Jon is 5 years older than Dana. Ella is twice as old as Jon and Zach is twice as old as Dana. The sum of their ages is 93. How old is Jon?

The equation which can be used to determine x is 55+2.5x = 70 and the number of visits Mackenzie must make to earn a free movie ticket 6.

Let x represent the number of visits that Mackenzie must make

Hence,

Formulate an equation

55+2.5x = 70

Combine like terms

2.5x  = 70 - 55

2.5x  =  15

Divide both side by 2.5x

x  = 15/2.5

x  = 6

Therefore the number of visits is 6.

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There will be 165,001 Bacteria after 12 hours.

Given: initial number of bacteria = 200

Growing rate of bacteria = 75% per hour = 1.75 per hour

Now, number of bacteria after one hour = 200 + 200 x 1.75 = 350

Again the number of bacteria after two hours = 350 + 350 x 1.75 = 612.5

Similarly,

The number of bacteria after 12 hours = 200 x \(1.75^{2}\) = 165,001 (approx.)

Hence, Approximately there will be 165,001 bacteria will be there after 12 hours.

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Answer:

Best i can give is the area of the square inside of the heart is

5in x 5in = 25in (25^2)

Add the semicircle

Step-by-step explanation:

+2a semicircle

I dont know the full answer but if you can figure it out with that go ahead.

Good luck!

Front-end estimation is a particular way of rounding numbers to estimate sums and differences.

To use front- end estimation, add or subtract only the numbers in the greatest place value. Then add the decimals rounded to the nearest tenth.

Step-by-step explanation:

In front end estimation we are going to replace the original number with a number that is close by but only has one non zero digit. Examples: {20, 300, -50, 1,000, 80,000}. For example take the number 32, the choices to replace it with are 30 or 40 (they both have only one non-zero digit).

Answer:

you would need a square and a rectangle to equal that

Step-by-step explanation:

Answer:

a. x = 180 - (j + k)

b.

j + k = (5x - 2) + (2x - 2) = 7x - 4

l = x

x = 180 - (7x - 4)

x = 180 - 7x + 4

8x = 184

x = 184/8

x = 23

l = 23°

j = 5x - 2

j = 5 × 23 - 2

j = 115 - 2

j = 113°

k = 2x - 2

k = 2 × 23 - 2

k = 46 - 2

k = 44°

or k = 180 - (23 + 113) = 180 - 136 = 44°

The proof of "if group G has exactly one subgroup H of order k, then H is normal in G" is explained below.

If a "group-G" has exactly one subgroup H of order k, we want to show that H is normal in G. This means that for any element g in G, when we conjugate H by g, we get H again.

To prove this, we consider the left cosets of H in G. A left coset of H is formed by taking an element g in G and multiplying it with each element of H. Since H is the only subgroup of order k, each left coset has k elements.

Now, we take any element-g from G. Since the left cosets partition G, g must be in one of these left cosets, which we can write as gH.

When we conjugate H by g, we get gHg⁻¹. This means we multiply each element of H by g and then multiply the result by g⁻¹, the inverse of g.

Since G is a group, this multiplication follows the group's properties.  When we multiply any element of H by g and then by g⁻¹, the result is still an element of H.

Because of this, we can conclude that for any element g in G, the conjugate of H by g (gHg⁻¹) is still a subset of H.

Therefore, H is normal in G.

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The given question is incomplete, the complete question is

If a group G has exactly one subgroup H of order k, prove that H is normal in G.

There is no point of intersection between line u and line v.

Given that

These points on line u and line v.

Line u: (9, –8), (5, 4)

Line v: (4, 2), (7, –7)

We have to determine

How many points of intersection are there between line u and line v?

According to the question

To determine the point of intersection follows all the steps given below.

Line u: (9, –8), (5, 4)

The slope of the line u is,

\(\rm Slope = \dfrac{4-(-8)}{5-9}\\\\Slope = \dfrac{4+8}{-4}\\\\Slope = \dfrac{12}{-3}\\\\Slope = -4\)

And the value of c is at point (5, 4) is,

\(\rm y = mx+c\\\\4= -3\times 5+c\\\\c = 4+15\\\\c=19\)

The equation of u is y = -3x + 19.

And

Line v: (4, 2), (7, -7)

The slope of line V is,

\(\rm Slope = \dfrac{-7-(2)}{7-4}\\\\Slope = \dfrac{-7-2}{3}\\\\Slope = \dfrac{-9}{3}\\\\Slope = -3\)

And the value of c is at point (4, 2) is,

\(\rm y = mx+c\\\\2= -3\times 4+c\\\\c = 2+12\\\\c=14\)

The equation of u is y = -3x + 14.

The slopes of them are equal and their y-intercepted are not equal.

Line u is parallel to line v.

Hence, there is no point of intersection between line u and line v.

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Answer:

Zero

Step-by-step explanation:

There are 0 points of intersection for this equation

Answer:

179.3 square units

Step-by-step explanation:

We have to find the area of the rectangle and area of semicircle using the formula and then add the areas.

Area of rectangle:

                  length = 14 units

                   width = 10 units

          \(\sf \boxed{\text{\bf Area of rectangle = length * width}}\)

                                             = 14 * 10

                                             = 140 square units

Area of semicircle:

                diameter of semicircle = width of the rectangle

                                                 d =  10 units

                                                 r = d ÷ 2

                                                    = 10 ÷ 2

                                                    = 5 units

                     \(\boxed{\text{\bf Area of semicircle = $\dfrac{1}{2}\pi r^2$}}\)

                                                       \(\sf = \dfrac{1}{2}*3.14*5*5\\\\ = 39.26\\\\ = 39.3 \ square \ units\)

Area of the figure = area of rectangle +  area of semicircle

                             = 140 + 39.3

                             = 179.3 square units

Answer:

This question makes no sense please fix it

Step-by-step explanation:

Step-by-step explanation:

it would be 128 ounces

hope i helped

Answer:

The answer is 4

Step-by-step explanation:

Answer: 6 biscuits each

Step-by-step explanation:

biscuits: 12

ratio shared 1:2 (in fraction form : 1/2)

one half of 12 is 6 therefore they each get 6:12 biscuits

If you simplify 6:12 you will get 1:2

Gemma and Zak receive 6 biscuits.

Hope that helped!

Answer:

Step-by-step explanation:

If the ratio between Gemma and Zak is 1:2, then Gemma gets 1 biscuit for every 2 Zak gets. If the total number of biscuits is 12, then 1x + 2x = 12 and

3x = 12 and

x = 4. That means that Gemma gets 4 biscuits and Zak gets twice that many, which is 8.

The balanced chemical equation for the given reaction is:Fe2O3 + 3CO → 2Fe + 3CO2The molar mass of Fe2O3 is 159.69 g/mol. Mass of Fe2O3 = 50.7 g Moles of Fe2O3 = 50.7 g / 159.69 g/mol = 0.3179 mol According to the balanced chemical equation, 1 mole of Fe2O3 reacts with 3 moles of CO.

Hence, the number of moles of CO used = 3 × 0.3179 mol = 0.9538 mol. The molar mass of CO is 28.01 g/mol. Mass of CO used = 0.9538 mol × 28.01 g/mol = 26.7 g Hence, the mass of CO2 formed will be equal to the mass of CO used, i.e., 26.7 g. The molar mass of Fe is 55.85 g/mol. Mass of Fe formed = 0.3179 mol × 2 × 55.85 g/mol = 35.27 g

The number of grams of Fe and the number of grams of CO2 formed when 50.7 g of Fe2O3 reacts with excess CO are 35.27 g and 26.7 g, respectively.

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The inequalities represents the number of students the classroom can

accommodate is Number line C.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

We have,

A classroom can accommodate less than 24 students.

For less than we use the inequality as '<'.

let the x be the number of students than the condition is

x < 24.

Now, For '<' inequality the arrow should head towards left side of 24 which means for x= 23, 22, 21, .....

Thus, the number line for the situation is C.

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Answer:

120 miles

Step-by-step explanation:

You payed $74, 35 of which came from the daily charge, meaning $36 came from the total miles driven. 36 / 0.30 = 120

Answer:

120 million

Step-by-step explanation:

Multiply 132 million by 90% or 0.90:

0.90(132million)=118.8million.

To the nearest million,

120 million

Answer:

(23, 4)

Step-by-step explanation:

If we use substitution, we need to rewrite the 2nd equation so we can substitute it into the first.

Step 1: Rewrite 2nd equation

x = 5y + 3

Step 2: Substitution

2(5y + 3) - 5y = 26

Step 3: Distribute

10y + 6 - 5y = 26

Step 4: Combine like terms

5y + 6 = 26

Step 5: Isolate y

5y = 20

y = 4

Step 6: Find x

x - 5(4) = 3

x - 20 = 3

x = 23

And we have our final answer!

Answer:

(23, 4)

Step-by-step explanation:

Begin by defining x.  

x - 5y = 3

x = 3 + 5y

Now substitute.

2(3 + 5y) - 5y = 26

6 + 10y - 5y = 26

5y = 20

y = 4

Now substitute y for 4.

x - 5y = 3

x - 5(4) = 3

x = 3 + 20

x = 23

Ignoring minor details, one can think of the circulation of a vector field f along c as the line integral f along c given by. The statement is False. The statement is incomplete and lacks the necessary information to determine its truth value.

It seems to be referring to the circulation of a vector field along a curve, which is commonly represented by a line integral. However, without specifying the complete expression for the line integral or providing further context, it is not possible to definitively determine if the statement is true or false.

The statement provided is incomplete and lacks context, making it difficult to provide a comprehensive explanation. However, it seems to suggest a relationship between the circulation of a vector field and the line integral along a curve. In vector calculus, the circulation of a vector field represents the flow or rotation of the field around a closed curve. This can be computed by evaluating the line integral of the vector field along the curve. However, without specific details or equations, it is challenging to provide a more precise explanation within the given word limit. Additional information or context would be required to clarify the statement further.

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Answer:

70

Step-by-step explanation:

A=a+b

2h=8+12

2·7=70

Answer:

the least common denominator is 12

The median of a sample will always be equal to 50th percentile.

The median is defined as the middle value in a set of data, where half the values are below it and half are above it. It is also sometimes referred to as the 50th percentile, as it represents the point at which 50% of the data falls below and 50% falls above. Therefore, the correct answer is c) 50th percentile.The median is the middle number in a sorted, ascending or descending list of numbers and can be more descriptive of that data set than the average.

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Answer: B

\(x + 2y \leq 4 \textrm{ and } 3x + y \leq 4\)

Step-by-step explanation:

Insert the values of x and y for any point in the heavily shaded region and see if it satisfies both inequalities

We can see that the origin (0,0) is inside the shaded region so use these values because they are the easiest to compute

Plug in x = 0 and y = 0 into the first inequality
0 + 2.0 = 0 which is greater than 5.

So we can eliminate both A and D since they both contain incorrect inequalities

Now, test the second inequality with x = 0 and y = 0

For B we get

3.0 + 0 = 0 which is indeed less than 4

C is not applicable since 0 is not greater-than-equal to 4

Hence B is the correct solution

This can be verified using a graphing tool (see image)

The slope of the tangent to the curve is -5/14.

Apply implicit differentiation and the product rule to the curve:

\(3y^{2} \frac{dy}{dx} x + y^{3} + 2y\frac{dy}{dx} x^{2} + y^{2}2x = 0\)

Do some rewriting

\(3xy^{2}\frac{dy}{dx} + 2x^{2}y\frac{dy}{dx} + y^{3} + 2xy^{2} = 0\)

Factor and move terms without a  \(\frac{dy}{dx}\)  factor to the right side

\(\frac{dy}{dx}(3xy^{2}+2x^{2}y) = -y^{3} - 2xy^{2}\)

Now divide both sides by  \(3xy^{2}+2x^{2}y\)  and factor where you can

\(\frac{dy}{dx} = \frac{-y^{2}(y+2x)}{yx(3y+2x)}\)

\(\frac{dy}{dx} = \frac{-y(y+2x)}{x(3y+2x)}\)

Now evaluate the given point \((2,1)\)

\(\frac{dy}{dx} = \frac{-1(1 + 2(2))}{2(3(1) + 2(2))} = \frac{-1(5)}{2(7)} = \frac{-5}{14}\)

Therefore, the slope of the tangent to the curve is -5/14.

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Answer:

$1100 per week

Step-by-step explanation:

Amount made per week = $990

Increase amount per week  = $110

Unknown:

What will be his weekly pay per week = ?

Solution:

His weekly pay per week will be = amount made per week + Increase

                                                       = $990 + $110

                                                       = $1100

He now makes $1100 per week.

Answer:

c

Step-by-step explanation:

The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

The critical value(s) and rejection region(s) for the type of z-test with a level of significance a = 0.03 and a right-tailed test are as follows :Step 1: Determine the critical value of  zThe critical value is calculated by using the normal distribution table and the level of significance. A right-tailed test will have a critical value of zα. For a level of significance of 0.03, we will look for the z-value that corresponds to 0.03 in the normal distribution table.Critical value for a = 0.03 is z = 1.88 (approx).Step 2: Determine the Rejection Region The rejection region for a right-tailed test is defined as any z-value that is greater than the critical value. That is, if the test statistic is greater than 1.88, we reject the null hypothesis at the 0.03 level of significance, and if it is less than or equal to 1.88, we fail to reject the null hypothesis.Therefore, the rejection region for a right-tailed test with a level of significance of 0.03 is as follows:Rejection Region: Z > 1.88  OR  Z ≤ -1.88Graph: The graph for the given values will be as follows:The red line represents the critical value, and the shaded region on the right-hand side of the red line represents the rejection region. If the calculated test statistic is greater than the critical value of z, which is 1.88 in this case, we will reject the null hypothesis.

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With 2x-4 given to you, you can substitute x (input) and solve with that input to get y (output).

Ex. 2(0)-4=-4, (0, -4)

     2(1)-4=-2, (1, -2)

     2(2)-4=0, (2, 0)

Answer:

5/2

Step-by-step explanation:

(18/15)*(25/12)=(18*25)/(15*12)=450/180=5/2