A coffee shop has a group of seats at the counter and t individual tables, where each
table has the same number of seats. If 2t + 8 represents the total number of seats in the
restaurant, what does 8 represent?
a)the number of seats at each table
b) the number of seats at the counter
c) the total number of customers in the coffee shop
d) the total number of tables in the coffee shop

Answer:

5x² + 2x = 14y

Step-by-step explanation:

2x - 5y + 6y + 5x² = 15y

the only terms we can combine are 5y and 6y; the others are not 'like'

2x + y + 5x² = 15y

5x² + 2x = 14y

Answer:

X Y

-1 8

0 3

1 -2

2 -7

Step-by-step explanation:

Using the x values of the table, simply plug in those x values, replacing the x in the equation. For example:

y = -5x + 3

y = -5 * 2 + 3

y = -10 + 3

y = -7

Answer: 476.7 feet

Step-by-step explanation:

65 miles = 343200 feet

1 hour = 3600 seconds

(343200/3600) = 476.7 feet in 5 seconds

At the bicycle manufacturer, the average cost per bicycle is $77.

To find the average cost per bicycle, we need to find the total cost of making all three bicycles and divide that by the number of bicycles.

The total cost is of the bicycles is given by -

$72 (cost of first bicycle) + $83 (cost of second bicycle) + $77 (cost of third bicycle) = $232

Now to find the average cost per bicycle, we will divide the total cost by the number of bicycles.

Hence, $232 ÷ 3 = $77

Therefore, the average cost per bicycle is $77.

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The equation that is set up correctly using the Pythagorean Theorem for the triangle below is 9^2 + x^2 = 15^2.

The concept that will be used here is Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides:

According to theorem, the (adjacent)^2 + (opposite)^2 = (hypothenus)^2.

a^2+b^2=c^2

The 9^2 + x^2 = 15^2

Therefore, option C is correct.

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The interest rate on Malik's saving account is 4.62%. This was calculated by finding the total amount after 4 years, subtracting the original deposit, and then dividing the interest earned by the original deposit and multiplying by 100.

1. Calculate the total amount in the account after 4 years: 1050 + 241.50 = 1291.50

2. Calculate the interest earned: 1291.50 - 1050 = 241.50

3. Calculate the interest rate: 241.50 / 1050 x 100 = 4.62%

The interest rate on Malik's saving account is 4.62%. This was calculated by finding the total amount after 4 years, subtracting the original deposit, and then dividing the interest earned by the original deposit and multiplying by 100.

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Answer:

-5

Step-by-step explanation:

Our given equation is B-A, and we know that B = 2 and A = 7. Through what we know, we can plug in the variables' values and solve:

2 - 7 (from B-A)

= -5

Answer:

value for b-a is -5

if subsituition is only done b-a = 2-7

Step-by-step explanation:

if b=2

a=7,

b-a= 2-7

=-5

The equation of the line which passes through the point (0,-4) and has a gradient of 0. 5 is (x-8)/2.

A straight line can be represented by the "Point-Slope" form of the line.

In point-slope form, we can deduce an equation of any line on the Cartesian coordinate system with the help of its slope/gradient "m" and a point through which it passes (x1,y1).

the equation of Point Slope form is,

(y-y1)=m(x-x1),

where, x and y are any general point on the line.

in the given question the value of the slope/gradient (m) is given as 0.5

and it passes across the point (0,-4)

so according to the equation of the point-slope form,

the equation of line must be,

(y-(-4))=0.5(x-(0))

= y+4=0.5x

= 2y+8=x

= 2y = x-8

= y = (x-8)/2

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We see the same three numbers in situations 10,34 and 144.

In the first situation, there is one shopping cart with a length of 34 and then an unknown number of carts with a length of 10. Similarly, an architect has 34 dollars saved and will save 10 each week for an unknown number of weeks. Both situations have one part of 34 and then equal parts of size 10 that add together to 144. The equation is: 34 + 10x = 144.

Since it takes 11 groups of 10 to get from 34 to 144, the value of x in these two equations is ( 144 -34) ÷ 10 = 11.

There will be 11 shopping carts in each row and it will take 11 weeks to raise the money.

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The y intercept has been moved down, and the g(x) graph is less steep than the f(x) graph.

the fundamental duty of a family. Y = x or f(x) = x is the parent function for linear functions. Transformation: Modification of a figure's size or position. Child Function: The parent function is f(x) = x for all linear functions. y = x.

The simplest function in a family of functions that yet preserves the definition (or shape) of the entire family is known as a parent function in mathematics.

When the independent variable (often 'x') varies by a constant amount and the dependent variable (typically expressed by 'y') changes by a constant amount, the function is said to be linear.

Therefore, the correct answer is option C. The graph of g(x) is less steep than the graph of f(x) and the y intercept has been shifted down.

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The missing measures by using the rhombus LMNO graphic is, 90° is the measure of LPM,the PMN measurement is 102°, LN is 10 units in length.

A rhombus is a unique type of quadrilateral with four sides that is similar to a parallelogram. In a rhombus, the opposing sides are parallel and the opposing angles are equal.

LMNO LON = 102° NP = 5 units for a rhombus.

According to the rhombic characteristics, all of the sides are congruent (equal), hence LM = MN = NO = OL and the opposite angles are also equal, and the opposite sides are parallel.

Therefore, LON = 102° = LMN.

Since adjacent angles add up to 180 degrees.

L + M thus equals 180 degrees.

∠M + ∠N = 180°

∠N + ∠O = 180°

∠O + ∠L = 180°

So, ∠N = 180° - ∠O = 180° - 102° =78°

∠L = 180° - ∠O = 180° - 102° =78°

∠M = 180° - ∠L = 180° - 78° =102°

Alternatively, we can say that each of the two diagonals in a rhombus is the perpendicular bisector of the other. Diagonals bisect each other at an angle of 90°.

Thus, LPM = NP0 = MPN = LPO = 90 degrees.

So, 90° is the measure of LPM.

The PMN measurement is 102°.

LN is 10 units in length.

The completre question is,

Rhombus LMNO has mLON = 102° and NP = 5 units.

The Rhombus L M N O is depicted. Drawn as parallel lines, they connect at point P and extend from point L to point N and from point M to point O, respectively. Congruence exists on every side.

You may locate the missing measures by using the rhombus LMNO graphic.

° is how much LPM is measured.

° is used to measure PMN.

 Units are the length of LN

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It took approximately 5.3 hours for the temperature inside the freezer to increase from -10°C to -2°C.

If the temperature inside the freezer increased by 1.5°C per hour, and it started at -10°C, then to reach -2°C the temperature inside the freezer would have had to increase by 8°C.

To find out how long it took for this to happen, we can use the formula:

Temperature increase/rate of increase = time

8°C / 1.5°C per hour = 5.3 hours (approx).

The temperature was exactly -10°C at the start and exactly -2°C at the end. It means that the temperature increased by 1.5°C per hour on average.

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The graph of the linear inequality is shown below.

What is linear inequality?

A linear inequality is one that, if the equals relation were employed in place of the inequality, would result in a linear equation. The direction of the inequality is reversed when both sides are multiplied or divided by a negative integer to solve it. The solution set refers to all possible answers to an inequality.

We are given y < -x-4

In order to sketch the graph of the inequality, we need to have two points.

So, first let's put x = 0

So, we get y = -4

Now, let's put y = 0

So, we get x = -4

Thus, we get the points as (0,-4) and (-4,0)

From the points, the graph is sketched which is shown below.

Hence, the graph of the linear inequality is obtained.

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Since, there are multiple questions, so the question answered above is attached below

Answer:

10 cases

Step-by-step explanation:

We are given the equation: y = -0.25x + 85, where y is the # of cases, and x is the # of students who received the vaccine.

The question asks for the # of cases if 300 students received the vaccine. Since we know that 300 students received the vaccine, we can plug that in for x in the equation above, since x is that unit:

y = -0.25(300) + 85

Now, we can solve:

y = 10

Therefore, there will be 10 cases if 300 students received the vaccine.

Answer: 31

Step-by-step explanation:

Let's find the trapezoid area first:

(8-2 + 4) 3 / 2

= 10*3/2

= 15

And then the rectangle:

2 * 8

= 16

add the two areas together

15+16 = 31

The mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

Population 1: N = 35,X = 5.3, S = 2.8

Population 2: N = 21, X = 4.9, S = 3.2

We can use the t-test to test if the mean of the first population is larger than that of the second population. The formula for this is:

t = (x1 - x2) / (S√((1/N1) + (1/N2)))

Where x1 is the mean of population 1, x2 is the mean of population 2, S is the pooled standard deviation, and N1 and N2 are the sample sizes of the two populations.

Plugging in our values, we get:

t = (5.3 - 4.9) / (3.2√((1/35) + (1/21))) = 1.68

Using an online calculator, we find that the corresponding p-value is 0.093. Therefore, we fail to reject the null hypothesis that the two populations have the same mean and conclude that the mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

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According to one of Marvel's teachers, a typical learning-disabled student has an IQ of normal or above. Learning disabilities are not related to IQ, so a learning-disabled student could have an IQ of normal or above.

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a. The function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]

b. To graph the function, f(x), you can use a graphing calculator or software such as Excel or a Python library like Matplotlib.

c. It will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.

The problem states that Oscar wants to own a bee colony and extract honey from the hive. He starts with a colony of 5,000 bees and the number of bees grows exponentially with a growth factor of 12% each month. To solve this problem, we can use the exponential growth formula to determine the number of bees in the colony based on the month.

The exponential growth formula is [tex]P(t) = P_0 * (1 + r)^t[/tex] where

In this case, [tex]P_0[/tex] = 5000, r = 0.12, and t = x (the number of months). So, the function of the bee population is: [tex]f(x) = 5000 * (1.12)^x[/tex]

In order to get a decent amount of honey, Oscar feels that there should be at least 15,000 bees in the colony. To estimate how many months it will take Oscar until he has 15,000 bees, we can set f(x) = 15,000 and solve for x.

By doing this, we get x = log(15000/5000) / log(1.12) ≈ 7.9 months. This means it will take approximately 7.9 months for Oscar to have 15,000 bees in the colony.

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The complete question is:

Oscar wants to own a bee colony so that he can extract honey from the hive. He starts a colony with 5,000 bees. The number of bees grows exponentially with a growth factor of 12% each month.

a. Write a function, f(x), for the bee population that can be used to determine the number of bees in the colony, based on the month, x.

b. Use technology to graph the function, f(x).

c. Oscar feels that in order to get a decent amount of honey, there should be at least 15,000 bees in the colony. Estimate how many months it will take Oscar until he has 15,000 bees.

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The function that best represents the value of the computer in months is V(t) = 1,300(.61^(t/12)).Where t is the number of months since the computer was purchased

The given function V(t) = 1,300(.61), models the value of a computer in terms of the number of years since it was purchased. The value of the computer is represented by the function V(t) which is directly proportional to (0.61) raised to the power of t. Divide the t by 12, because there are 12 months in a year, to get the value in months.

As a consequence, the calculation V(t) = 1,300(.61(t/12)) displays the computer's value in terms of months from purchase. It demonstrates the decline in the value of the computer over time.

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Answer:

The value equivalent to the expression 2^3 + 3^4 is 19

The y intercept means that gallons of water in the base year is 10.

Y intercept is a coordinate of y which is the point where the line touches the Y axis.

The x coordinate corresponding to this point will be zero.

Given is a graph which relates the two variables year and the gallons of bottled water per person.

From the graph, it is clear that y intercept is at 10.

It is in the year 1990, which is the base value that we take.

All the other year values are based on the base value.

y intercept means in this context that in the year 1990, which is the initial year, gallons of water per person is 10.

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The Radius r changing with respect to time when volume v is  [tex]\frac{1}{9 \pi} \mathrm{cm} / \mathrm{s}\end{aligned}[/tex].

The volume here depends on the diameter of the radius of the sphere since if we take the cross-section of the sphere, it is a circle. The surface area of sphere is the area or region of its outer surface. To calculate the sphere volume, whose radius is ‘r’ we have the below formula:

Volume of sphere [tex]=\frac{4}{3} \pi r^{3}[/tex]

If you consider a circle and a sphere, both are round. The difference between the two shapes is that a circle is a two-dimensional shape and a sphere is a three-dimensional shape which is the reason that we can measure the Volume and area of a Sphere.

volume is,

[tex]$$\begin{aligned}& V=\frac{4}{3} \pi r^3 \\& \Rightarrow \frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t}\end{aligned}$$[/tex]

given that,

[tex]\frac{dV}{d t}[/tex][tex]=4 \mathrm{~cm}^3 / \mathrm{s}, V=36 \pi \mathrm{cm}^3 \text {. }$$[/tex]

[tex]$$find $\frac{d r}{d t}$ :$$[/tex]

[tex]\begin{aligned}& V=36 \pi \\& \frac{4}{3} \pi r^3=36 \pi \\& r^3=27 \\& \Rightarrow r=3 .\end{aligned}[/tex]

substitute the above values,

[tex]$$\begin{aligned}& \frac{d V}{d t}=4 \pi r^2 \frac{d r}{d t} \\& 4=4 \pi(3)^2 \frac{d r}{d t} \\& \frac{d r}{d t}=\frac{1}{9 \pi} \mathrm{cm} / \mathrm{s}\end{aligned}$$[/tex]

Therefore, the radius r changing with respect to time when the volume v is [tex]\frac{1}{9\pi } cm/s[/tex].

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The value of EF , DC , AB are 40,14, 37 respectively.

What is trapezoid ?

Trapezoid can be defined as the 4-sided shape in which it has one of sides parallel to it .

ABCD is trapezoid with median EF

so,

DC+AB = 2EF

(2x+10) + (3x+20) = 2 * 4x

5x + 30 = 8x

8x-5x = 30

3x = 30

x = 30/3

x = 10

EF = 4x = 4*10 = 10

3x+10(x-2) = 2 (4x+10)

3x+10x-20 = 8x+20

5x = 40

x = 8

DC = 3x = 32

7(x-2) + (4x-6) = 2*3x

7x-14+4x-6 = 6x

5x = 20

x = 4

DC = (7*(4-2) ) = 14

(2x+3) + (8x+5) = 2*6x

8 = 2x

x = 4

AB = 8*4+5 = 37

Therefore, The value of EF , DC , AB are 40,14, 37 respectively.

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Answer: m * 4/7 > 12/5

The area of the circle is 26.4 square meters

From the question, we have the following parameters that can be used in our computation:

Diameter, d = 5.8 meters

Start by calculating the radius of the circle

r = 5.8/2

Evaluate

r = 2.9

The area of the circle is then calculated as

A = πr²

Where

r = radius

substitute the known values in the above equation, so, we have the following representation

A = 3.14 * 2.9²

Evaluate

A = 26.4

Hence, the area is 26.4 square meters

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Answer:

15r-40

Step-by-step explanation:

By the Distributive Property, [tex]5(3r-8)=5(3r)+5(-8)=15r-40[/tex]

The cable is 805.4 ft long.

Draw a triangle to represent the situation.

Label the sides of the triangle.

Let x = length of cable
Let 1200 = height of mountain
Let 30 = angle of elevation

Use the Law of Cosines to solve for x.

x² = (1200)² + (1200)² - (2)(1200)(1200)cos(30)

x² = 288000 + 288000 - 1,728,000cos(30)

x² = 576000 - 1,728,000cos(30)

x = √576000 - 1,728,000cos(30)

x = √576000 - 1728000(0.866)

x = √576000 - 1511360

x = √646340

x = 805.4 ft

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If x is the point reached by F after t seconds, and y is the point reached by S after t seconds, then x = 3t, y = 2t. 30 seconds after leaving point 0, 30 units far apart are F and S. At 100 seconds, F and S will be 100 units apart.

The speed of F reached 12 units in 4 seconds or 3 units per second.

 x = 3t

The speed of S reached 8 units in 4 seconds or 2 units per second.

 y = 2t

x - y = 3t -2t = t

After 30 seconds, the bugs will be apart by (x -y) = 30 units

x - y = 100 = t

After 100 seconds, The bugs will be 100 units apart.

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Answer:

The three side lengths given, 12 ft, 16 ft, and 20 ft can form a right triangle. This is because the Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, 20^2 = 12^2 + 16^2, so the sides 12 ft, 16 ft and 20 ft can form a right triangle.