It means 3 km in 1 minutes.

I think this is a speed of an object which shows that it can run or walk 3km in 1 minutes.

hope you understand.

Answer: x= -1

Step-by-step explanation:

5(x+2)= 3(x+3)-1

5x + 10 = 3x + 9 -1

5x + 10 = 3x + 8

2x = -2

x= -1

Using HCF to determine the integer with smallest number of factors, the value is 24

HCF stands for Highest Common Factor. It is the largest positive integer that divides two or more given numbers without leaving a remainder.

In this problem, we are asked to find number that will have the same number of factors as 2022, we can start by listing all factors of 2022.

The HCF of 2022 are

2022 : 1, 2, 3, 6, 337, 674, 1011, 2022

The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24

24 has 8 factors, which is the same number of factors as 2022. 24 is the smallest positive integer with 8 factors.

From the explanation above, the smallest integer with same number of factors as 2022 is 24.

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The compass needle always points north because it is magnetic north pole.

Earth has magnetic field due to magnetic elements present in Earth's core in molten form. They are assumed to be in the form of giant bar to ease the calculations concerning magnetic field and polarity. The assumptions are geographic south pole harbours magnetic north pole and vice versa for the opposite pole.

So, we know that like poles attract each other and unlike poles repel each other. The north end of magnetic needle will point towards the magnetic south pole which is geographic north pole. Thus, we see compass needle directed to North pole.

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A linear relationship is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.

What does the term "linear relationship " mean?

A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association).

                         Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.

Why are relationships linear and nonlinear?

Plotting a linear relationship on a graph results in a straight line, whereas plotting a nonlinear relationship results in a curve.

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The results of the evaluation of the given expression; (2t+3g) divided by 4 as required is; 7.

It follows from the task content that the result of the evaluation of the given expression is to be determined according to the information provided.

Therefore, since the expression to be evaluated is; ( 2t + 3g ) / 4.

Where; g = 2, r = 3 and t = 11.

Therefore, we have;

( 2(11) + 3(2) ) / 4

= ( 22 + 6 ) / 4

= 28 / 4

= 7.

Therefore, the result of the expression evaluation is; 7.

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Classification model

What is Classification model?

A subset of supervised machine learning is classification models. A categorization model takes in some input and produces an output that categorises the input. For instance, after reading an email, a model may binary identify it as spam or not.

This is a classification model. This is a categorization model because we are categorising people here according to their age and location.

A categorization model takes in some input and produces an output that categorises the input.

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Answer:

The second one

Step-by-step explanation:

The first graphic would be correct if the connector was "AND" instead of "OR"

"AND" --> Both conditions must ALWAYS be fulfilled

"OR" ---> It's only necessary that one of the conditions is fulfilled

The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.

The ratio of the actual worth to the total value multiplied by 100 is the formula for calculating the percentage.

The percentage formula is given by

Here we have

A family buys a studio apartment for $ 150,000

The down payment paid by the family is $ 22500

a. Percentage of down payment in the purchase

From the above data,

The percentage of the down payment = [tex][ \frac{22500 }{150,000} \times 100 ][/tex]  

= [tex][ \frac{22500 }{1500} ][/tex] =  15

Therefore,

The percentage of the down payment is 15%  

b. The percentage of the purchase price would be a $67500 down payment?    

Let x  be the percentage of the down payment in the purchase amount  

=>  [tex]\frac{x}{100} \times $ 150,000 = 67500[/tex]  

=>  [tex]x \times 1500 = 67500[/tex]

=>  x = 67500/1500

=>  x = 45%

Therefore,

The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.

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They both make 3 baskets. The number of points Norma and vincent have after first time out are 6 points and 9 points respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time.

If the number of basket is x, and the total point is y, thus

for Norma, the total point = 19+2x=y equation 1

for vincent, the total point = 16+3x= y equation 2

subtract equation 1 from 2

16-19+3x-2x = 0

-3+x = 0

x= 3

substitute 3 for x in equation 1

19+2(3)= y

25= y

y = 25

therefore they both made 3 basket after the first time out and Norma make extra 6 points and Vincent made extra 9 points

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A student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.

What is percentile rank?

A percentile rank describes a student's performance in relation to other students in the same grade and subject who made up the specific norm group. The percentile rank of a student indicates whether their score was equal to or higher than the percentage of students in the norm group.

The percentage of scores in a frequency distribution that are lower than a given score is known as the percentile rank of that score in statistics.

A percentile rank of 75 indicates that the student outperformed 75% of the other students in his or her norm group, and 25% of the students outperformed your student.

Hence, a student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.

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All veterinarians that responded to the questionnaire were included in the sample.

Complete Question : Veterinarians often use non-steroidal anti-inflammatory drugs to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statement is correct?

a. The sample consisted of all veterinarians on the list and therefore equaled the target population.

b. The sample consisted of all veterinarians who returned the questionnaire.

c. The sample consisted of all veterinarians who treat horses with NSAIDs.

d. None of the choices are correct.

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-x2+3x-3=0 is the equation that  has the sum of its roots as 3.

A quadratic equation's roots are equal to the second term's coefficient negated, divided by the leading coefficient. The constant term (the third term), divided by the leading coefficient, is equivalent to the product of the roots of a quadratic equation.

Sum of roots= -b/a

Sum of root is defined as:

Sum of root = -b/a

Consider option B -x^2+3x-3

a=-1 , b=3

Sum of root= - 3/(-1)=3

So B is the correct option of the following question.

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Answer:

Step-by-step explanation:

2,637

Answer:

B

Step-by-step explanation:

Based on the provided table and equation when the class size is 1, gymnastics is less expensive, and when the class size is 3 or 4, ice skating is less expensive.

Given that y denotes the price and x denotes the number of classes, the gymnastics programmed is completed by the table, whereas the ice skating program is concluded by the equation y = 18x + 20.

Find the cost of the ice skating programmed for classes 1, 2, 3, and 4 as the table already lists the price for each specified number of gymnastics courses.

For 1 class, substitute x = 1 into y = 18x + 20:

y = 18(1) + 20

y = $38

For 2 class, substitute x = 2 into y = 18x + 20:

y = 18(2) + 20

y = $56

For 3 class, substitute x = 3 into y = 18x + 20:

y = 18(3) + 20

y = $74

For 4 class, substitute x = 4 into the equation y = 18x + 20:

y = 18(4) + 20

y = $92

We may infer from the foregoing that gymnastics is less expensive when the number of lessons is 1. When there are three or four courses, ice skating is less expensive.

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There are 144 ways to place 4 pairs of shoes per shelf in the store.

What is a permutation?

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged. Put simply, a permutation is a word that describes the number of ways things can be ordered or arranged. With permutations, the order of the arrangement matters.

This question can be solved using basic logic . One can also solve this by using permutations.
Since 12 different models arrive and 4 pairs of shoes should be placed per shelf , the answer can be sort by

4!×3! = [ 4×3×2×1] × [3×2×1] = 24×6 = 144.

( Because 4 pairs of shoes can be interchanged among themselves , therefore 4! , and 12/4=3 , so the 12 pair of shoes can be organised amongst 3 shelves , and hence 3!)
Therefore , none of the options is correct. The correct answer is 144 ways.
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Answer:

there should be 1 customer waiting in line at the ticket outlet.

Step-by-step explanation:

To calculate the expected number of customers in the queue, we can use the following formula:

Expected number of customers = Arrival rate * Average waiting time

In this case, the arrival rate is 10 customers per hour and the average waiting time is 6 minutes. Converting the waiting time to hours, we get:

Expected number of customers = 10 customers/hour * (6 minutes / 60 minutes/hour) = 1 customer

So the expected number of customers in the queue is 1. This means that on average, there should be 1 customer waiting in line at the ticket outlet.

The function represented in graph is f(x) = 4cos(x) - 1. We can find it by putting given points in following options and checking whether it is matching to graph or not  (hit and trial method)

What are trigonometric functions?

6 trigonometric functions are Sine, Cosine, Tangent, Cotangent, Secant, Cosecant .

Cosine ranges from (-1 to 1) for x.

Given points are 0, pi, and 2pi

For 0 , cos(0)= 1

For pi, cos(pi) = -1

For 2pi, cos(2pi) = 1

In f(x) = 4cos(x)-1

For x = 0,

f(0)=4cos(0)-1

3 = 3 i.e. correct.

For x = pi

f(pi) = 4cos(pi)-1

-5 = -5 i.e.  correct

also correct for 2pi.

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The required value of the given inverse function f⁻¹(22) will be 7.

The inverse function is defined as a function obtained by reversing the given function.

Given that f(7) = 22

To determine the value of the given inverse function f⁻¹(22)

An inverse function's main objective is to show the value that occurs in a specific function value. Which means :

If we have f(x) and f⁻¹(x), then

if f(a) = b then f⁻¹(b) = a

As per the given question, we have

⇒ f(7) = 22 then f⁻¹(22) = 7

Therefore, the required value of the given inverse function f⁻¹(22) will be 7.

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The value of x in the first question is 11 and the value of y is 3.

The value of x in the second question is 4 and the value of y is 4.

The value of x in the third question is -5 23/26 and the value of y is -1/13

2x + y = 25 equation 1

2x - 3y = 13 equation 2

The first step is to subtract equation 2 from equation 1:

-4y = -12

Divide both sides of the equation by -4

y = -12 / -4

y = 3

Substitute for y in equation 1:

2x + 3 = 25

2x = 25 - 3

2x = 22

x = 22 / 2

x = 11

-3x + 4y = -18 equation 1

x = -2y - 4

x + 2y = -4 equation 2

Multiply equation 2 by 2

2x + 4y = -8 equation 3

Subtract equation 3 from equation 2:

-5x = -20

Divide both sides of the equation by -5

x = -20 / -5

x = 4

Substitute for x in equation 2:

4 + 2y = -4

4 + 4 = 2y

8 = 2y

y = 8/2

y = 4

-2x + 3y = -15 equation 1

3x + 2y = -23 equation 2

Multiply equation 1 by 3 and equation 2 by 2

-6x + 9y = -45 equation 3

6x + 4y = -46 equation 4

Add equation 3 and equation4 together

13y = -1

y = -1/13

Substitute for y in equation 1:

-2x + 3(-1/13) = -15

-2x  -3/13 = -15

-2x = -15 + 3/13

-2x = 11 10/13

x = 11 10/13 ÷ -2

x = 153/13 x -1/2

x = -153/26

x =-5 23/26

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Answer:

Step-by-step explanation:

4/14

Divided both by 2

2/7

Answer:

48/7

Step-by-step explanation:

8/7/6

= 8 × 1/7/6

= 8× 6/7

48/7

A.

3 × 5 - (5 - 12)

= (3 × 5) - (5 - 12)

= 15 - (5 - 12)

= 15 - (-7)

= 15 + 7

= 22

B.

5 - (3 - 5 × 6)

= 5 - (3 - (5 × 6))

= 5 - (3 - 30)

= 5 - (-27)

= 5 + 27

= 32

C.

4 × (2 - 3 × 9) + 7

= 4 × (2 - (3 × 9)) + 7

= 4 × (2 - 27) + 7

= 4 × (-25) + 7

= -100 + 7

= -93

D.

9 × (-2 - 4 × 5) - 3

= 9 × (-2 - (4 × 5)) - 3

= 9 × (-2 - 20) - 3

= 9 × (-22) - 3

= -198 - 3

= -201

E.

63 ÷ (2 - 3 × 7 + 5 × 2) - 11

= 63 ÷ (2 - (3 × 7) + (5 × 2)) - 11

= 63 ÷ (2 - 21 + 10) - 11

= 63 ÷ (-9) - 11

= (63 ÷ (-9)) - 11

= -7 - 11

= -18

F.

48 ÷ (2 - 12 ÷ 4 - 7) - 4

= 48 ÷ (2 - (12 ÷ 4) - 7) - 4

= 48 ÷ (2 - 3 - 7) - 4

= 48 ÷ (-8) - 4

= (48 ÷ (-8)) - 4

= -6 - 4

= -10

Answer:

Step-by-step explanation:

23

Answer:

Step-by-step explanation:

2^x + 7 = 3

2^x = -4          this cannot be solved

Maybe you meant

2^(x+7) = 3    

LOG both sides to get

 (x+7)  LOG 2 =  LOG 3

x+7 = log3/log2      subtract 7 from both sides to get

x = - 5.415