Suppose that you're designing a concrete patio. The patio will have height of 6 inches (1/2 foot) and have a rectangular base with a perimeter of 70 feet. If you have 138 cubic feet of concrete, what are the dimensions of the concrete patio?

The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Answer:

the mean is 8

Step-by-step explanation:

added them all together and divided by 7

The mean of numbers will be 8.

What is Addition?

The process of combining two or more numbers is called the Addition.

Given that;

The numbers are,

⇒ 5,6,12,2,5,12,14

Now,

Since, The numbers are,

⇒ 5,6,12,2,5,12,14

Hence, The mean = 5 + 6 + 12 + 2 + 5 + 12 + 14 / 7

                             = 56/7

                             = 8

Thus, The mean of numbers will be 8.

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The scale factor used to dilate triangle D to create triangle D' is 1/3. This means that each side length in triangle D' is one-third of the corresponding side length in triangle D.

To determine the scale factor used to dilate triangle D to create triangle D', we can compare the corresponding side lengths of the two triangles.

In triangle D, the side lengths are given as 18, 24, and 30. In triangle D', the corresponding side lengths are given as 6, 8, and 10.

To find the scale factor, we can divide the corresponding side lengths of D' by the corresponding side lengths of D.

Scale factor = Length of corresponding side in D' / Length of corresponding side in D

For the corresponding sides, we have:

Scale factor = 6/18 = 1/3

Please note that the scale factor can also be determined by comparing the area or perimeter of the two triangles. However, in this case, we used the corresponding side lengths to find the scale factor.

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Answer:

m<JMK = 54

m<JKH = 63

m<HLK = 90

m<HJL = 27

m<LHK = 63

m<JLK = 27

Step-by-step explanation:

1. Solve for m<JMK

It is given that (<HMJ) and (<JMK)  form line (HK), meaning that they are supplementary angles. Thus, their degree measures add up to (180), using this one can form the following equation,

(<HMJ) + (<JMK) = 180

126 + (<JMK) = 180

(<JMK) = 54

2. Solve for m<JKH

It is given that the figure is a rectangle, one of the properties of a rectangle is that diagonals are congruent, and the diagonals bisect each other. This means that segments (JM) and (MK) are congruent. Hence, the triangle (JMK) is an isoceles triangle. Therefore, one can use the base-angles theorem, which states that (<MJK) is congruent to (<JKH). Since the sum of angle measures in any triangle is (180), one can form the following equation,

(<JMK) + (<MJK) + (<JKH) = 180

54 + 2(<JKH) = 180

<JKH = 63

3. Solve for m<HLK

As per its definition, the corner angles in a rectangle are always (90) degrees, this property is applicable for the given rectangle. Thus, (<HLK) = 90 degrees.

4. Solve for m<HJL

To solve for this angle, one can use similar logic as they did to solve for (<JKH).  Form the following equation and solve,

(<HMJ) + (<HJL) + (<JHK) = 180

126 + 2(<HJL) = 180

(<HJL) = 27

5. Solve for m<LHK

The vertical angles theorem states that when two lines intersect, the opposite angles are congruent. One can apply this theorem here and say (<JMK) = (<HML). Then, to solve for this angle, one can use the same logic that they used to solve for (<JKH) and (<HJL). Form the equation and solve,

(<HML) +(<LHK) + (<HLJ) = 180

54 + 2(<LHK) = 180

<LHK = 63

6.Solve for m<JLK

To solve for this angle, one can use the same logic that they used to solve for (<LHK). Form the equation and solve,

(<LMK) + (<JLK) + (HKL) = 180

126 + 2(<JLK) = 180

<JLK = 27

The mystery divisor to the question based on the information given is 18.

Dividing the first dividend 4 by the unknown divisor x and getting the first number 2 in the quotient and when the quotient 2 is multiplied by the divisor gives 36, so definitely, 4 cannot be used

Using 40 as the dividend, 40 divided by the divisor x gives 2 as the first quotient. And the first quotient 2 multiplied by the divisor x gives 36.

And to interpret this, 2x=36

Dividing through by 2x=36

x = 36/2

x = 18

So, the divisor is 18

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The solution is

a) The number is 6

b) The equation of the parabola is y = x² + 4x + 96 with vertex ( -2 , 92 ) and the y intercept is ( 0 , 96 ) and the axis of symmetry is x = -2

What is a Parabola?

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

a)

Let the equation be represented as A

Now , the value of A is

Let the number be = n

A = Two-fifth of the sum of a number and 24 is equal to 5 times the number decreased by 18

Substituting the values in the equation , we get

2/5 ( n + 24 ) = 5n - 18

On simplifying the equation , we get

Multiply by 5 on both sides of the equation , we get

2 ( n + 24 ) = 25n - 90

2n + 48 = 25n - 90

Subtracting 2n on both sides of the equation , we get

23n - 90 = 48

Adding 90 on both sides of the equation , we get

23n = 138

Divide by 23 on both sides of the equation , we get

n = 6

Therefore , the number is 6

b)

The equation of parabola is given as

y = x² + 4x + 96

Now , the equation can be simplified as

y = (x + 2)² + 92

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

Substituting the values in the equation , we get

The vertex of the parabola is P ( -2 , 92 )

The y intercept of the parabola is ( 0 , 96 )

The axis of symmetry of parabola is x = -2

Hence , the equation of parabola is y = (x + 2)² + 92

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Note that the parameters of the graph a and graph b are given below.

Graph A - y=2(x-1)²

See graph attached.

Graph B - y = 1/2x² + 3

Vertex: The vertex of the function is (0, 3).

Axis of symmetry: The axis of symmetry is the vertical line passing through the vertex, which is x = 0.

Y-intercept: The y-intercept is the point where the graph intersects the y-axis. It is (0, 3).

Minimum or maximum: The coefficient of x² is positive, which means the parabola opens upwards, and therefore the function has a minimum value. The minimum value is 3.

Solutions: To find the solutions or roots of the quadratic equation, we need to set y or f(x) equal to zero and solve for x.

0 = 1/2 x² + 3

Subtracting 3 from both sides, we get:

-3 = 1/2 x²

Multiplying both sides by -2, we get:

6 = -x²

Taking the square root of both sides, we get:

x = ±√(-6)

Since the square root of a negative number is not a real number, the function has no real roots.

Minimum or maximum value: The minimum value of the function is 3.

Range: The range of the function is y ≥ 3, because the function has a minimum value of 3.

Domain: The domain of the function is all real numbers, because there are no restrictions on the values of x for which the function is defined.

Stretch/Shrink/Standard: The coefficient of x^2 is positive and less than 1, which means that the graph of the function is narrower than the graph of y = x². This is an example of a standard quadratic function that has been vertically compressed by a factor of 1/2.

See graph attached.


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Answer:

C. 38cm

Step-by-step explanation:

hope this helps

Answer: 125/27 as a decimal 4.62963

Step-by-step explanation:

((32)(5−2))−2(3(5−1))

((32)(5−2))−2(3(5−1))

Answer:

x=0

Step-by-step explanation:

x = amount (kg) of 25% coper alloy

y = amount (also kg) of 70% copper alloy

Each kilogram of the 25% alloy contains 0.25 kg of copper, while each kilogram of the 70% alloy contains 0.7 kg of copper. When combined, the metalworker ends up with (x + y) kg of an alloy that should consist of 52% copper, so that it contains 0.52 (x + y) kg of copper.

The metalworker wants to make 50 kg of this new alloy, so that

x + y = 50

of which 52%, 0.52 (50 kg) = 26 kg, is copper, so

0.25x + 0.7y = 26

Solve for y in terms of x :

y = 50 - x

Substitute this into the other equation and solve for x :

0.25x + 0.7 (50 - x) = 26

0.25x + 35 - 0.7x = 26

9 = 0.45x

x = 20   →  y = 30

Answer:

Savings

Step-by-step explanation:

If you don't have a lot of money in general and an emergency occurs savings is the easiest way to go because you money money saved up for issues like these. But if u don't even have a savings account credit cards might be the way to go but it will damage your credit score pretty badly. So Savings is my final answer.

A statistical question that can result in numerical data is How many times did you go swimming this year? So, the correct option is A).

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?" and "How many times did you go swimming this year?".

These questions involve counting or measuring quantities, which can be represented using numerical data. The other two questions do not involve numerical data and therefore cannot be considered statistical questions that result in numerical data. So, the correct answer is B).

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Answer:

How many pink erasers do the students in your class have?

Answer:

40000, 20000

Step-by-step explanation:

Let the amount a grandchild receives be \(x\). Then, the amount a child receives is \(2x\).

Thus, \(220000=2(2x)+7x=11x \implies x=20000\).

This means each grandchild gets $20,000 and each child gets $40,000.

Answer:

1.6538461538461538461538461538462

Step-by-step explanation:

I don't get is it dividing?

The standard error tells us how much we can expect the sample proportion to vary from the true proportion in repeated samples of the same size. Option (d) correctly states that "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion." This means that if we were to take many samples of 100 students from the same school and calculate the proportion of students who bring a reusable water bottle from home in each sample, about 95% of the sample proportions would fall within +/-0.048 of the true proportion.

The correct option is (d) "In samples of size 100 from this school, the sample proportion of students who bring a reusable water bottle from home typically varies by about 0.048 from the true proportion."

The standard error of the sample proportion can be calculated using the formula:

SE = √[p*(1-p) / n]

where p is the sample proportion and n is the sample size.

In this case, the sample proportion is 37/100 = 0.37 and the sample size is 100. Plugging in these values, we get:

SE = sqrt[0.37*(1-0.37) / 100] = 0.048

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The number of whole cup of milk that Charlene would use for all 8 packages would be = 8 cups of whole milk.

A square is a type of quadrilateral that has four sides with four angle 90° at each edge.

The number of chocolate square mixture Charlene would use for the party = 8 packages.

The number of packages that require a cup of milk = 1

Therefore the number of whole cups of milk that would be used for the whole 8 packages would be = 8×1 = 8 cups of whole milk.

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Answer:

0.36363.....

repeating

Step-by-step explanation:

given :

total songs downloaded = 44

total favorite band songs = 16

number of favorite songs out of total songs downloaded

= total favorite band songs ÷ total songs downloaded

= 16 ÷ 44

= 0.3636363636363636363...  (answer for part A)

by observation, we can see that the decimals 36 repeats over and over again and never stops. Hence we can say that the decimal is repeating (Answer for part B)

Answer:

1/5x

Step-by-step explanation:

1/5x

Answer:

D 105%

Step-by-step explanation:

As 1.05=105/100%

To express as a percentage - you have to multiply it with 100,

→ 1.05 × 100

→ 105% {final answer}

Thus, D. 105% is the correct answer.

Answer: B

Step-by-step explanation:

Add 47.6 and 7.32 to get 54.92.

Add 54.92 and 0.0574 to get 54.9774.

Add 54.9774 and 6 to get 60.9774.

We conclude that the correct option is alternative "B".

The balance for each value of n is calculated by using the formula A = P(1 + r/n) ^nt. The rounded balance values are shown in the last column of the table above.

To complete the table and find the balance A if $3100 is invested at an annual percentage rate of 4% for 10 years and compounded n times a year.

The formula for calculating compound interest is as follows:

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

where P represents the principal investment amount, r is the interest rate, n is the number of times the interest is compounded, t represents the time in years, and A represents the total amount, which includes the principal amount and the interest earned.

The table is given below:
\(\begin{array}{|c|c|c|} \hline \text{n} &

\text{A = P(1 + r/n) }^{nt} &

\text{Balance (rounded to nearest cent)} \\ \hline \text{1} &

\text{3100(1 + 0.04/1)}^{1*10} &

\text{\$4788.03} \\ \hline \text{2} &

\text{3100(1 + 0.04/2)}^{2*10} &

\text{\$4798.76} \\ \hline \text{4} &

\text{3100(1 + 0.04/4)}^{4*10} &

\text{\$4817.46} \\ \hline \text{12} &

\text{3100(1 + 0.04/12)}^{12*10} &

\text{\$4861.94} \\ \hline \end{array}\)

The balance is obtained by substituting the values of P, r, n, and t into the compound interest formula.

In this case, the investment is $3100, the annual interest rate is 4%, the investment is for 10 years, and n is the number of times the interest is compounded.

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Answer:

the answer to your problem is 5/7.

The graph demonstrates that local producers will provide 8,000 tonnes of apricots at the global price of $400 per tonne.

A graph is a visual representation of data that's frequently used to demonstrate how variables relate to one another or to show how trends change over time. Graphs can come in many various forms, including line graphs, bar graphs, pie charts, scatter plots, and more. Graphs are frequently used to simplify the presentation of complicated data in disciplines like economics, mathematics, science, and the social sciences.

given

The graph indicates that the cost of apricots in the globe is $400 per tonne. In the absence of the quota, the US would purchase 5,000 tonnes of apricots at the market rate. The United States will only be permitted to acquire 3,000 tonnes of apricots under the quota, though.

As a result of this quota, the United States will purchase 3,000 tonnes of apricots at the world price.

The graph demonstrates that local producers will provide 8,000 tonnes of apricots at the global price of $400 per tonne.

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Answer:

the first one is no it's nonproportional

and the second one it yes its proportional

Answer:

1. No it is nonproportional

2. Yes, it is proportional

Step-by-step explanation:

To find the ratio, divide the number of oranges with the total cost. If you get equal ratio(s) then the data is proportional.

Answer:

Midsegment=1.7

Step-by-step explanation:

Distance formula

d = √(x2 - x1)^2 + (y2-y1)^2}

d=√(4-(-2)^2+(3-4)^2

simplify and solve

we find d=1

Now side lenght

d=√((-2-(-2))^2+(4-(-2))

d=2.44949

length of midsegment=1/2 x (2.44949+1)

1.724745

simplifies to

1.7

Answer:

Midsegment is 1.7

Step-by-step explanation: