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2 years ago

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Mathematics

1 answer:

Arada [10]2 years ago

8 0

The exponential function f(x) can represent growth or decay

The value of f(14) is 226.07

<h3>How to determine the value of f(14)?</h3>

The given parameters are:

f(-2) = 25 and f(7) = 85

An exponential function is represented as:

f(x) = ab^x

So, we have:

ab^-2 = 25

Also, we have:

ab^7 = 85

Divide both equations.

This gives

b^9 = 3.4

Take the 9th root of both sides

b = 1.15

Recall that:

ab^7 = 85

This gives

a* 1.15^7 = 85

Solve for a

a = 31.95

So, the exponential function is:

f(x) = 31.95 * 1.15^x

Substitute 14 for x

f(14) = 31.95 * 1.15^14

f(14) = 226.07

Hence, the value of f(14) is 226.07

Read more about exponential functions at:

brainly.com/question/11464095

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According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47.

UNO [17]

Answer:

Probability that the proportion of Americans who can order a meal in a foreign language is greater than 0.5 is 0.19766.

Step-by-step explanation:

We are given that according to a study done by Wake field Research, the proportion of Americans who can order a meal in a foreign language is 0.47.

Suppose a random sample of 200 Americans is asked to disclose whether they can order a meal in a foreign language.

Let $\hat p$ = sample proportion of Americans who can order a meal in a foreign language

The z-score probability distribution for sample proportion is given by;

Z = $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion

p = population proportion of Americans who can order a meal in a foreign language = 0.47

n = sample of Americans = 200

Probability that the proportion of Americans who can order a meal in a foreign language is greater than 0.5 is given by = P( $\hat p$ > 0.50)

P( $\hat p$ > 0.06) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ > $\frac{0.5-0.47}{\sqrt{\frac{0.5(1-0.5)}{200} } }$ ) = P(Z > 0.85) = 1 - P(Z $\leq$ 0.85)

= 1 - 0.80234 = 0.19766

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.85 in the z table which has an area of 0.80234.

Therefore, probability that the proportion of Americans who can order a meal in a foreign language is greater than 0.5 is 0.19766.

4 0

4 years ago

The endpoints of the directed line segment AB are A(−7, 4) and B(8, 9). Find the coordinates of point P along line segment AB so

bekas [8.4K]

Answer:

(-1,5)

Step-by-step explanation:

When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:

The coordinates of x and y are:

$(x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)$

Given:

$A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3$

The coordinates of P is:

$(x,y)=\left(\dfrac{2*8+3*-7}{2+3}, \dfrac{2*9+3*4}{2+3}\right)\\=\left(\dfrac{-5}{5}, \dfrac{25}{5}\right)\\\\=(-1,5)$

7 0

3 years ago

(.75/0.03-23.5)/1.5*2/3+7/6 WILL GIVE BRAINLIEST PLEASE HELP QUICK

ra1l [238]

Answer:

th answer is 1.83333333

6 0

4 years ago

Compute the exact value of the function for the given x-value without using a calculator. f(x) = 4x for x = -1

bija089 [108]

So when x = -1, you just substitute the variable x to -1.

"4x" means 4 times x, so when x is replaced to -1, that would be 4 times -1.

f(-1) = 4(-1) = -4

So the value of function at x = -1 would be -4.

Hope this helps.

3 0

4 years ago

Translate and solve using proportions 6.5% of what number is $3.77

marshall27 [118]

Answer:

The quantity is US$ 58, which 6.5% is US$ 3.77

Step-by-step explanation:

Number = x

6.5% of x = $ 3.77

6.5% = 0.065 = 65/1,000 = 13/200 (Dividing by 5)

3.77 = 3 + 77/100 (We can't simplify 77/100)

Thus,

13/200 * x = 3 77/100

13x/200 = 377/100

13x = 754 (Multiplying by 200 at both sides)

x = 754/13 (Dividing by 13 at both sides)

x = 58

7 0

4 years ago