Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:

A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.

What is the maximum length of the seesaw?

1.4 meters
2 meters
0.5 meters
1 meter

Answer:

1.5, -1.5

Step-by-step explanation:

Using the quadratic formula, you should have a plus, and minus solution. These should be your answers.

The equation that satisfies the data in the table is,

y = -4x - 4 [Option D]

Definition of an Equation:

An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.

The (x, y) coordinates from the given table are,

(-1,0), (0, -4), (1, -8)

Now, these points must satisfy the required equation.

Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.

Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.

Taking the fourth equation, y = -4x - 4

Putting x = -1 in this equation, we get,

y = -4(-1) - 4

y = 4 - 4

y = 0

Likewise, this equation satisfies the rest of the data in the table too.

Therefore, y = -4x - 4 is the required equation.

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Answer:

There are 36 members in the Science Club.

Step-by-step explanation:

25 minus one is 24 and half of 24 is 12. 12 times 3 is 36, which is the full 3/3 of the Science Club.

The function to calculate the speed is S = 260.52/t.

From the information given, there are 78 laps through the Monte Carlo and each lap has a distance of 3.34 km. Therefore, the total length of the race will be:

= 78 × 3.34

= 260.52km

The function to calculate the speed will be:

Speed = Distance/Time

S = 260.52/t

Complete question:

The famous Grand Prix has 78 laps through the Monte Carlo and each lap has a distance of 3.34 km.

a. What is the total length of the race?

b. Write a function that can be used to model the race where the independent variable represent the average speed.

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Answer:

tan 33° = 0.6494

C = 65°

Step-by-step explanation:

Use a calculator.

tan 33° = 0.6494

cos C = 0.4226

Use the inverse cosine function on a calculator.

C = 65°

Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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The volume of the igloo is 523.43 m^3

We know that the volume of a sphere of radius R is:

[tex]V = (4/3)*pi*R^3[/tex]

Where pi = 3.14

Then the volume of a hemisphere is half of that.

In this case, we have a hemisphere with a radius of 6.3m, then the volume will be:

[tex]V = (1/2)*(4/3)*3.14*(6.3m)^3 = 523.43 m^3[/tex]

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The attached figures represent the shaded areas of the given set operations

To shade the given regions of the sets, we need to highlight the following set operations

Using the above definition of set operations and the Venn diagram, we have the following values:

See attachment for the shaded areas of the above set operations

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Answer:

2.0

Step-by-step explanation:

Skew lines and parallel lines do not intersect

As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect

Using the above definition as a guide, the skew lines in the figure are:

Parallel lines and skew lines are different in the following ways:

Parallel lines and skew lines are alike in the following way:

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Answer:

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m represents the slope and b represents the intercept.

x - 3y = 6

3y = x - 6

y = [tex]\frac{1}{3}[/tex]x - 2

4x - y = 1

y = 4x - 1

6x + 5y = -15

5y = -6x - 15

y = -[tex]\frac{6}{5}[/tex]x - 3

13x - 11y = -12

11y = 13x + 12

y = [tex]\frac{13}{11}[/tex] + [tex]\frac{12}{11}[/tex]

Answer:

1800(5/6)^t

Step-by-step explanation:

I don't see any answer choices, but this would be another form if it is listed. The negative exponent means that you get the reciprocal of the fraction (in this case 1.2). This turns 1.2 into (1/1.2), which is equivalent to 5/6.

The researchers could utilize a probability sample.

Meaning of a Probability Sample

Every member of a population must have an equal chance of being chosen for a study in order for a sample to be considered a probability sample, and the researcher must be aware of this likelihood. The most typical type of sampling used in public opinion research, election polling, and other studies whose findings will be generalized to a larger population is probability sampling in which probability samples are made use of.

Probability Sample as the Representative of Population Sample

Here, a sample that qualifies for a representative of the population the researchers are studying, must consist of members having equal chances to be chosen for the study. Thus, a probability sample is the best representative of their study population.

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Answer: y=-1/5x+ 8/5    (Third one down)

Answer:

[tex]0,35[/tex]

Step-by-step explanation:

In view of the fact that our events are independent of each other, we should multiply their probabilities: [tex]P(A \cap B) = P(A) * P(B) = 0,7 * 0,5 = 0,35[/tex].

Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.

The relations in a right triangle are given as follows:

In this problem, we have that:

Hence:

[tex]\sin{\alpha} = \frac{10}{12}[/tex]

[tex]\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}[/tex]

[tex]\alpha = 56.4^\circ[/tex].

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Answer:

1.

x=-10

x=-6

2.

x=10

x=-3

Step-by-step explanation:

to find the zeros of a function you need to set it equal to zero:

x^2+16x+60=0

then you factor

(x+10)(x+6)=0

then you have to finish factoring/simplifying

x+10=0

  -10

x=-10

x+6=0

 -6

x=-6

and the same thing for number 2

x^2-7x-30=0

(x-10)(x-3)=0

x=10, x=3

Answer:

1.) x = -10, x = - 6

2.) x = 10, x = -3

Step-by-step explanation:

1.) factorize and set the equation to zero by multiplying a and c and finding factors of it that will result in b once added/subtracted

[tex]x^2+16x+60\\(x+10)(x+6)\\(x+10)(x+6)=0\\x=-10, x=-6[/tex]

2.) do the same for number 2:

[tex]x^2-7x-30\\(x-10)(x+3)\\(x-10)(x+3)=0\\x = 10, x = -3[/tex]

i hope this helped!

The value of the probability P(A and C) is 0.18

The complete question is added as an attachment

From the attached tree diagram, we have:

P(A) = 0.6

P(C) = 0.3

The required probability is then calculated as:

P(A and C) = P(A) * P(C)

This gives

P(A and C) = 0.6 * 0.3

Evaluate

P(A and C) = 0.18

Hence, the value of the probability P(A and C) is 0.18

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Answer:

he buts 20 protein bars and 40 water bottles

Step-by-step explanation:

so first u set up an equation like this

46=.90x+.70(2x)

next you multipy

46=.90x+1.4x

Then add

46=2.3x

then divide by 2.3 to solve for x

x=20 so u have 20 protein bars

and 20 times 2 to find the amount of water bottles

Answer:

20 Protein bars and 40 waters.

Step-by-step explanation:

Let x = protein bars and y = waters

y = 2x          .9x + .7 y = 46

Looking at the second equation, I would rather not work with decimals, so I will multiple the whole equation through by ten.  That now gives m

9x + 7y = 460 Substitute in 2x for y (from my first equation above)

9x + 7(2x) = 460

9x +14x = 460  Combine 9x and 14x

23x = 460  Divide both sides by 23

x = 20  This is the number of protein bars.  To find y plug 20 into the first equation above.

y = 2x

y =20(2)

y = 40

The height that should be used is DE

From the question, we are to determine what should be used as the height

The area of a parallelogram is given by the formula,

A = b × h

Where A is the area

b is the base

and h is the perpendicular height

In the given diagram, if AB is used as the base, then the height that would be used will be DE. This is because DE is perpendicular to AB

Hence, the height that should be used is DE

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The value of the expression [tex]2 \div 6.3[/tex] is 0.32

The expression is given as:

[tex]2 \div 6.3[/tex]

Rewrite as:

[tex]2 \div 6.3= \frac{2}{6.3}[/tex]

Multiply the expression by 10/10

[tex]2 \div 6.3= \frac{20}{63}[/tex]

Divide 20 by 63

[tex]2 \div 6.3= 0.31746031746[/tex]

Approximate to the nearest hundredth

[tex]2 \div 6.3= 0.32[/tex]

Hence, the value of the expression [tex]2 \div 6.3[/tex] is 0.32

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Answer:

Step-by-step explanation:

The area of a circle is πr²

so your area is 114.99

The equation of the logarithmic function is y = log(x - 1)

The points are given as:

(0,3) and (2,0)

The equation is represented as:

y = A log(x + B)

Substitute (2,0) in y = A log(x + B)

y = A log(x + B)

This means that:

0 = A log(2 + B)

This means that:

A = 0 or log(2 + B) = 0

Take the antilog of both sides of log(2 + B) = 0

2 + B = 1

Solve for B in 2 + B = 1

B = -1

Substitute B = -1 in y = A log(x + B)

y = A log(x - 1)

Substitute (0,3) in y = A log(x - 1)

3 = A log(0 - 1)

So, we have:

3 = A log(-1)

The above equation is undefined.

Hence, the equation of the logarithmic function is y = log(x - 1)

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Complete question

Write an expression, of the type A log(x + B), for the transformed logarithmic function shown below:

(0,3) and (2,0)

The amount invested in the account that has a rate of 14% is $1767

The amount invested in the account that has a rate of 6% is $1425.

0.06a + 0.14b = 342 equation 1

b - a = $950 equation 2

Where:

a = amount invested in the account that has a rate of 6%

b =  = amount invested in the account that has a rate of 14%

Multiply equation 2 by 0.06

0.06b - 0.06a = 57 equation 3

Subtract equation 3 from equation 2

285 = 0.2a

a = 285 / 0.2

a = 1425

Substitute for a in equation 2

b - 1425 = 342

b = 1425 + 342

b = $1767

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The correct statement based on the data is: A. Mean, because there are no outliers to affect the data.

Outliers are data point that appears extreme from other data values of a data distribution. When there is an outlier in a data distribution, the median is a better measure of center, while the mean is best when outliers are absent.

From the data distribution for both bakeries, no data seem extreme from the rest of the data, therefore, the mean is a better measure of center.

The answer is: A. Mean, because there are no outliers to affect the data.

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The correct option is (2)  [tex]\frac{8}{5}[/tex] and (3)  [tex]\frac{1}{6}[/tex].

The factor of equation  f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

[tex]$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.[/tex]

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex] can be written in the form:  

[tex]\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}[/tex]

Therefore, the rational roots of polynomial f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

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The complete question is-

Which is a factor of f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8? use the rational root theorem to help you find your answer.

The sum of a+b+c = 307.

According to the statement

[tex]$\sqrt[3]{\sqrt[3]{54}+\sqrt[3]{250}}$[/tex] is written as [tex]$a\sqrt[b]{c}$[/tex]

now we find the sum of these

in these terms a=54 and b=3 and c=250

Then

a+b+c = 54+3+250

a+b+c = 307

So, The sum of a+b+c = 307.

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The equivalent expressions indicated are;

1) 1/a^6b^4

2) a^6/b^6

3) a^6/b^5

4) b^6/a^6

5) a^5b^3

We have to note that when we talk about the equivalent expressions, we mean the expressions that we have to get from each other when we carry out a little computational work on the original expression.

Thus, the equivalent expression has shown that the expression that is in the bracket is the same as the original expression by the use of the laws of exponents.

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Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0,2) ← 2 points on the line

m = [tex]\frac{2-0}{0-(-1)}[/tex] = [tex]\frac{2}{0+1}[/tex] = [tex]\frac{2}{1}[/tex] = 2