Ten ice cream bars and 6 ice cream cones cost $13. But if you buy 6 ice cream bars and 10 ice cream cones, the bill will be $11. How much does an ice cream bar cost?

Answer:

The answer is 5.875

Step-by-step explanation:

Negatives cancel out, so you're essentially just dividing 47 into 8 parts, which equals 5.875. Hope it helps :)

Answer:

5.875

Step-by-step explanation:

[tex]\frac{-47}{-8}[/tex]

Remember, two negatives equal a positive.

[tex]\frac{47}{8}[/tex]

47/8=5.875

let's first change the mixed fraction to an improper fraction.

[tex]\stackrel{mixed}{3\frac{1}{7}}\implies \cfrac{3\cdot 7+1}{7}\implies \stackrel{improper}{\cfrac{22}{7}} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{22}{7} \right)^7\implies \cfrac{22^7}{7^7}\implies \cfrac{2494357888}{823543}[/tex]

Answer:

The possible values of x:

-5, -4, -3, -2, -1, 0, 1

Answer:

V = 20 cm³

Step-by-step explanation:

the volume (V) of the prism is calculated as

V = lbh ( l is the length , b the breadth and h the height )

here l = 5 , b = 2 , h = 2 , then

V = 5 × 2 × 2 = 20 cm³

The three angles that will be congruent are angle AED , BEC and DEC

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

Congruent angles are two or more angles that are identical to each other.

Thus, the measure of these angles is equal to each other.

When two chords meet at a point , it's practical that all the angles will be congruent i.e they will be equal especially when the chords are perpendicular to each other.

Therefore the three angles that will be congruent are angle AED , BEC and DEC.

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Question

Chords AC and DB intersect at point E. List 3 pairs of angles that must be congruent.

See attachment for missing figure

When chord AC and DB intersect at point E , the three pair of angles that must be congruent are angle DEA, AEB and CEB

The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle.

A chord could be the diameter of the circle but not all not all chords are diameter.

when two chords intercept, there is high probability that each angle will be 90° and virtually all the angles will be congruent.

The three angles that must be congruent are angle DEA, AEB and CEB.

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Question

Check the image attached for the illustration to the question.

The statement that are consistent with the guidelines for hitching trailers are:

A. Trailers must be connected to the tow vehicle before loading.

D. Customer vehicles must have at least a frame mounted Class 3 receiver hitch with a 2" or 2 5/6" ball.

Option A: Because it guarantees that the weight of the cargo is evenly distributed and attached to the trailer before the vehicle is driven this recommendation is consistent with safe hitching techniques.

Option D: Because it guarantees that the trailer is securely fastened to the tow vehicle and can support the weight of the cargo this recommendation is consistent with safe hitching techniques. A 2" or 2 5/16" ball ensures the trailer is firmly fastened to the hitch and a Class 3 hitch is made to support the weight of heavier trailers.

Therefore the correct option is A and D.

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Answer:

20 x 20 x 20 x 20 × 15 × 15 ×15 = 540000000

Answer: 540000000

Step-by-step explanation: Please mark

1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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The population of the district in 2037 will be approximately 107,592.

To calculate the population in 2037 using the exponential growth function,

we need to use the formula P(t) = P₀(1 + r)^t,

where P(t) is the population at time t, P₀ is the initial population, r is the annual growth rate, and t is the time elapsed in years.

In this case, the initial population (P₀) is 31,700, the annual growth rate (r) is 5% or 0.05, and the time elapsed (t) is the difference between 2037 and 2012, which is 25 years. Plugging these values into the formula, we get

P(25) = 31,700(1 + 0.05)^25

P(25) = 31,700(1.05)^25

P(25) ≈ 107,592

According to the exponential growth function, the population of the district in 2037 will be approximately 107,592. This calculation takes into account the continuous annual growth rate of 5% over the 25-year, demonstrating the power of exponential growth in modeling population increases over time.

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Answer:

[tex] \sqrt{ {2}^{2} + {3}^{2} + {4}^{2} } = \sqrt{4 + 9 + 16} = \sqrt{29} [/tex]

The diagonal is √29 feet, or about 5.39 feet.

The data set are outliers are 150 and 240 and the table for same will be the graph D.

Given that the Chris sells his paintings at art fairs on the weekends.

Amount earned (S) =

105 150 170 170 175 180 180 200 240

Since we know outliers are values at the extreme ends of a dataset.

So, here the outliers are = 150 and 240

Now the graph to show his earning should start around 150 and end at 240 so the graph will be D.

Hence the data set are outliers are 150 and 240 and the table for same will be the graph D.

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Considering the inverse function definition, we have that:

a) [tex]f^{-1}(4) = 6[/tex]

b) f(-5) = -2.

To find the inverse function that exchanges the x and y-coordinates, we can follow these steps:

Hence, the situation can be resumed as follows:

If f(x) = y, then [tex]f^{-1}(y) = x[/tex], which is used to obtain the numeric values for both functions in the context of this problem.

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Answer:

Step-by-step explanation:

40=-16(t-2)²+64

-16(t-2)²=40-64

-16(t-2)²=-24

(t-2)²=24/16=3/2=1.5

t-2=±√1.5

t=2±√1.5

either t=2+√1.5≈3.22

or

t=2-√1.5≈0.78

If only 2,836 students were admitted into the Ateneo among 27,813 students, who took the ACET this year, the Ateneo’s acceptance rate is b. 10.2%.

The rate is the ratio of one value, expression, measurement, or quantity compared to another.

The rate represents the quotient of the numerator and the denominator.

The rate is expressed as a percentage by multiplication with 100.

The number of students who took the ACET this year = 27,813

The number of students who were admitted into the Ateneo = 2,836

The percentage or rate admitted = 10.19667% (2,836 ÷ 27,813 × 100)

= 10.2%

Thus, we can conclude that the acceptance rate or percentage is Option B.

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When the equation is graphed in the xy-plane, the slope of the graph is -75 and it represent the rate of decrease of the amount of money in Bo’s bank account.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided above, a linear equation that models the amount of money in Bo’s bank account with respect to its rate of decrease is given by;

y = mx + c

y = -75x + 5,000

In conclusion, the amount of money in Bo’s bank account decreases by $75.

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The number that belongs to the green box in the triangle shown in the diagram given in the question is 14

From the diagram given in the question, we can see that one side and two angles of the triangle are given.

Thus, we shall use sine rule to obtain the missing side (i.e the green box). Details below:

Sine rule state as follow:

a / Sine A = b / Sine B

Inputting the given parameters, side a can be obtain as follow:

a / Sine 61 = 15 / Sine 70

Cross multiply

a × Sine 70 = 15 × Sine 61

Divide both sides by Sine 70

a = (15 × Sine 61) / Sine 70

a = 14

Thus, we can conclude from the above calculation that the number in the green box is 14

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The probabilities are, 1) 0.25, 2) 0.25, 3) 0.5, 4) 0.5 and 5) 0.25

1) Calculating the ratio of favorable outcomes (blue or green marbles) to all possible outcomes (marbles) can help us determine the likelihood of pulling a blue or green marble from the given bag.

There are a total of 20 marbles in the bag:

3 blue marbles, 2 green marbles, 8 yellow marbles, 4 red marbles, and 3 orange marbles.

Favorable results equal 3 (blue) + 2 (green), which adds up to 5 (blue or green marbles).

The likelihood of drawing a blue or green marble is thus:

Probability = Positive results / Total results = 5 / 20 = 1/4 = 0.25

2) There are 52 cards altogether in a normal deck, with 13 cards in each of the four suits (hearts, diamonds, clubs, and spades).

Calculating the ratio of the number of hearts to the total number of cards is necessary because we want to know the likelihood of selecting a card that has a heart on it.

There are 13 hearts total.

As a result, the likelihood of selecting a card with a heart on it is:

Probability is calculated as follows: 13/52 (the number of hearts) or 1/4 (0.25).

3) You need to know the total number of possible outcomes as well as the number of favorable outcomes if you have the choice of receiving an A, B, C, or F for a paper and you want to calculate the likelihood of receiving an A or B.

There are four alternative outcomes in this situation (A, B, C, and F), and there are two (A and B) that are more favorable.

Consequently, the likelihood of receiving an A or B on the paper is:

P(A or B) = Number of positive results / Total number of possible results = 2 / 4 = 0.5

4) There are only two outcomes that can occur when a fair coin is flipped: heads or tails.

Since the coin is impartial and fair, there is an equal chance of receiving heads or tails.

The likelihood of achieving a heads or tails result on a coin flip is therefore:

Probability = 1 (number of favorable outcomes) / 2 (total number of possible outcomes) = 1/2 = 0.5

5) Calculate the ratio of the number of favorable outcomes (pulling a 3 or a 7) to the total number of possible outcomes (all numbers) if the bag includes the numbers 1–8 inclusive and we want to know the likelihood of drawing a 3 or a 7.

The bag has the following sum of numbers: 8 total numbers

If you draw a 3 or a 7, you have the following chances of success:

Positive results: 2 (3 and 7).

As a result, the likelihood of getting a 3 or a 7 is:

Probability = Positive results / Total results = 2 / 8 = 1/4 = 0.25

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Answer:

To investigate the different sizes of ponds and their effects on the garden, I followed these steps:

1. I drew several sizes of ponds on a grid paper, using the given dimensions of 18 ft2, 24 ft2, and 30 ft2. I made sure that the length and width of each pond were whole numbers. I also drew borders around the ponds to represent the tiles needed for each pond. Here is an example of how I drew a 24 ft2 pond:

| | | | | | | | | | |

| | | | | | | | | | |

|X|X|X|X|X|X|X|X|X|X|

|X|O|O|O|O|O|O|O|O|X|

|X|O|O|O|O|O|O|O|O|X|

|X|O|O|O|O|O|O|O|O|X|

|X|X|X|X|X|X|X|X|X|X|

In this drawing, X represents a tile and O represents water.

2. I recorded the number of tiles needed for each pond in a table, as well as the length and width of each pond. Here is the table I made:

Pond size (ft2) Length (ft) Width (ft) Number of tiles

18 6 3 22

24 6 4 28

30 6 5 34

3. I looked for patterns in the table and noticed that the number of tiles increased by 6 for every increase of 1 ft in width. I also noticed that the number of tiles was always equal to twice the length plus twice the width minus four.

4. I came up with a numerical expression that relates the length and width to the number of tiles needed. The expression is:

Number of tiles = 2 x Length + 2 x Width - 4

This expression works for any pond size with whole number dimensions.

By following these steps, I was able to compare different pond sizes and their tile requirements. I hope this helps you decide on the best size for your pond and garden.

________________________________________________________

MARK AS BRAINLIEST!!!

Answer:

B. Those who do not have a brother tend not to have a sister.[tex][/tex]

Step-by-step explanation:

To determine the relative frequency of the data in the two-way table, we need to calculate the proportion of each category in relation to the total number of students.

First, let's calculate the relative frequencies for each category:

Relative frequency of having a sister and a brother:

5 (students with sister and brother) / 30 (total students) = 1/6 ≈ 0.1667

Relative frequency of having a sister but no brother:

12 (students with sister but no brother) / 30 (total students) = 2/5 = 0.4

Relative frequency of having a brother but no sister:

9 (students with brother but no sister) / 30 (total students) = 3/10 = 0.3

Relative frequency of having neither a sister nor a brother:

4 (students with no sister and no brother) / 30 (total students) = 2/15 ≈ 0.1333

Now, let's analyze the relative frequencies to determine the association suggested by the two-way table.

The highest relative frequency is for the category "Those who have a sister but no brother" with a relative frequency of 0.4. This suggests that the most common association in the data is that "Those who do not have a brother tend not to have a sister." Therefore, the answer is:

B. Those who do not have a brother tend not to have a sister.

Answer:

[tex]y=\frac{1}{3}x-8[/tex]

Step-by-step explanation:

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where

Step 1:  Currently 3x + y = -5 is in standard form, but we can isolate y to convert the line to slope-intercept form (y = mx + b) to find the slope, m:

3x + y = -5

y = -3x + 5

Thus, the slope of the first line is -3.  We plug in -3 for m1 in the perpendicular slope formula to find m2 or the slope of the line we're still trying to find:

m2 = -1 / -3

m2 = 1/3

Step 2:  Now that we know the slope of the other line, we plug in the point (3, -7) for x and y and 1/3 for m in the slope-intercept form.  Then, we must solve for b to find the y-intercept of the other line:

-7 = 1/3(3) + b

-7 = 1 + b

-8 = b

Thus, the equation of the line that is perpendicular to 3x + y = -5 and passes through (3, -7) = y = 1/3x - 8

For the given quadratic equation we have:

Vertex = (-3/2, 0)

Axis of symmetry x = -3/2

y-interept: y = 9

x-intercept: x = -3/2

First we can find the vertex, is at the value of x equal to minus the lineal coefficient over two times the leading coefficient.

x = -b/2a

So here the vertex is at:

x = -12/(2*4) = -3/2

So the axis of symmetry is also at that value:

x = -3/2

Evaluating there we will get the y-value of the vertex:

y = 4(-3/2)² + 12*(-3/2) + 9 = 0

The vertex is at (3/2, 0)

The y-intercept is equal to the constant term, in this case 9.

The x-intercepts are at:

[tex]x = \frac{-12 \pm \sqrt{12^2 - 4*4*9} }{2*4} \\\\x = \frac{-12 \pm 0 }{8}\\\\[/tex]

So the x-intercept is at x = -3/2

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We can use proportions to solve this problem.

Let's start by setting up a proportion:

female doctors/total doctors = 27.7%/100%

We can then substitute the values we know and solve for the total number of doctors:

44,900/x = 27.7%/100%

To solve for x, we can cross-multiply and simplify:

44,900 * 100% = x * 27.7%

449,000 = 0.277x

x = 449,000/0.277

x ≈ 1,621,464.33

Rounding this to the nearest whole number, we get:

The total number of registered doctors is about 1,621,464.

The population of the city is given as follows:

273,073.

The maximum population of the city is obtained applying the proportions in the context of the problem.

The results indicated that 46% of voters would support the initiative. The survey had a margin of error of 1.9%, hence the maximum proportion is given as follows:

0.46 + 0.019 = 0.479.

The maximum number of voters who support the initiative is 130,802, hence the population is obtained as follows:

0.479p = 130802

p = 130802/0.479

p = 273,073.

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Answer:

40π inches

Step-by-step explanation:

What is the formula for the circumference of a circle?

The formula for the circumference of a circle is:

(where C is the circumference and r is the radius)

If the radius of the circle is 20 inches, then its circumference in terms of π would be:

Therefore, the circumference of a circle when the radius is 20in is 40π inches.

Answer:

C = 40π

Step-by-step explanation:

To calculate the circumference of a circle, we will use the formula

C = 2πr

And we're asked to find C in terms of pi.

So all I need to do is plug in 20 for the radius, and then multiply.

I plug in 20 for the radius, r:      C = 2π × 20

Multiply:                                       C = 40π

Therefore, C = 40π.

Answer:

4 hours 52 minutes

Step-by-step explanation:

I think the easiest way to handle these problems is to break them into chunks of time and then add up those chunks.

7:46am to 11:46 am is 4 hrs.

11:46 to 12pm is 14 minutes.

then 12:00 to 12:38pm is 38 minutes.

4 hrs + 14 minutes + 38 minutes = 4 hours 52 minutes

All the solutions are,

⇒ x = 1/2 (w- v)

⇒ x = (b - 9)/(a - 2)

⇒ x = (4 + w) / (7 - v)

⇒ x = 2 / (v + w)

⇒ x = 7v/(3w - 4)

Given that;

Expressions are,

⇒ 6x + v = 4x + w

⇒ ax + 9 = 2x + b

⇒ 7x - w = vx+4

⇒ 6 - wx = vx + 4

⇒ 3(wx - v) = 4(x + v)

We can simplify as;

⇒ 6x + v = 4x + w

⇒ 6x - 4x = w - v

⇒ 2x = w - v

⇒ x = 1/2 (w- v)

⇒ ax + 9 = 2x + b

⇒ ax - 2x = b - 9

⇒ (a - 2)x = b - 9

⇒ x = (b - 9)/(a - 2)

⇒ 7x - w = vx+4

⇒ 7x - vx = 4 + w

⇒ (7 - v) x = 4 + w

⇒ x = (4 + w) / (7 - v)

⇒ 6 - wx = vx + 4

⇒ vx + wx = 6 - 4

⇒ (v + w)x = 2

⇒ x = 2 / (v + w)

⇒ 3(wx - v) = 4(x + v)

⇒ 3wx - 3v = 4x + 4v

⇒ 3wx - 4x = 7v

⇒ (3w - 4)x = 7v

⇒ x = 7v/(3w - 4)

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