GRADE O7 MATHEMATICS MCA / MATHEMATICS MCA / 22 OF 49
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The table shows the average annual precipitation over a 30-year period for 7 states. The values for Michigan and Nebraska are missing.
• When the missing values are included, the range for the data is 18.1.
• The mean of the values for Michigan and Nebraska is 28.2 inches.
• Michigan has a greater amount of annual precipitation than Nebraska.
• Indiana has the greatest average annual precipitation.
What are the missing values?
Drag the numbers into the table.

The function does not have any x-intercepts since it is always positive. The graph of f(x) is a U-shaped curve opening upwards, with vertex at (1, 1) and no x-intercepts. Option (b) is the correct answer.

The given function f(x) = x^2 - 2x represents a parabola. The coefficient of x^2 is positive, indicating that the parabola opens upwards. The vertex of the parabola is at (1, 1), obtained by completing the square.

The x-coordinate of the vertex can be found by using the formula -b/2a, where a and b are the coefficients of x^2 and x respectively. The axis of symmetry is a vertical line passing through the vertex, which is x = 1 in this case.

The y-intercept can be found by setting x = 0, which gives f(0) = 0. Option (b) is the correct answer.

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The simplified expression with only positive exponents is 2197x⁻⁵/z¹⁰.

Now, let's look at the expression you provided: 13x⁻⁵y⁰/5⁻³z⁻¹⁰. We want to simplify this expression by using only positive exponents.

To do this, we can use the following rules:

A negative exponent means we take the reciprocal of the base raised to the positive exponent.

A zero exponent means the base is equal to 1. For example, y⁰ is the same as 1.

When dividing two terms with the same base, we can subtract the exponents.

Now, let's apply these rules to simplify the expression:

13x⁻⁵y⁰/5⁻³z⁻¹⁰

= 13x⁻⁵/5⁻³z⁻¹⁰

= 13(5³/z¹⁰)x⁻⁵

= 2197x⁻⁵/z¹⁰

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Answer:

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

The diameter of the base is 20in, so the radius is half of that, or 10in.

Plugging in the given values, we get:

V = π(10in)^2(16in)

V = 1600π cubic inches

V ≈ 5026.55 cubic inches (rounded to the nearest tenths place)

Therefore, the volume of the cylinder is approximately 5026.55 cubic inches.

Answer: The cylinder's volume is roughly 5026.55 cubic inches.

explanation: The volume of a cylinder is calculated using the formula V = r2h, where r is the radius of the base and h is the cylinder's height.

The radius of the base is half the diameter of the base, or 10in.

With the provided values, we get: V = (10in)2(16in).

1600 cubic inches = V

V 5026.55 cubic inches (rounded to the nearest tenths of a millimeter)

As a result, the cylinder's volume is roughly 5026.55 cubic inches.

There are 10 pentagons to form close ring.

In the pentagon

The number of sides = 5

Let interior angles of pentagon = q degree

Therefore,

p = (5-2)x180/5 = 108

q = 360 -2p = 360- 2x108 = 144

Now, q = (n-2)x180/n

 ⇒ 144 = (n-2)x180/n

 ⇒  -36n = -360

 ⇒ n = 10

Hence, n = 10

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Answer: $1.69

Step-by-step explanation:

To find Lenaert's expected gain, we need to calculate the average value of a single bill if he selects and keeps one bill from the bag.

First, let's calculate the total value of all the bills in the bag:

3 x $1 = $3

5 x $5 = $25

6 x $10 = $60

1 x $20 = $20

Total value = $3 + $25 + $60 + $20 = $108

Now, let's calculate the probability of selecting each type of bill:

Probability of selecting a $1 bill = 3/15 = 0.2

Probability of selecting a $5 bill = 5/15 = 0.33

Probability of selecting a $10 bill = 6/15 = 0.4

Probability of selecting a $20 bill = 1/15 = 0.067

Finally, we can calculate the expected value of a single bill with the formula:

Expected value = (probability of selecting a bill) x (value of the bill)

So Lenaert's expected gain if he selects and keeps one bill from the bag is:

(0.2 x $1) + (0.33 x $5) + (0.4 x $10) + (0.067 x $20) = $1.69

Therefore, Lenaert can expect to gain an average of $1.69 if he selects and keeps one bill from the bag.

Answer:

A

Step-by-step explanation:

x2 + 14x + 49 is a polynomial, and since it is the product of (x + 7)2, it demonstrates the closure property of multiplication because multiplying two polynomials results in another polynomial. Therefore, the statement that shows how the product of (x + 7)2 demonstrates the closure property of multiplication is: "x2 + 14x + 49 is a polynomial."

Answer:

0.46

Step-by-step explanation:

Pretty easy actually, you just have to take the degree of the red area and divide it by the total which is 360°

Probability = 165/360 = 0.458333 = 0.46 (nearest hundredth)

The depth of the water after 5 minutes is 29 inches.

Given that Samantha is draining her swimming pool.

The function D (t) models the depth of the water, in inches, minutes after she began draining the pool,

We need to find the depth of the water after 5 minutes,

So according to the table it is 29 inches.

Hence the depth of the water after 5 minutes is 29 inches.

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The equation of the line which passes through the points (-4,-5) and (6,4) is [tex]y = \frac{9}{10}x - \frac{7}{5}[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

The line passes through the points (-4,-5) and (6,4).

First, detremine the slope of the line using the slope formula:

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

m = ( 4 - (-5) ) / ( 6 - (-4) )

m = ( 4 + 5 ) / ( 6 + 4 )

m = ( 9 ) / ( 10 )

m = 9/10

Next, using the point-slope form, plug in one of the given points and slope m = 9/10 to find the equation of the line.

Using the point (-4,-5):

y - y₁ = m(x - x₁)

[tex]y - (-5) = \frac{9}{10}( x - (-4))\\ \\ y + 5 = \frac{9}{10}( x + 4)\\\\ y + 5 = \frac{9}{10}x + \frac{18}{5}\\\\ y = \frac{9}{10}x + \frac{18}{5} - 5\\ \\ y = \frac{9}{10}x - \frac{7}{5}[/tex]

Therefore, the equation of line is [tex]y = \frac{9}{10}x - \frac{7}{5}[/tex].

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The quotient written in scientific notation is:

[tex]1.69*10^{10}[/tex]

To do so, we can separate the quotients between the powers of 10 and the rational numbers, then we can rewrite the quotient as follows:

[tex]\frac{5.5*10^7}{3.25*10^{-3}} = \frac{5.5}{3.25}*\frac{10^7}{10^{-3}}[/tex]

Now solve these two:

[tex]\frac{5.5}{3.25}*\frac{10^7}{10^{-3}} = 1.69*10^{7 - (-3)} = 1.69*10^{10}[/tex]

That is the quotient between two numbers in scientific notation, expressed in scientific notation.

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The estimated population mean with

80% confidence =  [30.856, 33.135]

90% confidence = [30.543, 33.456]

Since, For a population with unknown mean  and known standard deviation , a confidence interval for the population mean, based on a simple random sample of size n, is x + - z*  × σ /√n  , where z* is the upper (1-C)/2 critical value for the standard normal distribution.

Here, Population standard deviation = 5.6

Sample mean = 32

Sample size = 40

Given confidence level = 80%

at 80% confidence level = 1.28

Upper confidence interval = 33.135

Lower confidence interval = 30.865

Population mean lies between [30.856, 33.135] at 80% confidence level.

Given confidence level = 90%

at 90% confidence level = 1.65

Upper confidence interval =33.456

Lower confidence interval = 30.543

Population mean lies between [30.543, 33.456] at 90% confidence level.

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Answer:

n1=0 n2=4 n3=8 n4=12

Step-by-step explanation:

tn=4(n-1) is the formula to determine the value of the nth term, so all you have to do is plug in what term you want for the variable and solve.

for example

n1=4(1-1)=0

n2=4(2-1)=4

n3=4(3-1)=8

n4=4(4-1)=12

Hope you understand and have a great day.

The student can select the questions in 10 different ways.

We have,

The student can select any 3 out of the 5 essay questions.

The number of ways to do this can be calculated using the binomial coefficient formula:

C(5, 3) = 5! / (3! x 2!)

= (5 x 4 x 3) / (3 x 2 x 1)

= 10

Therefore, the student can select the questions in 10 different ways.

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Answer:

The correct option is B. Pyramids have triangular faces and a polygonal base.

Answer:B. Pyramids have triangular faces and a polygonal base.

Step-by-step explanation:

A pyramid is a three-dimensional shape that has a polygonal base and triangular faces that meet at a single point called the apex. Here's how to identify which of the given descriptions best suits a pyramid:

A. Pyramids have polygonal faces and a triangular base.

This description is incorrect because pyramids have a polygonal base, not a triangular base.

B. Pyramids have triangular faces and a polygonal base.

This description is correct because it correctly identifies that pyramids have triangular faces and a polygonal (meaning multi-sided) base.

C. Pyramids have triangular faces and a circular base.

This description is incorrect because pyramids have a polygonal base, not a circular base.

D. Pyramids have polygonal faces and a polygonal base.

This description is partly correct because pyramids do have a polygonal base, but their faces are always triangular.

E. Pyramids have curved faces and a polygonal base.

This description is incorrect because pyramids have flat, triangular faces, not curved faces.

So, in summary, option B, "Pyramids have triangular faces and a polygonal base," is the description that best suits a pyramid.

6x+146<200 will represent the largest number of days this facility can continue to take in cats without exceeding its occupancy.

Here, we have,

Given,

Cat occupancy = below 200

Facility has cats already = 146

Cats per day = 6

Let,

x be the number of days.

Cats per day*number of days + Cats already in facility < Cat occupancy

6*x+146<200

6x+146<200 will represent the largest number of days this facility can continue to take in cats without exceeding its occupancy.

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complete question:

a cat adoption facility takes in an average of 6 cats per day. The facility has to keep their cat occupancy below 200. Currently, the facility has 146 cats. If none of their cats get adopted, how many more days, x, can the facility continue to take cats? select the inequality that includes the largest number of days this facility can continue to take in cats without exceeding its occupancy limit

The many log statement 2log(w) + log(7) - 3log(x) - 8log(y) converted to a single log statement is  [tex]log(\frac{7w^2}{x^3y^8})[/tex].

Given the logarithm expression in the question:

2log(w) + log(7) - 3log(x) - 8log(y)

To convert the logarithm into a single logarithm.

First, simplify using the logarithmic rule:

nlog(a) = log(aⁿ)

Hence:

2log(w) + log(7) - 3log(x) - 8log(y)

log( w² ) + log(7) - log( x³ ) - log( y⁸ )

Next, using the product property of logarithm.

log(a) + log(b) = log(ab)

log( 7w²) - log( x³ ) - log( y⁸ )

Using the quotient property of logarithm.

log(a) - log(b) = log(a/b)

log( 7w²/x³ ) - log( y⁸ )

Still using the quotient property of logarithm.

[tex]log( \frac{\frac{7w^2}{x^3} }{y^8} ) \\ \\Simplify\\\\log( \frac{7w^2}{x^3}*\frac{1}{y^8})\\ \\ log(\frac{7w^2}{x^3y^8})[/tex]

Therefore, the single log is [tex]log(\frac{7w^2}{x^3y^8})[/tex].

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The table that correctly represents the ratio is

Students           Adults

5                         2

15                       6

25                      10

(option d).

Ratios are a way of comparing two quantities by expressing their relationship in a simplified form. They are commonly used in various real-life situations, such as determining the student to adult ratio on a field trip. In this case, the ratio of students to adults is given as 5 to 2, which means that for every 5 students, there are 2 adults present on the trip.

To represent this ratio in a table, we need to choose values that are in the same proportion as the given ratio. For example, if we have 10 students, we need to have 4 adults (since 5 to 2 is equivalent to 10 to 4). Similarly, if we have 15 students, we need to have 6 adults.

Looking at the given tables, we can see that only option D correctly represents the ratio of 5 to 2. In this table, for every 5 students, there are 2 adults, and the other values in the table are also in the same proportion as the ratio.

Therefore, option D is the correct table that represents the ratio of students to adults on the field trip.

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In the given experiment, the researchers and the subjects would not know which medication the subjects are taking, which will help to ensure that the results are accurate and unbiased.

Double-blind means that neither the subjects nor the researchers conducting the experiment will know which group each subject is assigned to. This is important to reduce the chances of bias influencing the results. For example, the doctors may be more likely to report more positive results in the group taking the new medication if they know which group the subject is in. By remaining blind to the group assignment, the doctors can objectively report the results without bias.

Therefore, in the given experiment, the researchers and the subjects would not know which medication the subjects are taking, which will help to ensure that the results are accurate and unbiased.

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Answer:

468ft²

Step-by-step explanation:

Triangles: 9x12=108 (sides)

TIP: Since there are two of these triangles, you don't need to divide by 2

Rectangles: 12x10=120 (bottom)

                    9x10=90 (Back)

                    15x10=150 (top)

108+120+90+150=468ft²

Answer:b

Step-by-step explanation:

The experimental probability of the next balloon sold being green is 4/15.

Probability is a crucial concept in the field of mathematics that is used to measure the likelihood of an event happening.

According to the information given, the number of green balloons sold is 20, and the total number of balloons sold is the sum of all the colors, which is:

20 + 17 + 12 + 19 + 7 = 75

Now we can use these numbers to calculate the experimental probability of a green balloon being sold:

Experimental probability of a green balloon being sold = Number of green balloons sold / Total number of balloons sold

Experimental probability of a green balloon being sold = 20 / 75

Experimental probability of a green balloon being sold = 4/15

This means that if we randomly select a balloon from the store, the likelihood of it being green is 4 out of 15 or approximately 0.27 or 27%.

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Answer:

4/15

Step-by-step explanation:

Answer:

95234

Step-by-step explanation:

5602 x 17 = 95234

The number of prescriptions were filtered in second hour that is the value of missing data is 13.

Hence, the correct option is (A).

We know that the mean of a data set is given by,

Mean = Total value of observations/Number of observations.

Here numbers of prescriptions in each hour of 8 hours be 18, x, 22, 25, 16, 24, 22, 28.

So the total value of observations = 18 + x + 22 + 25 + 16 + 24 + 22 + 28 = 155 + x

Number of observations here the number of hours = 8.

So the mean = (155 + x)/8

and given that mean is 21.

According to data we can say that,

(155 + x)/8 = 21

155 + x = 21*8 = 168

x = 168 - 155 = 13

So the number of prescriptions were filtered in second hour is 13.

So the correct option is (A).

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The question is incomplete. Complete question will be -

The area covered by the face of the building which has the shape of a parallelogram would be = 2,464m².

The parallelogram is defined as a type of quadrilateral that has two sides that are parallel which are opposite each other.

To calculate the area of one face of the building, the formula that needs to be used is the formula for the area of a parallelogram.

That is;

Area of parallelogram = base × height.

where;

height = 28 meters.

Base = 88 meters.

Therefore the area of the parallelogram = 28×88 = 2,464m²

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The volume of the hexagonal pyramid is 508.93 cubic inches.

The formula for the volume of a pyramid is:

Volume = (1/3) x base area x height

In this case, we are given that the base of the pyramid is a regular hexagon with an area of 92 square inches, and the height is 6 inches.

To find the volume of the pyramid, we need to first find the area of one of the triangles that make up the hexagonal base. Each of the six triangles in the base is an equilateral triangle, so we can use the formula for the area of an equilateral triangle to find the area of one of the triangles:

Area of an equilateral triangle = ([tex]\sqrt{3}[/tex]/4) x [tex](side)^{2}[/tex]

Since the base of the pyramid is a regular hexagon, all six sides are equal. Let's call the length of one side "s". Then we have:

Area of one triangle = ([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex]

To find the total area of the hexagonal base, we can multiply the area of one triangle by the number of triangles in the base:

Area of hexagonal base = 6 x([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex]

We are given that the area of the hexagonal base is 92 square inches, so we can solve for "s":

6 x ([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex] = 92

([tex]\sqrt{3}[/tex]/4) x [tex]s^{2}[/tex] = 92/6

[tex]\sqrt{3}[/tex]  x [tex]s^{2}[/tex] = 46

[tex]s^{2}[/tex]  = 46/[tex]\sqrt{3}[/tex]  

s ≈ 6.21 inches

Now that we know the length of one side of the hexagonal base, we can find the area of the base by using the formula for the area of a regular hexagon:

Area of hexagonal base = (3[tex]\sqrt{3}[/tex]  /2) x  [tex]s^{2}[/tex]  

Area of hexagonal base ≈ 254.47 square inches

Finally, we can use the formula for the volume of a pyramid to find the volume of the hexagonal pyramid:

Volume = (1/3) x base area x height

Volume = (1/3) x 254.47 x 6

Volume ≈ 508.93 cubic inches

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The height of the pentagonal prism is approximately 2.94 units

The formula for the volume of a pentagonal prism is;

V = (1/2) × base_area × height × (1 + √(5))

where base_area is the area of the base of the prism, height is the height of the prism, and sqrt(5) is the square root of 5.

In this problem, we are given that the base area is 36 units and the volume is 237.6 units. We can use this information to set up an equation and solve for the height;

237.6 = (1/2) × 36 × height × (1 + √(5))

Dividing both sides by (1/2) × 36 × (1 + √(5)), we get;

height = 237.6 / [18 × (1 + √(5))]

Simplifying this expression, we get;

height = 4.8 / (1 + √(5))

Rationalizing the denominator by multiplying both the numerator and denominator by (√(5) - 1), we get;

height = [4.8 × (√(5) - 1)] / [4]

Simplifying further, we get;

height = 1.2 × √(5) - 1)

height = 2.94 units

Therefore, the height is 2.94 units

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When a product's profits from sales equal its manufacturing costs, this is called the break-even point.

Since the break-even point is the point at which total costs and total revenues are equal, or "even," in economics, business, and specifically cost accounting.

Therefore, if opportunity costs were paid and capital received the expected return after adjusting for risk, there is no net loss or gain, and one has "broken even."

The break-even point is the point at which total cost and total revenue are equal in the realm of banking and economics.

The amount of units required to cover all costs is determined using the BEP analysis. Fixed and variable costs make up the overall cost in this case.

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