The cable for a certain suspension bridge is modeled by a parabola with vertex (0,0) at the center of the bridge. At a point that is 150 ft from the center of the bridge, the height of the cable is 30 ft. Which equation represents the height of
the cable at a distance x feet from the center?

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

             {4,  6}

      C) -  The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

MAKE A PLAN:

List The OUTCOMES for EACH EVENT and their COMBINATIONS:

        a) -  EVENT  "A":  {2, 4, 6, 8}

               EVENT "B":   {3, 4, 5, 6}

               EVENT "A" or "B": {2, 3, 4, 5, 6, 8}

        b) - EVENT "A"  or "B":  {4, 6}

        c) -  The COMPLEMENT of the EVENT "A":  {1, 3, 5, 7}

       A) -  Event  "A  or  B"  Consists  of  the Outcomes:

               {2, 3, 4, 5, 6, 8}

      B) - Event  "A  or  "B"  Consists  of the Outcomes:

            {4,  6}

      C) - The "COMPLEMENT  of EVENT  "A"  Consists of the Outcomes:

             {1, 3, 5, 7}

I hope this helps!

Answer:

10 units

Step-by-step explanation:

The diagnonals of a rhombus meet at right angle to their selves and bisect each other.

So one quarter will form a right angle triangle of base 6 and height 8.

Let The length of one side of the rhombus be x

X²= 8²+6²

X²= 64+36

X²= 100

X= √100

X= 10 units

Answer:

answer is C. 10 units. Just took the test

Step-by-step explanation:

Answer:

supplementary

linear

Step-by-step explanation:

The population of North Carolina will reach 12 million in the year 2028.

Population growth is defined as the increase in the number of people which is calculated using population growth rate.

Given that,

Population in 2010 = 9.5 million

Population is increasing to 1.3% per year.

Annual growth rate = 1.3% = 1.3/100 = 0.013

We have the population growth formula,

P = P₀ e^(r t)

Here, P₀ = 9.5 million = 9,500,000

and P = 12 million = 12,000,000

r = 0.013

We have to find t.

12,000,000 = 9,500,000 e^(0.013t)

120 / 95 = e^(0.013t)

Taking natural logarithm on both sides and also ㏑(e^m) = m ㏑ e, we get,

㏑(12/9.5) = 0.013t × ㏑e

[㏑(12/9.5) ÷ 0.013] = t  [since ln e = 1]

t = 17.97 ≈ 18 years

The year is 2010 + 18 = 2028

Hence in the year 2028, the population will be 12 million.

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Answer:

length is 5cm

area is 15cm^2

perimeter is 16cm

Answer:

  x = 31.2

Step-by-step explanation:

You want the solution to the proportion 12/x = 5/13.

You can eliminate the fractions by multiplying this equation by the least common denominator. That value is 13x, the product of these denominators. Multiplying by 13x, we have ...

  \(\dfrac{12}{x}\times13x=\dfrac{5}{13}\times13x\\\\\\12\cdot13=5\cdot x\qquad\text{simplified}\)

Now, the value of x is found by dividing both sides by its coefficient.

  \(\dfrac{12\cdot13}{5}=\dfrac{5x}{5}\\\\\\\dfrac{156}{5}=x\\\\\boxed{31.2=x}\)

__

Additional comment

The first step we did, multiplying by 13x, is also sometimes called "cross multiplication." The result of that step is that each numerator is multiplied by the opposite denominator.

Multiplying both sides of the equation by the same value (13x) is supported by the multiplication property of equality. The term "cross multiplication" is descriptive of the result, but is not a recognized property of equality. It is a good idea to keep the math operations you do grounded in the properties of equality.

You will notice that the steps we did were "multiply by 13x" and "divide by 5". These can be done at once by "multiply by 13x/5". Of course, that operation is done to both sides of the equation.

Any proportion can be written 4 ways:

  \(\dfrac{12}{x}=\dfrac{5}{13}\qquad\dfrac{x}{12}=\dfrac{13}{5}\qquad\dfrac{x}{13}=\dfrac{12}{5}\qquad\dfrac{13}{x}=\dfrac{5}{12}\)

These can be thought of as "upside down" and "sideways." We like the versions with the variable on top of a fraction, because the solution to that is simply multiplication by the variable's denominator.

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Answer:

a number plus five times two

Step-by-step explanation:

a number plus five times two

Answer:

x is -1/b yw

Step-by-step explanation:

The value of y is 48.

To find the value of y in this scenario, we need to use the fact that the angle bisector of ∠JSL splits it into two congruent angles.

Let's denote one of these congruent angles as ∠HSL and the other as ∠LSJ. Since ∠JSL is bisected, we have:

m∠JSL = m∠HSL + m∠LSJ

Given that m∠JSL = (4y - 10)° and m∠HSL = m∠LSJ = ∠HSJ = (y + 43)°, we can substitute these values into the equation:

4y - 10 = (y + 43) + (y + 43)

Simplifying the equation:

4y - 10 = 2y + 86

Subtracting 2y from both sides:

2y - 10 = 86

Adding 10 to both sides:

2y = 96

Dividing both sides by 2:

y = 48

Therefore, the value of y is 48.

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Answer:

g(f(4)) = -3

Step-by-step explanation:

f(x)=x-7

g(x) = x

g(f(4))

f(4) = 4-7

f(4) = -3

g(-3) = -3

Answer:

11 buses

Step-by-step explanation:

=> 22+10x

=> 2(5x+11)

This is the answer for your question

Answer:

Yes

Step-by-step explanation:

Find the GCF of 22 and 10.

22 - 1, 2, 11, 22.

10 - 1, 2, 5, 10.

The GCF is 2.

22/2=11

10/2=5

So the factorized expression is 2(11+5x)

-hope it helps

Answer:

its b4 + 7b3 + 4b2 + b5 + 7b4+ 4b3= b5+8b4+11b3+4b2

Answer:

When multiplying, add the exponents, (example) remember if there is "7b" the exponent is one.

Multiply b^2 * b^3 = b^5  (add the exponent 2 + 3 = 5)

Multiply 7b * b^3 = 7b^4 (the exponent of 7b is one, add 1 + 3 for the exponent to become 4)

Multiply 4 * b^3 = 4b^3 (4 doesn't have a variable, the exponent will be 3)

b^2 * b*2 = b^4 (add exponents)

7b * b^2 = 7b^3 (add the exponents 1 + 2)

4 * b^2 = 4b^2

              b^2             +               7b             +        4

b^3           b^5              +           7b^4            +   4b^3

+                                                                                      

b^2           b^4             +           7b^3            + 4b^2

b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2

\(b^5 + 7b^4 + 4b^3 + b^4 + 7b^3 + 4b^2\)

Answer:

log(3x⁹y⁴) = log 3 + 9 log x + 4 log y

Answer:

\(\log 3+ 9\log x +4 \log y\)

Step-by-step explanation:

Given logarithmic expression:

\(\log 3x^9y^4\)

\(\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay\)

\(\log 3+\log x^9 +\log y^4\)

\(\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax\)

\(\log 3+ 9\log x +4 \log y\)

Systematic random sampling involves a selection technique in which samples are selected at fixed intervals. Hence, the true statement is "Systematic random sampling can be used, even if knowledge of the entire population is not known."

However, without knowing the entire population size, systematic random samples could be selected from the population.

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The 99% confidence interval for the population proportion p is (0.776, 0.824).

To find the 99% confidence interval for a proportion, we can use the formula:

CI = p^ ± z*(SE)

where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.

For a 99% confidence interval, the critical value z is 2.576.

Substituting the given values into the formula, we have:

CI = 0.80 ± 2.576*(0.03/√200)

Simplifying this expression, we have:

CI = 0.80 ± 0.024

This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.

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The range of the equation f(x) = 3ˣ ⁻ ¹ - 2 is  y > -2

From the question, we have the following parameters that can be used in our computation:

f(x) = 3ˣ ⁻ ¹ - 2

The above equation is an exponential function

The rule of an exponential function is that

In this case, it is -2

So, the range is y > -2

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For percentages, we divide the part by the whole. In this case, the part is the number of calories from fat and the whole is the total number of calories.

10 / 210 = 0.0476 = 4.76%

Then, we need to round to the nearest tenth.

The answer is 4.8%

Hope this helps!

The probability that their mean length is less than 17.4 inches is 28.26%

Given :

A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches , If 25 items are chosen at random .

z = ( X - μ ) / σ, where X = date , μ = mean , σ = standard deviation .

substitute the values

z = 17.4 - 19.7 / 4

= -2.3 / 4

= -0.575

P - value at z = -0.575 is 0.2826

Converting into percentage :

= 0.2826 * 100%

= 28.26 %

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Answer:

The second one is right

The third one is wrong.

Answer:

a

Step-by-step explanation:

the data is represented in the dot plot

Answer:

answer is 77.67

Step-by-step explanation:

explain by the x axis is 68 to y axis is 84 so the median is 77.67

Answer:

-7

Step-by-step explanation:

-9x-3=60

add 3 to each side to cancel -3

-9x-3+3=60+3

simplify

-9x=63

divide by -9 to cancel the -9

-9x/-9=63/-9

simplify

x=-7

Answer:

-14

Step-by-step explanation:

I might be wrong, but this is my interpretation of the problem.

To solve this problem, find the endpoints of the line in the interval. Then draw a line between those two points. Finally, find the slope of the line that passes between the two points.

The line is f(x) = -2x^(2) + 2x + 1

The interval (in standard notation) is (3 \(\leq\) x \(\leq\) 5)

So when x = 3,

-2x^(2) + 2x + 1

-2(3)^(2) + 2*3 + 1

-2 * 9 + 6 + 1

-18 + 7

- 11

One endpoint is: (3, -11).

When x = 5

-2x^(2) + 2x + 1

-2(5)^2 + 2*5 + 1

-2 * 25 + 10 + 1

-50 + 11

-39

The other endpoint is; (5, -39).

Find the slope of a line passing through these two points.

The formula to find the slope of a line is:

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

\(x_{1}\) = 3

\(y_{1}\) = -11

\(x_{2}\) = 5

\(y_{2}\) = -39

((-39) - ( -11))/((5) - (3))

Simplify

-28/2

-14

Answer:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

Step-by-step explanation:

Since the ratio of fruit mass to biscuit mass is 2:3, the fraction of fruit mass to the total of fruit and biscuit mass is 2/5 and the fraction of biscuit mass to the total of fruit and biscuit mass is 3/5.

For Monkey A, the total of fruit and biscuit mass is 73 g, which means that the fraction of fruit mass is 2/5 × 73 g = 29.2 g and the fraction of biscuit mass is 3/5 × 73 g = 43.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 29.2 g

Biscuit mass = 43.8 g

For Monkey B, the total of fruit and biscuit mass is 73 + 85 = 158 g, which means that the fraction of fruit mass is 2/5 × 158 g = 63.2 g and the fraction of biscuit mass is 3/5 × 158 g = 94.8 g. Therefore, the values for fruit mass and biscuit mass are:

Fruit mass = 63.2 g

Biscuit mass = 94.8 g

Answer:

Step-by-step explanation:

$3.75 (Bauer) + 5*2 (2 friends) = $13.75

20 - 13.75 = $6.25 in change

Answer:

The brightest star in the night sky is Sirius, located 500,000 times further away than the sun. Sirius is also 20 times brighter than the sun, which is why it is so easy to see at night. Our sun is a medium star of average size and brightness.