rk
d not
4 Fill in the gaps in the following paragraphs to summarise the
information about the learners' masses.
4.1
The boys' masses range from a minimum of ..... to a maximum
of ..... kg.
4.2
The girls' masses range from a minimum of ..... to a maximum
of ..... kg.
5 Organise the data into the following frequency table.
Mass interval Tally
Tally
Number of female
learners who have a
mass in this interval
40 - 49,9 kg
50 - 59,9 kg
60 - 69,9 kg
70-79,9 kg
80 - 89,9 kg
Number of male
learners who have a
mass in this interval
6 Compare the frequencies for the female and male learners and
describe any differences that you notice.

Answer:

Radius is 3 units

Center is (0,5)

Step-by-step explanation:

Compared to the standard form of the equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], we have a center of [tex](h,k)\rightarrow(0,5)[/tex], and a radius of [tex]r=3[/tex].

Answer: -18x² + 3x +14y - 6

10y - 14x² + 3x - 4x² + 4y - 6

- 14x²- 4x² + 3x + 10y + 4y -6

-18x² + 3x +14y - 6

Answer:

Step-by-step explanation:

To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:

A = P * (1 + r/n)^(nt)

where:

A is the amount of money Louise will have after "t" years,

P is the initial investment of $20,000,

r is the annual interest rate of 4.28%,

n is the number of times the interest is compounded per year (12 times per year), and

t is the number of years.

We can rearrange this formula to solve for t:

t = (log(A/P)) / (log(1 + r/n))

Plugging in the values:

t = (log(30000/20000)) / (log(1 + (0.0428/12)))

t = 5.97 years

Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.

The expected value of the policy for the insurance company: $359.38

Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.

Probability of Event = Favorable Outcomes/Total Outcomes = X/n

The expected value of the policy for the insurance company can be calculated as follows:

Expected value = (Probability of survival) x (Annual payment)

= 0.999057 x $360

= $359.38

So, the expected value of the policy for the insurance company is $359.38.

It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.

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Answer:no

Step-by-step explanation:

The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

f(x) = x(x + 5)(x - 2)

x(x + 5)(x - 2) = 0

x = 0, x + 5 = 0, x - 2 = 0

x = 0, -5 and 2

The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

Hence, the graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

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Answer:

So Andrea and Casey each make $52 after working for 3 hours.

Step-by-step explanation:

Let's call the number of hours that Andrea and Casey work "x".

The amount of money that Andrea makes in a given hour can be represented as 25 + 9x.

The amount of money that Casey makes in a given hour can be represented as 10 + 14x.

We want to find the number of hours it takes for Andrea and Casey to make the same amount of money, which we can represent as:

25 + 9x = 10 + 14x

To solve for x, we can isolate x by subtracting 10 from both sides of the equation:

15 + 9x = 14x

Next, we can isolate 9x by subtracting 14x from both sides of the equation:

15 = -5x

Finally, we can divide both sides of the equation by -5 to solve for x:

-3 = x

So it takes 3 hours for Andrea and Casey to make the same amount of money. To find the amount of money, we can plug in x = 3 back into either of the equations:

Andrea's equation: 25 + 9x = 25 + 9 * 3 = 25 + 27 = 52

So Andrea and Casey each make $52 after working for 3 hours.

Answer:

20% reduction in price

Step-by-step explanation:

Let the original price of each box be P and original quantity be Q. The unit rate is P/Q

Jack's approach

increase quantity by 25% = 0.25Q

New quantity = Q + 0.25Q = Q(1  +0.25) = 1.25Q

Unit rate = P/1.25Q

Sadia's approach

Reduce price and keep quantity same

Let price reduction be d% = d/100

Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10

Price reduction = P x r = Pr

New price = P - Pr = P(1-r)

Unit rate by this method =P(1-r) /Q

Both unit rates have to be the same if both values are the same

So
[tex]\dfrac{P}{1.25Q} = \dfrac{P(1-r)}{Q}\\\\\dfrac{P}{Q} \cdot \dfrac{1}{1.25} = \dfrac{P}{Q} \cdot (1-r)\\\\[/tex]

Eliminate [tex]\displaystyle {\dfrac{P}{Q}}[/tex]   common factor from both sides to get

[tex]\dfrac{1}{1.25} = 1- r[/tex]

[tex]\dfrac{1}{1.25} = 0.8\\\\[/tex]

So we get
[tex]1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\[/tex]

0.2 works out to 0.2 x 100 = 20%

So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%

4x³ + 9x² - x - 6 is a volume of the container.

What does volume mean in plain terms?

Any three-dimensional solid's volume is just the amount of space it takes up. These solids can have the shape of a cube, cuboid, cone, cylinder, or sphere.

                                The 3-dimensional space that is occupied by matter or surrounded by a surface is measured in volume, which is expressed in cubic units. A derived measure called the cubic meter (m3) serves as the SI unit of volume.

= (4x-3) . (x+1) . (x+2)

= [ 4x .x + 4x . 1 - 3x - 3] . ( x + 2)

= ( 4x² + 4x - 3x - 3 ) ( x + 2 )

= ( 4x² + x - 3 ) ( x+ 2 )

= 4x³ + x² - 3x + 8x² + 2x - 6

 = 4x³ + 9x² - x - 6

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The length x of the right triangle is 8.66 units.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the right triangle can be found using trigonometric ratios as follows:

Hence,

tan 60° = opposite / adjacent

where

opposite side = x

adjacent side = 5

Therefore,

tan 60° =  x  / 5

cross multiply

x = 5 tan 60°

x = 5 × 1.73205080757

x = 8.66025403784

x = 8.66 units

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If G is the midpoint of EH, FG= GI, then triangle EFG= triangle HIG

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Given G is the midpoint of EH,

FG≅ GI,

We need to Prove triangle EFG= triangle HIG

∠E and ∠H are right angles, FG≅ GI from given.

∠E≅  ∠H from given

G is midpoint of EH from given

EG≅ GH by definition of congruent triangles.

triangle EFG≅ triangle HIG by SAS congruence postulate.

Hence, if  G is the midpoint of EH, FG= GI, then triangle EFG= triangle HIG

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The total volume of lemonade held by 24 bottles would be 18,000 mL (750 mL x 24) or 24x 0.75 liters = 18 liters.

And it would be to express the total volume in terms of the volume of one bottle. You can say that 24 bottles of lemonade is equal to 18 times the volume of one bottle, or 18 x 750 mL = 18,000 mL. This can also be written as 24 x 0.75 liters = 18 liters. This can also be expressed as 18 liters, since 1 liter is equal to 1000 mL.

Regardless of how you choose to express the answer, both methods give us the same result: 24 bottles of lemonade hold a total of 18,000 mL or 18 liters of the beverage. This information can be useful in various contexts, such as for planning a party or for ordering supplies for a lemonade stand. It's important to note that while both answers give the same result, they present the information in different ways. The first answer provides the total volume of lemonade held by all 24 bottles, while the second answer provides the number of times the volume of one bottle is contained within the total volume. Both answers provide useful information and the choice of which one to use may depend on the specific context in which the question is being asked.

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Answer:

160 pounds of algae

Step-by-step explanation:

10 times 2 is 20   ( first 5 hours )

20 times 2 is 40  (10 hours)

40 times 2 is 80 (15 hours)

80 times 2 is 160 ( 20 hours)

there would be 160 pounds of algae

Answer:

4/23

Step-by-step explanation:

I Did The Quiz :)

Bearing is measured from reference line clockwise or counter-clockwise - FALSE.

A bearing is an angle that is calculated clockwise from the north.

The vertical angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.

Angles are measured in comportments clockwise from north.

The direction of north must be identified before taking a bearing measurement.

The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion. Since all bearings must be reported in three figures, we must begin the three-figure bearing with zero if the angle measured is less than 100 degrees.

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Answer:

x=7/6

Step-by-step explanation:

add 2/3 to both sides

Given the angle bisector, the statements and reasons for the proof are explained.

A bisector splits a given line or angle into two equal parts. A straight line is said to be an angle bisector if it divides a given angle into two equal measures. Such that on comparison, the sum of the angles formed is equal to the measure of the bisected angle.

The statements and reasons for the proof are given below;

      STATEMENT                                                    REASONS

1. MK bisects <HKO and <HMO                           Given

2. m<HMK = m<OMK and m<HKM = m<OKM    Definition of angle bisector

3. HK ≅ KO, and HM ≅ OM                                 Congruent side property

4. ΔHMK ≅ ΔOMK                                               Angle-Angle-Side theorem

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Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high, since the ratio of ice cream to caramel is much higher than her ideal ratio.

Ari's ideal ratio of ice cream to caramel for a milkshake is 5 scoops of ice cream for every 3 spoonfuls of caramel. Freeze Zone's milkshakes, however, have a ratio of 10 scoops of ice cream for every 7 spoonfuls of caramel, which is significantly higher than Ari's ideal ratio. Therefore, Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high. The higher ratio of ice cream to caramel means that the milkshake will be sweeter, and may not have the desired balance of flavors that Ari prefers. Ari may also think the milkshake is too heavy or overly sweet, since the extra caramel creates a consistency that is different from what she is used to. Ultimately, Ari will likely think that the amount of caramel in Freeze Zone's milkshakes is too high for her liking.

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To make 50 ounces of a 40 percentage alcohol solution, eight ounces of the 30% solution must be mixed with the 70% solution.

1. Round the two solutions' initial concentrations to the nearest tenth (30% alcohol = 0.3; 70% alcohol = 0.7).

2. Determine the combined solution's overall alcohol content

(30% + 70%): 0.3 + 0.7 = 1.

3. Multiply 50 ounces by 0.4 to get the total amount of alcohol required for a 40% solution:

50 x 0.4 = 20 ounces.

4. Determine how much 30% solution is required to reach the desired concentration. 1 divided by 20 equals 20 ounces.

5. Subtract the quantity of the existing 70% solution:

(50 ounces x 0.7)/20 ounces = 8 ounces.

6. The outcome is that 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.

The original concentrations of the two solutions must first be converted to decimals (30% alcohol = 0.3; 70% alcohol = 0.7) in order to determine how much of a 30% alcohol solution has to be added to a 70% alcohol solution to create 50 ounces of a 40% alcohol solution. The two decimals can then be added to determine the total amount of alcohol present in the combined solution: 0.3 + 0.7 = 1. In order to determine the entire amount of alcohol required for a 40% solution, multiply 50 ounces by 0.4, which results in 20 ounces. The amount of the 30% solution required to reach the specified concentration can be estimated by dividing 20 ounces by 1, which is 20 ounces. Then, 20 ounces must be divided by the amount of the 70% solution that is already present to get 8 ounces. As a result, 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.

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Hi there, here's your answer:

Given, a basketball team averaged 68 points per game in the last season and averaged 77 points per game in the present season.

To find:

The approximate percentage of increase.
Solution:

If 68 points was the average last season, and 77 points was the increase this season, then the number of increase in points is 9.

Also we have that % increase = [tex]\frac{Difference}{Original}[/tex] × 100

Which is [tex]\frac{9}{68}[/tex] × 100 = 0.1323 × 100 = 13.23%

Therefore, the approximate percent increase is 13%.

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Greta feeds Lizzy 56 crickets when she feeds Draco 77.

Proportion, in general is referred to as a part, share or number considered in comparative relation to a whole.

According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b

Given:

For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Let solve it by an equality

[tex]\frac{11}{8} = \frac{77}{x}[/tex]

We want to solve for x.

We can do so by finding how much larger the second fraction is than the first.

In this case, 77 is 7 times larger than 11.(77/11 = 7)

So, we know that x must be 7 times larger then 8( because the fractions are proportinal)

Since x is 7 times larger than 8, we can use 7 times 8 to find the value.

7 times 8 i s56

56 crickets for Lizzy.

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x is 7 times larger than 8, we can use 7 times 8 to find the value, 7 times 8 is 56. Greta feeds Lizzy 56 crickets while she feeds Draco 77.

What is the Proportion?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole.

According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b

Given:

For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.

Let solve it with an equality

11/8 = 77/x

We want to solve for x.

We can do so by finding how much larger the second fraction is than the first.

In this case, 77 is 7 times larger than 11.(77/11 = 7)

So, we know that x must be 7 times larger than 8( because the fractions are proportional)

Hence, x is 7 times larger than 8, we can use 7 times 8 to find the value.

7 times 8 is 56.

56 crickets for Lizzy.

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Answer:

M (-4; 4)

Step-by-step explanation:

A ( -6; 1), B ( -2; 7)

M (midpoint) = ( ?; ?)

Midpoint coordinates formulas are

x = (x1 + x2) / 2

y = (y1 + y2) / 2

xM = (xA + xB) / 2 =

= (-6 + (-2)) / 2 = (-6 - 2) / 2 = -8 / 2 = -4

yM = (yA + yB) / 2 =

= (1 + 7) / 2 = 8 / 2 = 4

M (-4; 4)

130 estimated to the nearest integer is 130 itself as 130 itself is an integer.

Integers are numbers which includes the set of natural numbers, 0 and the negatives of all those natural numbers.

Set of integers are usually denoted as Z.

A number is normally rounded to the nearest integer when it is decimal.

First we have to look at the tenths place.

When the digit in the tenths place is 5 or numbers greater than 5, then increase digit in the ones place by 1.

If the digit in tenths place is less than 5, then leave the ones place as such.

Suppose that the number is 1.30.

Then the digit in tenths place is 3, less than 5. So leave the digit in one place which is 1, as such.

So 1.30 rounded to the nearest integer is 1.

Here 130 itself is an integer.

Hence 130 rounded to nearest integer is 130.

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The ratio of the sides' lengths of a triangle with sides of 30-60-90 is:

short leg : long leg : hypotenuse = 1 : √3 : 2

Consequently, the triangle's short leg's measurement is 8.

A triangle is a 3-sided shape with 3 vertices. The angles of the triangle are formed by the connection of the 3 sides end to end at a single point. The triangle's three angles sums up to 180 degrees.

Triangles can be divided into three varieties based on the lengths of their sides, which are:

Scalene.

Isosceles.

Equilateral.

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Answer:

[tex]\huge\boxed{\sf -3x\² + x + 5}[/tex]

Step-by-step explanation:

g(x) = 4x + 5

f(x) = -3x² - 3x

= 4x + 5 + (-3x² - 3x)

= 4x + 5 - 3x² - 3x

= 4x - 3x + 5 - 3x²

= x + 5 - 3x²

[tex]\rule[225]{225}{2}[/tex]

The order of processes that support the central dogma are:1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

The central dogma of molecular biology describes the flow of genetic information within a biological system. The method by which DNA instructions are translated into useful products is known as the "Central Dogma." Francis Crick, who discovered the structure of DNA, first put up the idea in 1958.

The order of processes that support the central dogma are:

1.DNA replication: the process by which DNA makes a copy of itself.

2.Transcription: the process by which RNA is synthesized from a DNA template.

3.Translation: the process by which proteins are synthesized from RNA templates.

In summary, the central dogma can be described as follows: DNA is replicated to make more DNA, DNA is transcribed into RNA, and RNA is translated into proteins.

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The equation for the perimeter will be (4/5)d + 18d = 282. The value of d is 15.

The perimeter of any two-dimensional figure is defined as the sum of all the sides of the figure. For a trapezoid, the perimeter will be the sum of all the sides of the trapezoid.

Given that the four sides of the figure are,

12d + 4

4/5d -9

2d

4d - 6

The perimeter of the figure is 271. The equation can be written as:-

(4/5)d - 9 +12d + 4 + 4d - 6 + 2d = 271

(4/5)d + 12 d + 4d + 2d -15 + 4 = 271

(4/5)d + 18d = 282

94d = 282 x 5

d = 15

Therefore, the perimeter will be calculated as (4/5)d + (18d) = 282. D has a value of 15.

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his selling rate is: 750 balloons / 15 days = 50 balloons per day . To calculate Jack's selling rate in balloons per day, we need to divide the total number of balloons he sold by the number of days he worked.

This means that Jack sold an average of 50 balloons per day over the last 15 days. This information is useful for several reasons. For example, the party supply store might use this information to evaluate Jack's performance and determine whether he is meeting their expectations. It might also be useful for forecasting future sales, since if Jack continues to sell balloons at a rate of 50 per day, we can estimate how many balloons he will sell in a future period of time by multiplying the number of days by 50. In this case,

Jack sold 750 balloons in 15 days, so his selling rate is: 750 balloons / 15 days = 50 balloons per day

It's important to note that the selling rate of 50 balloons per day is an average, and it's possible that Jack's sales varied from day to day. For example, he might have sold more balloons on some days and fewer on others. However, by calculating the average selling rate, we get a general sense of how many balloons Jack sold per day over the course of the last 15 days.

In conclusion, Jack's selling rate in balloons per day over the last 15 days was 50 balloons. This information provides insight into Jack's performance and can be used to make informed decisions about future sales.

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