Please help me solve!

Answer:

5 bags of popcorn

3 drinks

Step-by-step explanation:

Let's set up a system of equations!

Let p equal the number of bags of popcorn and d be the number of drinks.

We know Ruby bought 8 total, so we know [tex]p + d = 8[/tex]. We also know that she spent $42 total, so we can multiply their respective costs by the number to set up another equation: [tex]6p+4d=42[/tex]. We have our system of equations now!

Let's use substitution to solve this. From the first equation, subtracting p from both sides gives us that [tex]d=8-p[/tex]. We can plug this into our second equation to solve for p. Plugging in this for d gives us [tex]6p+4(8-p)=42[/tex]. Multiplying through and then combining like terms results in [tex]32+2p=42[/tex]. We then can subtract 32 from both sides and divide us by 2, which gives us that p = 5.

Now we solve for d! We can plug in the value of p into the equation [tex]p+d=8[/tex], to get that d = 3. To check our work, we can plug these values into the other equation, which gives us [tex]6*5 + 4*3 = 42[/tex]. This is true, so our values are correct!

Thank you! Feel free to contact me with any questions about my answer. I hope this helps!

The required competition mark is given as 60, as of the given condition.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
A competition mark is calculated by doubling the sum of the top and bottom four scores and then averaging them.
According to the question,
Competition mark = 2 [7 + 6 + 8 + 5] + [7 + 9] / 2
Competition mark = 52 + 8 = 60

Thus, the competition mark is  60.

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The exact value of the logarithmic expression 12 · ㏒₃ [z⁷ / (y⁵ · t²)] is equivalent by logarithm properties to -711 / 5.

In this question we must determine the exact value of a logarithmic expression by means of logarithm properties, which are described below:

Logarithm of a product

㏒ (a · b) = ㏒ a + ㏒ b

Logarithm of a division

㏒ (a / b) = ㏒ a - ㏒ b

Logarithm of a power

㏒ aⁿ = n · ㏒ a

Now we proceed to determine the exact value of the expression:

12 · ㏒₃ [z⁷ / (y⁵ · t²)]

12 · [㏒₃ z⁷ - ㏒₃ (y⁵ · t²)]

12 · (㏒₃ z⁷ - ㏒₃ y⁵ - ㏒₃ t²)

12 · (7 · ㏒₃ z - 5 · ㏒₃ y - 2 · ㏒₃ t)

12 · (7 · 7.74 - 5 · 11.03 - 2 · 5.44)

-711 / 5

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Triangles MNO and QPO are congruent.

It is given that

O is the midpoint of NP,

NP is perpendicular to MN, and

NP is perpendicular to PQ.

Therefore, Triangles MNO and QPO are congruent.

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The statistic said to be Unbiased Estimator If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated.

The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. Statistics are numerical representations of sample characteristics. One population parameter is the average income in the United States. On the other hand, a sample statistic is the average income for a sample taken from the United States. Although both figures correspond to the mean income, only one is a statistic.

Here,

The reported statistic is Independent Estimator If the mean of the sampling distribution for a statistic used to estimate a parameter matches the actual value of the parameter being estimated.

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The decibel level of the noise from a motorcycle with intensity 10⁻² watts per square inch (W/in²) is equal to 50 dB.

In Science, sound intensity can be defined as a measure of the power of a sound wave per unit area. This ultimately implies that, sound intensity is a quantity that is typically be used for measuring the energy of sound and its unit of measurement is Watts per square meter (W/m²) or .

Mathematically, sound intensity level or decibel level can be calculated by using this formula:

[tex]\beta = 10 log(\frac{I}{I_{ref}} )[/tex]

Note: The reference value of sound intensity is equal to 1.0 × 10⁻¹² watts per square inch (W/in²).

Since the intensity of the noise from this motorcycle is 10⁻² W/in², the decibel level (in dB) would be calculated as follows:

Decibel level, β = 10 × log(10⁻²/10⁻¹²)

Decibel level, β = 10 × log(10¹⁰)

Decibel level, β = 10 × 10

Decibel level, β = 100 dB.

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Answer:  d/ 30x +200 <= 1400

Step-by-step explanation:

It can't be the first two answers because the truck can only hold 1400

So it must be < or = 1400

It says that she loaded computers for 200 pounds and x number of books, 30 pounds each.

So the equation is 30x + 200 <=1400

The median would lie in the mean of the 15th and the 16th position.

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

The mean (average), mode, and standard deviation are some other descriptive statistics that are frequently contrasted with the median.

Given, the total number of basketball players present (n) = 30

Total number of attempts made = 6

Since there are even number of players present, 30, the location of the median would be n/2 and n/2 + 1 positions.

For 30, the positions would be

= 30/2 and 30/2 + 1

= 15 and 16th position

Hence, the median would lie in the mean of the 15th and the 16th position.

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The mass of the ball is 278.1 g, the material used to make the ball must be brass which having density of 8.6 g/cm³.

To determine the material used to make the ball, we need to first calculate the volume of the ball.

The volume of a sphere with radius r is given by:

V = (4/3) * π * r^3

Plugging in the given values, we get:

V = (4/3) * π * (2 cm)^3

= (4/3) * π * 8 cm^3

= (4/3) * 8π cm^3

= 32π cm^3

We can then use the density of each material (given in g/cm³) to calculate the mass of the ball if it were made of that material:

Copper: 8.3 g/cm³ * 32π cm³ = 266.4 g

Brass: 8.6 g/cm³ * 32π cm³ = 275.2 g

Iron: 7.8 g/cm³ * 32π cm³ = 250.4 g

Since the mass of the ball is 278.1 g, the material used to make the ball must be brass.

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The equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.

What is a linear equation in one variable?

The linear equation in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

For the first case:

If 2 movies are streamed, the cost is $14 per month

So the cost = number of movies * cost per movie

            y = 2*x

           14 = 2x

For the second case:

If 6 movies are streamed, the cost is $20 per month

So the cost = number of movies * cost per movie

            y = 6*x

           20 = 6x

Hence the equation to model the cost 'y' based on the number of movies streamed 'x' would be 14 = 2x and 20 = 6x.

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Answer: 10: 6 is

ration add them 16

Step-by-step explanation:

Using the elimination method, the solution to the system of equations is as follows:

x = 19 / 13  and y = - 74 / 13

System of equations can be solved using different methods such as the elimination method, substitution method, and graphical method.

Let's use the elimination method to solve the system of equations as follows:

The elimination method is the process of eliminating one of the variables in the system of equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Therefore,

4x - 7y = 10

3x + 2y = -7

multiply equation(ii) by 3.5

4x - 7y = 10

10.5x - 7y = 24.5

subtract equation(i) from equation(ii)

6.5x = 14.5

x = 14.5 / 6.5

x =  145 / 65

x = 19 / 13

Let's find y

3(19 / 13) + 2y = -7

57 / 13 + 2y = -7

2y = - 7 - 57 / 13

2y = -91 - 57  / 13

2y = - 148 / 13

cross multiply

26y = - 148

y = - 148 / 26

y = -  74 / 13

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Answer:

1 minute, Because per minute is $2, 12 cents

Answer:SLOPE

Step-by-step explanation:M in a equation is slope

7) The minimum temperature is 31⁰F. So, the answer is option B.

The frequency of various types of values can be easily observed using a stem and leaf plot, also known as a stem and leaf diagram. This graph displays numerical data that is arranged in chronological order. There is a stem and a leaf for each piece of data.

Each first or second digit of the data value is divided into a stem, and the last digit is represented by a leaf, in a stem and leaf plot, which is represented by a particular table. The stem and leaf plot key is the "|" symbol that is used to indicate the values of the stem and the leaf. In the case of 46, the stem is 4 and the leaf is 6.

7) The minimum value in the stem is 3

And the minimum value in the leaf is 1

So, according to the given key 4|3=43°F

Here | denotes the key symbol.

So, in this solution the minimum value of stem is 3 and the minimum value of leaf is 1

Therefore, it must be 3|1

Hence, from the given key

This can be written as 31⁰F

Therefore, the answer is option B.

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Answer:

11, 13, 17, and 19!

Step-by-step explanation:

Answer:

11, 13,17 and 19

Step-by-step explanation:

prome numbers are natural numbers that are greater than 1 and not a product of two natural numbers eg 2×5 =10 so it's not a prime number 2×6 or 3×4 =12 it's not also a prime number e.t.c

One of the six countries sent 41 representatives to the congress.

What, in the simplest words, is the Congress?

The Congress is our country's legislative body, which drafts our laws. The United States Senate and the United States House of Representatives are the two branches of Congress.

                    Each state has two U.S. Senators and a minimum of one U.S. Representative; the number of U.S. Representatives that can be elected depends on the number of citizens in the state.

(1) One of the six countries sent 41 representatives to the congress

(2) Country A sent fewer than 12 representatives to the congress

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Answer:

58 teams

Step-by-step explanation:

This is a division problem. There are a total of 1043 players and there is a max number of 18 members per team. 1043 divided by 18 = 57 and a remainder. Because there is a remainder you add one more team for the remaining members.

Answer: 57.9

Step-by-step explanation:

Based on the given conditions, formulate: 1043 / 18

Evaluate the equation/expression: 57.9444

get the result: 57.9444

After rounding: 57.9

Answer: 57.9

The intersection region of every solution in the system of inequalities is the system's solution. Inequality y≤x2 should be graphed first. y=x2 serves as the related equation.

Example

Graph the inequalities and solve the system:

y≤x−2y>−3x+5

Inequality yx2 should be graphed first. y=x2 serves as the related equation.

The border line is solid due to the inequality's, which is not a rigid one.

The inequality yx2 should be substituted in for a point that is not on the line, such as (0,0).

0≤0−20≤−2

It's untrue. The point (0,0) is therefore not part of the solution. Subtract from the line's lower half.

To do the same for the second inequality's related equation, y>3x+5, which has a rigorous inequality, draw a dashed line. The half that does not contain the point (0,0) should be shaded because it does not satisfy the inequality at that location.

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Answer:

68 feet tall

Step-by-step explanation:

Imagine the shadows for both the tree and the person are set up like right triangles. The length of their shadows are the bases of the triangles, while the actual heights of the tree and person are the heights of the triangle. We can set up proportions since  "height of the person" divided by " their shadow's length" should equal "height of tree" divided by "tree shadow length".

Set up a proportion of the person's high height relative to their shadow's length (which is 6/4.5). Set this equation equal to the tree's proportion (which is x/51).

Solve for x.

[tex]\frac{6}{4.5} = \frac{x}{51}\\Isolate x by multiply 51 to both sides\\\\(306/4.5)=x\\68=x[/tex]

The proportion is solved and the height of the tree is A = 68 feet

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the proportion be represented as A

Now , the value of A is

Now , we can set up the following proportion:

Height of tree / length of tree's shadow = height of person / length of person's shadow

On simplifying , we get

A / 51 = 6 / 4.5

Now we can solve for A by cross-multiplying and simplifying:

A = 51 x 6 / 4.5

A = 68 feet

Therefore, the tree is 68 feet tall

Hence , the proportion is solved

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Answer: 30 meters

Step-by-step explanation:

A boy is standing on an elevator which is traveling downward with a constant velocity of 30 meters per second.

The value of the shortest of the three sides of the triangle is 13 cm.

A triangle is a polygon with threes sides. The perimeter of a triangle is the sum of the whole three sides.

The lengths of the three sides of a triangle (in centimetres) are consecutive odd integers. The perimeter is 45 cm.

The shortest side of the three sides can be calculated as follows:

let

the first side = x

second side = x + 2

third side = x + 4

Hence,

perimeter = x + x + 2 + x + 4

45 = 3x + 6

45 - 6 = 3x

3x = 39

divide both sides by 3

x = 39 / 3

x = 13

Therefore,

shortest side = 13 cm

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There is a 7°F difference in temperature between the morning and the afternoon.

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Answer: y = 1/12x

Step-by-step explanation:

(24, 2)

(12, 1)

find slope (y2 - y1) / (x2 - x1)

2 - 1 / 24 - 12

1 / 12

find y intercept

y = mx + b

1 = 1/12(12) + b

1 = 1 + b

b = 0

y = 1/12x + 0

y = 1/12x

The range of the function will be;

⇒ Range = (91, 16, - 5)

The set of all inputs of the function is called Domain of set.

Given that;

The function is,

⇒ f (x) = x² - 6x

And, The domain = (- 7, - 2, 1)

Now,

Since, The function is,

⇒ f (x) = x² - 6x

We know that;

The range of the function gives the value of y.

Here, The domain (x) = (- 7, - 2, 1)

Put x = - 7;

⇒ f (-7 ) = (-7)² - 6 × - 7

            = 49 + 42

            = 91

Put x = - 2;

⇒ f (- 2) = (-2)² - 6 × - 2

            = 4 + 12

            = 16

Put x = 1;

⇒ f (1) = (1)² - 6 × 1

         = 1 - 6

         = - 5

Thus, The range = (91, 16, - 5)

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a%2Bb=12 [1]

.75a%2B1.05b=10.20 [2]

Use elimination: multiply the first equation by .75 and then compare the two equations (i.e., subtract one equation from the other):

.75a%2B.75b=9

.75a%2B1.05b=10.2

.3b=1.2

3b=12

b=4

ANSWER: He bought 4 pounds of bananas, which means 8 pounds of apples.

CHECK: 8($.75)+4($1.05) = $6+$4.20 = $10.20