Today, I want you to challenge yourself. Don't let word problems intimidate you. In this task you are not solving but rather setting up equations. I know you have the
ability to do this. Here we go!
19
A store sells two brands of headphones: high definition (HD) and basic. It buys x HD headphones at z dollars each, and y basic headphones at w dollars each.
In a-c, write an equation whose solution is the given quantity. Solve Each Equation and set them up.
a) The number of basic headphones the store can purchase if it spends a total of $10,000 on headphones and buys 110 HD headphones for $70 each.
b)
The price the store pays for HD headphones if it spends a total of $2,000 on headphones and buys 55 basic headphones for $20 each.
c) The price the store pays for HD headphones if it spends a total of $800 on headphones and buys eight basic headphones for $80 each.
d) Please give me the actual cost of the headphones and an explanation with a-c

Answer:

The new mean is 3.6

Step-by-step explanation:

Since each piece of data is now doubled that means the data is now

4.8, 3.2, 6.4, 0.6, 3

Add up all of the data which comes out to 18

Divide 18 by the number of numbers there are which is 5

This will get you 3.6 which is the new mean of the data

The number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.

Given that, Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here, [tex]1\frac{1}{2} = \frac{3}{2}[/tex] and [tex]7\frac{1}{2} = \frac{15}{2}[/tex]

The number of batches of muffins can she bake

= 15/2 ÷ 3/2

= 15/2 × 2/3

= 5 batches

Hence, the number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.

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Answer: The answer is 5

Step-by-step explanation: I have my ways ;>

The slope of the line parallel to the line that has an equation of 2x + 4y = 56  is -2

The line equation is given as

2x + 4y = 56

Subtract 2x from both sides

This gives

4y = -2x - 56

Divide through the equation by 4

So, we have

y = -0.5x - 14

A linear equation is represented as

y = mx + c

Where m represents the slope

This means that

m = -0.5

Parallel lines have the same slope

This means that the slope of the line parallel to the line is -0.5

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Answer:

6cm square

Step-by-step explanation:

Answer:

  2/5 = 0.4 = 40%

Step-by-step explanation:

You want the relative frequency of students who go to Cook Middle School and prefer Energy Flow.

The table tells us the number of students who go to Cook Middle School is 35, of which 20 prefer Energy Flow. The total number of students is 50.

The relative frequency of interest is ...

  (Cook & Energy Flow) / (All students)

  = 20/50 = 2/5 = 0.4 = 40%

The relative frequency of students who go to Cook and prefer Energy Flow is 2/5, or 40%.

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The height of the building after using proportion is  110.5 ft.

What is proportion ?

The main conceptual underpinnings on which proportion is described are ratio and fractions. When two ratios are written as a fraction using the formula a/b, ratio a:b, and then a proportion, they are equal. A and b in this situation can be any two integers. For grasping the myriad concepts in science and mathematics, the ratio and proportion are crucial constructing elements. With the right amount of proportion, a variety of problems in daily life, such as those encountered in the kitchen or in business when processing transactions, can be resolved. It facilitates comparison by establishing a relationship between two or more quantities.

Here House height = 13ft

Shadow of the house height = 20 ft

Shadow of the building height = 170ft

Noe using proportion ,

=> [tex]\frac{House height}{shadow of the house} = \frac{building height}{shadow of the building}[/tex]

=> [tex]\frac{13}{20} = \frac{x}{170}[/tex]

=> x=[tex]\frac{13*170}{20}[/tex] =110.5 ft.

Hence the height of the building is 110.5 ft tall.

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The sentence which represents the equation [tex]8\frac{3}{4} = 17-x[/tex] is  First Option (i.e.  [tex]8\frac{3}{4}[/tex] is the same as the 17 decreased by a number).

What is a number sentence?

A mathematical statement made up of numbers and symbols is called a number sentence. The sentences illustrate many mathematical operations, including addition, subtraction, multiplication, and division.

Given, [tex]8\frac{3}{4} = 17-x[/tex]

where, [tex]x[/tex] is a number and ([tex]17-x[/tex]) represents [tex]17[/tex] is decreased by a number [tex]x[/tex]

And, [tex]8\frac{3}{4}[/tex]  will be equal to the [tex]17[/tex] is decreased by a number [tex]x[/tex].

Therefore, the required answer choice will be the first option i.e. [tex]8\frac{3}{4}[/tex] is the same as [tex]17[/tex] decreased by a number.

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Answer:

x = 3.5units

Step-by-step explanation:

Congruent means the same length, so set the given lengths equal to each other.

8x - 17 = -2x + 18

Add 2x to both sides.

10x -17 = 18

Add 17 to both sides.

10x = 35

Divide by 10

x = 3.5

When x is 3.5, KL and ST are the same length. Check.

8(3.5) - 17 = 11

and

-2(3.5) + 18 = 11

Answer:

4x

Step-by-step explanation:

the quotient of x and 2 is [tex]\frac{x}{2}[/tex] , then

8 × [tex]\frac{x}{2}[/tex] ( cancel 8 and 2 by 2 )

= 4 × x

= 4x

The inequality for this graph is:

x<2

Answer:

34 inches

Step-by-step explanation:

[tex]c = \sqrt{ {16}^{2} + {30}^{2} } [/tex]

[tex]c = \sqrt{256 + 900} [/tex]

[tex]c = \sqrt{1156} = 34[/tex]

Answer:

34 inches...................

Answer:

the answer is 1.4N/kg

A graph of the given system of linear equations is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is commonly used to graphically represent data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would rewrite the first equation in standard form as follows:

y - 2x = 0

Adding 2x to both sides of the equation, we have the following:

y - 2x + 2x = 0 + 2x

y = 0 + 2x

y = 2x

By critically observing the graph (see attachment), a solution to the given system of linear equations are 2.5 and 5.

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Sathish will pay $64.8

When Satish is alone, kilometres:

Beginning at 150 kilometres and ending at 150 kilometres will be travelled 300 kilometres in total

When Satish is with friends, the total kilometres travelled is 2100 km:

And when Satish went alone he travelled 300 km

When Satish is with friends, total kilometres travelled: 2100-300 = 1800 km

Gas consumed in litres when Satish is alone: 100 kilometres use 6 litres of gas.

300 kilometres at 6 x 3 equals 18 litres.

So, when Satish is with friends, litres of gas are consumed: 100 kilometres use 6 litres of gas.

So, 6 × 18 for 1800 kilometres is equal to 108 litres.

Gas prices when Satish is on his own:

$1.2 per litre

18 x $1.2 = $21.6

Gas prices when Satish is travelling with friends

$1.2 per litre

108 x 1.2 = $129.6

Cost for each friend = $129.6/3 = $43.2

Satish will pay: Cost when travelling with friends + Cost when travelling alone

=$43.2+ $21.6

=$64.8

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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.

The final expression of (-2/9)x² - (1/9)x² is (-1/3)x².

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,

(-2/9)x² - (1/9)x²

Taking out the common.

(-1/9) (2x² + x²)

Adding the like terms.

(-1/9)3x²

-1/9 x (3x²)

(-1/3)x²

Thus,

The final expression of (-2/9)x² - (1/9)x² is (-1/3)x².

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The number of students that went on the field trip is 137.

Let s represent the number of seventh grade students that went on the field trip.

Total number of participants = number of students + number of teachers

a + 19

Number of participants that rode the larger bus : 2/3 x (a + 19) = 104

In order to determine the value of a, take the following steps:

Multiply both sides of the fraction by 3 / 2

a + 19 = 104 x 3 / 2

a + 19 = 156

Subtract 19 from both sides of the equation:

a = 156 - 19

a = 137

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The value of the experimental probability of rolling a 6 is found as 1/5.

For the given question-

Thus, by the definition of the probability-

Probability (getting 6) = number of occurred outcomes/ Total outcomes

Probability (getting 6) = 18/90

Probability (getting 6) = 1/5

Thus, the value of the experimental probability of rolling a 6 is found as 1/5.

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Answer:

The sides of the triangle would be 14, 16, and 18.

Step-by-step explanation:

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May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The equation in the given question is answered in main body.

What is equation?

In arithmetic , an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

according to question :

A) equation for Saturday sale = 84c +157d = 2640

equation for Sunday sale = 67c +134d = 2211

when subtracted we will get, 17c +23d = 429

This equation shows the difference in sales of these 2 days in terms of ticket sold and collection.

B) According to second part solution are c= 9 , d= 12.

equation given : 17c+23d = 429

now substituting value of c and d.

⇒17(9) + 23(12)

⇒153+276

⇒429 = R.H.S

Hence equation satisfies.

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1) The speed of a horsefly in feet per second is; 0.63 beats per minute

2) The number of times that the dragonfly's wing beats per minute is; 3 ft/s

3) The number of times that a bumble bee travels in one minute is; 0.11 miles per minute

Dimensional analysis is defined as the study of the relationship that exists between physical quantities with the help of dimensions and units of measurement.

Dimensional Analysis is also defined as a method of problem solving that takes into consideration the identity property of multiplication whereby the product of a number and 1 will always give the same number, that is 1 × n = n whereby the value "n" remains the same after the multiplication.

1) We are given from the table that the speed of a horsefly in miles per hour = 4.4 miles per hour. We want to know the speed expressed in feet per second.

From conversions, we know that;

1 mile per hour = 1/1.467 ft/s

Thus; 4.4 miles per hour = 4.4 * 1/1.467 = 3 ft/s

2) We are given from the table that the dragonfly's wing beat per second = 38 beats per second. We want to know the dragonfly's in wing beat per minute

From conversions, we know that;

1 beat per second = 1/60 beat per minute

Thus; 38 beats per second = 38 * 1/60 = 0.63 beats per minute

3) We are given from the table that the speed of a bumble bee in miles per hour = 6.4 miles per hour. We want to know the speed expressed in miles per minute

From conversions, we know that;

1 mile per hour = 1/60 miles per minute

Thus;

6.4 miles per hour = 6.4 * 1/60 = 0.11 miles per minute

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The time it takes for a rocket following the path h(x)= -4x² + 16x to hit the ground is 4 seconds.

How to find the time for a rocket to hit the ground?

The given path equation is a function of x which is a time variable here. When the rocket hits ground, height of the rocket gets zero.

Hence equating the equation of height to zero and solving for x will give the time required for the rocket to hit the ground.

According to the given question:

We are given equation for height as

h(x) = -4x² + 16x

where x is the time in seconds

When object hits the ground the height becomes 0

So, we can set h(x) = 0 and then we can solve for x

-4x² + 16x = 0

Dividing by -4x from both sides

x - 4 = 0

x = 4 sec

So, the time it takes for a rocket  to hit the ground is 4 seconds.

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Out of the next 5 visitors, 2 will be asked to attempt the survey. (A) yes, because 2 out of 5 is equal to 40%.

It is given the probability that the randomly selected person is asked to participate in an online survey is 0.4

This means that there is a 40% chance of a visitor being asked to join the survey.

Probability of an event = no. of favorable outcomes / total no of outcomes

P(E) = n(E) / n

Therefore, if the number of visitors to the website is 5,

n = 5

P(E) = 0.4

Hence,

n(E) / 5 = 0.4

or, n(E) = 0.4  X  5

or, n(E) = 2

Therefore, out of the next 5 visitors, 2 will be asked to participate in the survey.

Correct Question

The probability that a randomly selected visitor to a certain website will be asked to participate in an online survey is 0.40. Avery claims that for the next 5 visitors to the site, 2 will be asked to participate in the survey. is Avery interpreting the probability correctly?

(A) yes, because 2 out of 5 is equal to 40%.

(B) yes, because participants in the survey are selected at random.

(C) no, because there could be voluntary response bias.

(D) no, because only 40% of all people will visit the site.

(E) no, because 0.40 represents probability in the long run over many visits to the site.

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This type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.

We are asked that, what would happen if you did not take absolute values before calculating the sum of differences between group means.

As, when we calculate the differences between group means then, some of the values may be negative.

When we add those negative values while evaluating the sum then the sum can be less than the absolute and to get over from this type of problem we always take absolute values of the differences between group means and then get the sum.

Also, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.

Hence, this type of calculation will not give the accurate values and hence, it is not useful to do calculation without taking absolute values.

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An ordered pair that is not marked on the coordinate plane of this graph is (8, 0).

In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which represent the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

An ordered pair can be defined as a pair of two (2) data points that are commonly written in a fixed order within parentheses as (x, y), in order to represent the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.

By critically observing the given graph, we can reasonably and logically deduce that data point (8, 0) is the missing ordered pair on the coordinate plane.

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Answer: 0.0099

Step-by-step explanation:

The equation of the straight line, in point-slope form, is  

          [tex]y +3 = \frac{1}{4} ( x + 4)[/tex]

we have , the required line is perpendicular to the given line.

Also let us take any two coordinates of the given line , like  (-1 , 1 ) and  

( 0 , -3) . So the slope (m₁) of given line = [tex]\frac{y2 -y1}{x2 - x1 }[/tex]

                                      m₁ = -4

as the required line is perpendicular to the given line so , we know

for two perpendicular lines

                                   m₁  m₂ =  -1

therefore ,                 m₂ = 1/4

Now the required line passes through (-4,-3)

and the equation of straight line in point slope form is given by

                                               [tex](y_{} - y_{1}) = m (x - x_{1} )[/tex]

here m = 1/4

y₁ = -3

x₁  = -4

therefore the required equation  in point-slope form is

         y + 3 = 1/4 ( x +4 )

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D

Step-by-step explanation:

The domain is the X-values in your function

as you can see, the X values continue to increase as the lines continue, infinitely

not sure how much she bought, but all you’d have to do is multiply the cost of salmon fillets ($8.30) times the amount she bought.

Example: if Mrs. Patrolia bought 3 pounds it would be $8.30 x 3.

Answer:

Step-by-step explanation:

5) f(1)= 2x^3-3x^2-2x+a=-4

     2^3- 3^2-2+a= -4

      a=-1

6)b= 42