The heights of a boys and girls track team are shown. Find the range of the heights
for each team. Compare your results.
Boys' heights (inches) 84 75 77 82
82
Girls' heights (inches) 70 66 68
72
72
80 80
80 81 78 79 80
70
67 70 72 67
75
75

Answer:

[tex]\frac{-8}{9}[/tex]

Step-by-step explanation:

Substitute in 7 for x

[tex]\frac{7^{2}-5(7) -6 }{7^{2}-6(7) - 16 }[/tex]

[tex]\frac{49-35-6}{49-42-16}[/tex]

[tex]\frac{-8}{9}[/tex]

Answer:

d = h(cot1 - cot2)

d = 100(cot30 - cot45))

d = 100* (1.732 - 1)

d = 100*0.732

d = 73.2 m

Answer:

(0, 139) and (139/35, 0)

Step-by-step explanation:

Answer:

1. Given

2. Subtraction P.O.E

3. Addition P.O.E

4. Division P.O.E

5. Symmetric P.O.E

Step-by-step explanation:

P.O.E stands for Property of Equality

Answer: x=3

Step-by-step explanation:

[tex]\displaystyle\\(9^{x-4})(9^{3x+2})=9^{10}\\\\9^{x-4+3x+2}=9^{10}\\\\9^{4x-2}=9^{10}\\\\4x-2=10\\\\4x-2+2=10+2\\\\4x=12[/tex]

Divide both parts of the equation by 4:

[tex]x=3[/tex]

Answer:

24

Step-by-step explanation:

4+5+6+4+5=24

simple

no big deal

The appropriate conclusion at the 5% significance level is b. Reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.

[tex]\bar{x_1}[/tex] = pounds per batch distributor A = 23

[tex]\bar{x_2}[/tex] = pounds per batch distributor B = 18

[tex]\sigma_{1}[/tex] = standard deviation distributor A = 4

[tex]\sigma_{2}[/tex] = standard deviation distributor B = 5

n = sample size = 4

α = significance level = 5% = 0.05

Test statistic is using z test to find the z value from two population, after that we can search p-value and then comparing the p-value with significance level.

If p-value is lower than significance level, the null hypothesis (H0) is accepted. But, if p-value is higher than significance level, the H0 is rejected.

Calculate test statistic by this formula,

Z = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1 + \sigma^2_2}{n}}}[/tex]

= [tex]\frac{23-18}{\sqrt{\frac{4^2 + 5^2}{4}}}[/tex]

= [tex]\frac{5}{\sqrt{\frac{16 + 25}{4}}}[/tex]

= 1.56

Using z table for 1.56, we get 0.9406. Since is right tailed test. So, p value is

p-value = 1 - 0.9406

= 0.0594

Then, p-value is 0.0594 is higher than significance level 0.05. So, H0 is rejected.

Thus, the conclusion is reject H0, we cannot conclude the mean amount of fertilizer per batch distributor A is greater than distributor B.

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The maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is  0 ≤ x ≤ 5 is 5^b.

Generally, To find the maximum value of a function on a given interval, it is generally helpful to find the critical points (points, where the derivative is equal to zero or the function, is undefined) and the endpoints of the interval, and then evaluate the function at these points to find the maximum value.

The d/dx f(x) is given by:

f'(x) = ax^(a-1)(5-x)^b - bx^a(5-x)^(b-1)

Setting this equal to zero and solving for x, we find that the critical points are x = 0, x = 5, and x = (5b)/(a+b).

We can then evaluate the function at these points to find the maximum value. At x = 0, f(x) = 0^a*(5-0)^b = 5^b.

At x = 5, f(x) = 5^a*(5-5)^b = 0.

At x = (5b)/(a+b),

f(x) = [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.

Since a and b are positive, the maximum value must occur at either x = 0 or

x = (5b)/(a+b).

To determine which of these points gives the larger value of f(x), we can compare the values of

5^b and [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b.

The expression [(5b)/(a+b)]^a*(5-[(5b)/(a+b)])^b is equal to [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b.

Since a and b are positive, [(5b)/(a+b)]^a and [(a+b-5b)/(a+b)]^b are both greater than or equal to 1, so the expression [(5b)/(a+b)]^a*[(a+b-5b)/(a+b)]^b is greater than or equal to 1.

Therefore, the maximum value of f(x) is 5^b, which occurs at x = 0.

Thus, the maximum value of f(x) = x^a(5 − x)^b on the interval 0 ≤ x ≤ 5 is 5^b.

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The dimensions of a rectangle are 19m.

Here we have to find the dimensions of a rectangle.

Data given:

Perimeter = 76m

The formula for the perimeter of the rectangle:

perimeter = 2( length + breadth)

So,

76 = 2 ( l+b)

l + b = 38

l = 38 -b

The formula for the area of the rectangle:

Area = length × breadth

A =( 38-b)×b

  = 38b - b²

At maximum point:

dA/ dw = 38 - 2b

38 - 2b = 0

b = 19

Therefore the dimension is 19m.

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the trigonometric function of all the given question is obtained.

What is Trigonometric Functions?

Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.

Given: Cos θ = (3/5), Find: Csc θ = 5/4

Given: Sin θ = (5/6), Find: Cot θ = 11/5

Given: tan θ = (3/4), Find: Cot θ= 4/3

Given: Sec θ = (7/2), Find: Cos θ= 2/7

Given: Sin θ = (2/3), Find: Cosec θ=3/2

Given: Sin θ = (2/3), Find: Cos θ=5/3

Given: Tan θ = (6/4), Find: Sin θ=6/7.21

Given: Tan θ = (7/5), Find: Cos θ=5/8.6

Given: Tan θ = (7/5), Find: Sec θ= 8.6/5

Hence the above trigonometric function of all the given question is obtained.

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The result of the following summation is 114.

We are given the following summation, i = 1 to 6 ∑(4i + 5)

To determine the sum by adding the values, we will substitute the values of i, starting from i = 1 to i = 6, in the expression.

= 4(1) + 5 + 4(2) + 5 + 4(3) + 5 + 4(4) + 5 + 4(5) + 5 + 4(6) + 5

= 4(1) + 4(2) +  4(3) + 4(4) + 4(5) + 4(6) + 30

= 4 + 8 + 12 + 16 + 20 + 24 + 30

= 114

Thus, the result of the sum is 114.

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The system of equations that describes Tammy and Luke's outcomes is written below

It can be deduced form the question that

x represents the number of points for a catch

y to represent the number of points for a miss

Tammy makes 5 catches and misses 1, ending the game with 23 points

5x - y = 23

Luke earns 8 catches and has 5 misses. Luke ends the game with 30 points

8x - 5y = 30

The system of equations required are

5x - y = 23

8x - 5y = 30

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The community will contain 15,000 people with the gene that causes a triangle on their forehead after 20 days.

The rate of change of n (t) with respect to time is 500 people per day. This means that the equation for n (t) is given by:

n (t) = 5,000 + 500t

where t is the number of days since time t. At time t, n (t) = 5,000, and as time passes, the number of people with the gene that causes a triangle on their forehead increases. After 20 days, n (t) = 5,000 +500*20 = 15,000, meaning that after 20 days, the community will contain 15,000 people with the gene that causes a triangle on their forehead.

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The equation of the line that passes through the point (4, -2) and has a slope of 5/4, in point-slope form is: y + 2 = 5/4(x - 4).

If we are given a point (a, b), that a line goes through and we also know the slope (m) of the line, the equation of the line can be written as y - b = m(x - a) in point-slope form

Given that the line has the following:

A point (a, b) = (4, -2)

The slope of the line (m) = 5/4

To write the equation of the line, substitute m = 5/4, a = 4, and b = -2 into y - b = m(x - a):

y - (-2) = 5/4(x - 4)

y + 2 = 5/4(x - 4)

The answer is: y + 2 = 5/4(x - 4).

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The measures of the angles formed by the parallel lines and their common transversal are;

Part A; B. c is equal to b

Part B; c = 60°

Second part; Angle P is 80°

Third part; The missing reason in step 3 is the option D.

Fourth part; Angle B is 72°

Parallel lines are lines in the same plane that have the same slope. The perpendicular distance between parallel is constant, such that they do not meet.

D. Vertical angles are congruent

Fourth part; Angle B is

Part A; JK is parallel to LM

Angle ∠c and angle ∠b are corresponding angles, therefore;

∠c and ∠b are congruent

∠c = ∠b

Therefore;

B. c is equal to b

Part B

Angle ∠b and 2·∠b are linear pair angles

Linear pair angles are supplementary, therefore

∠b + 2·∠b = 180°

3·∠b = 180°

∠b = 180°/3 = 60°

∠b = 60°

∠c = ∠b = 60°

B. c = 60°

Second part;

Angle P and the vertical angle to  the 100° angle are same side interior angles.

Vertical angles are congruent, therefore;

Angle P and 100° are same side interior angles

Same side interior angles are supplementary, therefore;

m∠P + 100° = 180°

m∠P = 180° - 100° = 80°

Third part;

Angle ∠2 and angle ∠3 are formed by the transversal t and w, therefore, they are vertical angles

Vertical angles theorem states that two sets of linear pair angles, that have congruent angles are formed from the intersection of two lines.

Therefore:

∠2 ≅ ∠3, reason: D. Vertical angles are congruent

Fourth part;

Line A is parallel to line B

The angles, 4·m -24, and 3·m are corresponding angles

Corresponding lines formed by the transversal and two parallel lines are congruent, therefore;

4·m - 24 = 3·m

4·m - 3·m = 24

m = 24 degrees

Taking angle ∠B as the angle formed at the intersection of line B and the transversal, 4·m - 24 we get;

∠B = 4·m - 24

∠B = 4 × 24 = 72°

Angle ∠B = 72°

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Solving a system of equations we will see that Edmund will plant 4 yellow tulips and 8 white lilies.

Let's define our variables as:

We know that for each yellow tulip he will plant two white lilies, then:

y  = 2x

And we also know that he wants to plant 12 flowers, so:

x + y = 12

Then we have a system of equations:

x + y = 12

y  = 2x

Substituting the second equation into the first one, we will get:

x + 2x = 12

3x = 12

x = 12/3

x = 4

Then the value of y is:

y = 2x

y = 2*4 = 8

Then he will plant 4 yellow tulips and 8 white lilies.

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The probability of winning or loosing the game is x/559

The term probability is known as  the occurrence of a random event and it can be written between zero to one.

Here we need to find how much would you expect to win or lose, if you played this game 559 times.

While we looking into the given question, we have known that there is no proper number of time that the coin has tossed so let us consider x be the amount of time the coin has been tossed.

AS we know that the formula to find the probability is written as

P(E) = n(E)/n(S)

here the value of n(S) is 559 and the value of n(E) is x.

So, the probability is written as,

=> P = x/559

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Sleep hours per night is independent.

Given the data:

Hours of Sleep 39 or younger 40 or older

> 6 _____38 36

6 to 6.9 _ 61 58

7 to 7.9 __76 74

8 or more 65 92

The analysis will be conducted using the Chisquare statistic:

The supposition

H0: The amount of sleep each night is independent

H1: The amount of sleep each night is not independent

χ² = (observed - Expected) (observed - Expected)2 / Predicted

to speed up computation. To conduct the analysis, we might utilize a Chisquare calculator:

The evaluation statistic is 4.0061.

Row - 1 * The degree of freedom (column - 1)

Degree of freedom is equal to (4-1)*(2-1)=3*1=3.

Pvalue is 0.261.

Since Pvalue >, we are unable to reject the hypothesis that sleep duration is independent total %

> 6 _____38 36_ 74 _ 14.8

6 to 6.9 61 58 _ 119 23.8

7 to 7.9 __76 74 150 30

8 or higher 65 92 157 31.4

_______240 260 500 100

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R possess Symmetric property.

Let S be the set of all polynomials of degree at most 3.

s(x) = ax³ + bx² + cx + d

we know that polynomial is a mathematical expression of one or more algebraic terms each of which consist of a constant multiplied by one or more variables raised to a non negative power.  

The reflexive property states that every element of the set is related to itself.

The symmetric property is defined as if one element in a set is related to the other, then we can say that the second element is also related to the first element.

The transitive property states that if a, b, c are three quantities, and if a is related to b and b is related to c then a and c are related  to each other.

So here we observe that R will posses symmetric property.

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Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

Rows with a defined pattern, in which the difference between two consecutive terms is equal and fixed, are referred to as arithmetic sequences and series, also known as rows and counting series. In other words, by adding a fixed integer to the previous term, each term in the arithmetic arrangement is obtained from the previous term. To put it another way, every term in the arithmetic series (except from the first term) is obtained by adding a specific integer to the term that comes before it.

Here,

This mathematical sequence can be written as follows:

A, A+D, A+2D, A+3D, A+4D, etc. , a+(n-1)d or

where:

First term: a

d stands for common variation.

It is stated that the arithmetic sequence formula is

a = a + (n-1)d

where

First term: a

n = the number of terms

d stands for common variation.

Common Difference

In mathematical terminology, the common difference is the difference between two words.

2, 5, 8, 11, and more problems

Answer: To determine if a row is an arithmetic sequence or not, first identify the similarities between the rows.

d = 5 - 2 d = 8 - 5 d = 11-8

d = 3.

Each of them differs by 3 points.

The following three words are then 2, 5, 8, 11, 11+3, 11+6, 11+9 or 2, 5, 8, 11, 14, 17, and 20.

Issues 2, 4, 6, 8, and 10 exist.

Answer:

d = -4 - 2 = -6

d = 6 - (-4) = 10

It does not contain arithmetic sequences because there is no common difference.

Challenge: -6, -10, -14, -18,...

Answer:

d = -10 - (-6) = -4

d= -14 - (-10) = -4

d= -18 - (-14) = -4

There is a -4 difference between them all.

The following three terms are then 6, 10, 14, 18, -18, -18 + (-4), -18 + (-8), -18 + (-12), or 6, 10, 14, 18, -18, -22, -26, -30.

Issues 40, 42, 44, 46,...

Answer:

d = 42 - 40 = 2

d = 44 - 42 = 2

d = 46 - 44 = 2

All of them differ by 2 points.

The subsequent three words are either 40, 42, 44, 46, 48, 50, 52 or 40, 42, 44, 46, 46 + 2, 46 + 4, 46 + 6.

Issues: 1.2, 1.8, 2.4,...

Answer:

d = 1.8 - 1.2 = 0.6

d = 2.4 - 1.8 = 0.6

They are all separated by 0.6.

1.2, 1.8, 2.4, 2.4 + 0.6, 2.4 + 1.2, 2.4 + 1.8 or 1.2, 1.8, 2.4, 3.0, 3.6, 4.2 are the following three words.

Issues 1, 5, and 9,13

Answer:

d = 5 - 1 = 4

d = 9 - 5 = 4

d = 13 - 9 = 4

They are all divided by 4 in common.

The subsequent three terms are either 1, 5, 9, 13, 17, 21, or 25. These are 1, 5, 9, 13, 13 + 4, 13, 8, 13, and 12.

Therefore the common difference in this AP series is 4 and the next 3 terms are  1, 5, 9, 13, 13 + 4, 13 + 8, 13 + 12 or 1, 5, 9, 13, 17, 21, 25.

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To beat the school long jump record, John must jump an additional 5 1/4 inches

From the given question, we are to determine how farther John must jump in order to break the record

From the given information,

"A high school track team's long jump record is 23 ft 1 3/4 in"

and

"John's best long jump is 22 ft 8 1/2 in"

First, we will convert the distances to inches

NOTE: 1 ft = 12 inches

23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in

22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in

Now, to determine how farther John must jump, we will subtract the distances

277 3/4 in - 272 1/2 in = 5 1/4 in

Hence, he must jump 5 1/4 in farther

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Answer: Attached to the post.

Step-by-step explanation:

First, label points A and B--given as (3, -3) and (3, 1) respectively. Now connect the points to form line segment AB.

We need to reflect this line segment over the line y = x. To visualize this easier, let's draw line y = x. Two coordinates on this line is (1, 1) and (0, 0). Plot these points and connect them to form line y = x.

Finally, we need to reflect line segment AB over y = x. Imagine the line y = x is a mirror and reflect the line segment AB over it. In my diagram, line segment A'B' is the answer.

Answer:

1.d

2.a

3.e

4.g

5.f

6.c

7.b

Step-by-step explanation:

did it already

If the triangle ABC is an equilateral triangle having the length as (4x - 3) , and perimeter as 63 in , then the value of x is 6 .

The triangle having all the sides of equal measure is termed as Equilateral triangle.

The triangle ABC is equilateral triangle,

The measure of length of side of triangle ABC is = 4x - 3 ;

The perimeter of the triangle is = 63

So, According to the question,

(4x - 3) + (4x - 3) + (4x - 3) = 63

12x - 9 = 63

12x = 63 + 9

12x = 72

x = 72/12

x = 6

Therefore, the value of x in the given triangle  is 6.

-- The given question is incomplete, the complete question is

"Find the value of x, if the triangle ABC is an equilateral triangle with length of each side as (4x - 3), and the perimeter of the equilateral triangle ABC is 63 inches." --

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Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.

Two or more expressions with an Equal sign is called as Equation.

Given,

Distance = Rate x Time

Let Kala's swimming speed = X

4 km =   (X-2)×Time

12 km = (X+2) × Time

4/x-2 = 12/x+2

Apply cross multiplication

4(x+2)=12(x-2)

4x+8=12x-24

Take all variables on one side

4x-12x=-24-8

-8x=-32

Divide both sides by 8

x=4

Kala swims 4 km/hour

With the current he swims 6 km/hour

Hence, Against the current he swims 2 km/hours where he swims 4 km in the same 2 hours.

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Answer:

Previous meter reading: 2090

Charge per unit: 12p per unit

Step-by-step explanation:

Answer:

£43.26

Step-by-step explanation:

Given readings:

Calculate the number of units used:

[tex]\begin{aligned} \textsf{Number of units used} &= \textsf{Present meter reading} - \textsf{Previous meter reading}\\&= \sf 2410 - 2090\\&= \sf 320\; units \end{aligned}[/tex]

Given charges:

Calculate the cost excluding VAT:

[tex]\begin{aligned}\textsf{Cost (exc. VAT)}&=\textsf{(\# of units $\times$ charge per unit)}+\textsf{(\# of days $\times$ service charge per day)}\\ & = \sf 320 \times \£0.12 + 14 \times \£0.20\\&= \sf \£38.4+\£2.8\\&= \sf \£41.20\end{aligned}[/tex]

To find the total cost including VAT at 5%, multiply the cost (exc. VAT) by 1.05:

[tex]\begin{aligned}\textsf{Cost (inc. VAT at 5\%)}&= \sf \£41.20 \times 1.05\\&= \sf \£43.26\end{aligned}[/tex]

So one angle is of measurement 130 degree and the other angle is of measurement 50 degree.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "pening" between these two rays. It is symbolized by the character. The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question-

One angle's measurement is 15 less than its supplement's measurement.

Let's say that the supplement angle is measured in degrees.

So the measurement of the other angle is

And the sum of the measurement of supplementary angles is 180.

Multiplying both sides by 2

Therefore, one angle is 130 degrees in length and the other is 50 degrees.

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The sampling method is independent as the rain samples were taken from two different locations. As the sample sizes are small, they can be approximately considered normal distributions and t-test can be used to check the hypothesis.

Used in inferential statistics, t test can be used when we need to compare two different sets value to check if their is a significant difference between them.

T tests can be paired and dependent, like measuring the weight of a same patient before and after a diet or they can be unpaired an independent. Unpaired datasets might sometime have the same variance or unequal variance. Different formular are used to calculate the t-tests involving different datasets. To prove a null or alternate hypothesis, the t values must be checked with t- test table.

As the following datasets measuring rain pH at different cities are indepent and have unequal variances, the following formula should be used for calculating the t-score and the degree of freedom:

T-value= [tex]\frac{Mean1-Mean2}{\sqrt(\frac{var1}{n1})+(\frac{var2}{n2})}[/tex]

Substituing the values of Mean1=4.77; Mean2=4.50, Var1=0.1366, Var2= 0.0242, n1= 12, n2= 14, we get the t value as 2.27

Now calculating degree of freedom, which comes around

Δ=14

At x=0.05, from the table, t value=2.145

Hence as the calculated t vale is more than critical t value, null hypothesis can be rejected and alternate hypothesis can be accepeted proving that their is a significant visible difference in pH in the rain of Chicago and Huston.

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The z-score for the time spent on advertisement as calculated is 1.666 .

According to a television station, there is 15  minutes on average of advertising every hour of broadcast time, with a standard deviation of 1.2 minutes.

i.e.

mean = 15

SD =1.2

Per hour's worth of advertising is represented by the random variable x.

z = x - mean / SD

Since x=17 , we have

z = ( 17 - 15 ) / 1.2

  = 2 / 1.2

  = 1.666

Consequently, this amount of advertising time has a z-score of -1.666.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

A standard normal table is a mathematical table for the values of, displaying the values of the cumulative distribution function of the normal distribution. It is also known as the unit normal table or the z-score table. The Z-score, commonly referred to as the standard score, expresses how far away from the mean an object is.

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Container B needs to be filled faster in order for both containers to gain the same amount of water per minute , and by 1/6 water per minute .

Since water enters container A at a rate of 2/3 cup per 1/2 minute, then we can say that;

Rate of Filling container A = (2/3)/(1/2) = 4/3 cups per minute

We are also told that in container A, water leaks out at a rate of 1/4 cup per 3/4 minute. Thus;

Rate of leaking container A = (1/4)/(3/4) = 1/3 cups per minute

Amount of water in Container A in one minute = (4/3) - (1/3)

= 1

Similarly;

Since water enters container B at a rate of 3/4 cup per 1/2 minute, then we can say that;

Rate of Filling container B = (3/4)/(1/2) = 3/2 cups per minute

We are also told that in container B, water leaks out at a rate of 1/2 cup per 3/4 minute. Thus;

Rate of leaking container B = (1/2)/(3/4) = 2/3 cups per minute

Amount of water in Container B in one minute = (3/2) - (2/3) = 5/6

Since amount of water per minute in container A is 1 and the amount of water per minute in container B is 5/6 , then it means that container A fills faster by container B by; 1 - 5/6 = 1/6

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Complete question is;

two leaky containers are filling with water. water enters container a at a rate of 2/3 cup per 1/2 minute and leaks out at a rate of 1/4 cup per 3/4 minute. water enters container b at a rate of 3/4 cup per 1/2 minute and leaks out at a rate of 1/2 cup per 3/4 minute. which container needs to be filled faster in order for both containers to gain the same amount of water per minute? by how much more water per minute? explain