Alicia is 7 years old. She is 1 year older than
one-eighth the age of her father. How old is
Alicia's father?

1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x

2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x

3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1

4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x

5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x

6.  When we simplify cos x + sin xtan x, the result obtained is sec x

We can simplify the trig identities as follow:

1. Simplification of sec² x + tan² xsec² x

sec² x + tan² xsec² x = sec² x(1 + tan² x)

Recall

sec² x = 1 + tan² x

Thus,

sec² x(1 + tan² x) = sec² x × sec² x

sec² x(1 + tan² x) = sec⁴x

Therefore, the simplified is written as

sec² x + tan² xsec² x = sec⁴x

2. Simplification of (sec² x - 1) / sin² x

(sec² x - 1) / sin² x

Recall,

sec² x - 1 = tan² x

Thus,

(sec² x - 1) / sin² x = tan² x / sin² x

Recall

tan² x = sin² x / cos² x

Thus,

tan² x / sin² x = (sin² x / cos² x) / sin² x

tan² x / sin² x = 1/ cos² x

Recall

1/ cos² x = sec² x

Therefore, the simplified expression is written as:

(sec² x - 1) / sin² x = sec² x

3. Simplification of (1/sec² x) + (1/csc² x)

(1/sec² x) + (1/csc² x)

Recall

sec² x = 1/cos² x

Thus,

cos² x = 1/sec² x

Also,

csc² x = 1/sin² x

Thus,

sin² x = 1/csc² x

Therefore, we have

(1/sec² x) + (1/csc² x) = cos² x + sin² x

Recall

cos² x + sin² x = 1

Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:

(1/sec² x) + (1/csc² x)  = 1

4. Simplification of (sec x / sin x) - (sin x / cos x)

(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x

Recall

sec x = 1/cos x

sinx sinx = sin² x

Thus,

(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x

(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x

Recall

1  - sin² x = cos² x

Thus, we have

[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x

[1 - sin² x] / sinx cos x = cos x / sin x

Recall

cos x / sin x = cot x

Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:

(sec x / sin x) - (sin x / cos x) = cot x

5. Simplification of (1 + sin x)(1 - sin x)

(1 + sin x)(1 - sin x)

Clear bracket

1 - sin x + sin x - sin² x

1 - sin² x

Recall

1 - sin² x = cos² x

Thus, we have

(1 + sin x)(1 - sin x) = cos² x

6. Simplification of cos x + sin xtan x

cos x + sin xtan x

Recall

tan x = sin x / cos x

cos x + sin xtan x = cos x + sin x (sin x / cos x)

cos x + sin xtan x = cos x + (sin² x / cos x)

cos x + sin xtan x = (cos² x + sin² x) / cos x

Recall

cos² x + sin² x = 1

cos x + sin xtan x = 1 / cos x

1/cos x = sec x

Thus,

cos x + sin xtan x = sec x

The simplified expression of cos x + sin xtan x is sec x

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Answer:

c is the answer

Step-by-step explanation:

The value of the cosine X is 0.724

We need to know the different trigonometric identities.

These identities are written as;

From the information given, we have that;

Z=90°, XZ = 20, YX = 29, and ZY = 21.

The ratio for the cosine identity is;

cos θ = adjacent/hypotenuse

Adjacent side = XZ = 20

Hypotenuse side; YX = 29

then, we have;

cos X  = 21/29

cos X = 0.724

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Answer:

-4m+10

Step-by-step explanation:

Answer:

-4m+10

explanation:

6m-10=-4m

+10

-4m+10

As per the given condition in question, if you have 50% chance of winning a game and if you want to maximize your winning chances, then the best amount of games you should be playing is 100.

What is probability?

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities. An event has a probability of 0 when there is no possibility it will happen, whereas an event has a probability of 1 when it will definitely happen.

What is the significance of probability?

Information about possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.

According to the given question:

As we've been told that there is 50% chance for winning a game, the more number of tries you do, the more chances are there for winning, for instance if you take 10 tries then you have chances to win 5 games and if you take 100 tries then you have chances to win 50 games. Hence, the best amount of games you should play to maximize your chances of winning is 100.

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Answer:

The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:

\( z_{\alpha/2}= -1.64\)

Step-by-step explanation:

\(n=8\) the same size given

[te]\sigma\) the population deviation is known

For this case we want to test if the population mean is less than 15 and that represent the alternative hypothesis and the complement would be the null hypothesis. So then the system of hypothesis are:

Null hypothesis: \(\mu \geq 15\)

Alternative hypothesis:  \(\mu <15\)

The signficance level is 0.05 and then based in the alternative hypothesis we can find a critical value who accumulates 0.05 of the area in the normal standard curve in the left and we got:

\( z_{\alpha/2}= -1.64\)

By using a statistical calculator, the actual sample mean and sample standard deviation are:

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:

Mean = ∑x/(n - 1)

In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:

Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)

By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;

Actual sample mean = 46.1500.

Actual ample standard deviation = 8.6256.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

1/4 ft

Step-by-step explanation:

A = l x w

5/24 = 10/12 x w

Solve for w

5/24 divided by 10/12 = w

Take inverse of 10/12 and multiply

5/24 times 12/10

1/4

Answer:

2,4,2,4.

Step-by-step explanation:

Answer:

2,4,2,4.

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

55 divide 5 = 11

11 + 3 = 15

5 × 11 = 55

The transformation was a reflection over the x-axis. This is because \(g(x)=-f(x)\).

Answer: ( -0.731,  0.682)

Step-by-step explanation:

The unit vector is defined as a vector that points in the same direction as our vector (137 degrees from the x-axis) and has a magnitude of 1.

Knowing the angle, is really simple to do it.

First, we know that for a radius R and an angle A, the rectangular coordinates can be written as:

x = R*cos(A)

y = R*sin(A)

And if we want that the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

x = 1*cos(137°) = -0.731

y = 1*sin(137°) = 0.682

Then the unit vector is: ( -0.731,  0.682)

The unit vector is ( -0.731,  0.682)

\(x = R\times cos(A)\\\\y = R\times sin(A)\)

And the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 137°

so,  

\(x = 1\times cos(137) = -0.731y = 1\times sin(137) = 0.682\)

Then the unit vector is: ( -0.731,  0.682)

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The revenue equation is given by:

R = –360p^2 + 28,800p

To find the maximum revenue that can be expected, we need to find the vertex of the parabola represented by this equation. The vertex of a parabola is given by the formula:

Vertex = (-b/2a, f(-b/2a))

where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.

In this case, a = -360 and b = 28,800.

The x-coordinate of the vertex is given by:

x = -b/2a = -28,800/(2*(-360)) = 40

Substituting x = 40 into the revenue equation gives:

R = –360(40)^2 + 28,800(40) = 576,000

Therefore, the maximum revenue that can be expected is $576,000.

Again let me know what other ones you need help with

Answer:

27%

Step-by-step explanation:

The approximate value of the relative frequency of students with green eyes from the given sample population is; 27%

From the given table, the number of students with Blonde hair = 78

Number of students with blonde hair and green eyes = 21

Now, relative frequency is defined as the ratio of the number of outcomes in which a specified event occurs to the total number of trials, in an actual experiment.

Thus, in this question;

Relative frequency of students with green eyes = 21/78 = 2.7 = 27%

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Answer:

Step-by-step explanation:

The total amount of interest earned is the sum of the amounts of interest earned by each of the accounts.

Let x represent the amount invested at 8%. Then 2x is the amount invested at the lower rate of 6%. The interest earned by each investment is the product of the amount and the interest rate. The total earned is ...

  0.08x +0.06(2x) = 2920

We can simplify this equation, then divide by the x-coefficient.

  0.20x = 2920 . . . . . . . . . . . simplify

  x = 14600 . . . . . . . . . . divide by 0.2

  2x = 29200 . . . . . . . . multiply by 2

Jolene invested $29,200 at 6%, and $14,600 at 8%.

Answer:

Step-by-step explanation:

540x0.30=378

378x0.08=30.24

378+30.24=408.24

Answer:To find the mean of a data set, add all the values together and divide by the number of values in the set.

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

see photos attached

blah blah

The total number of winning hands are 276.

Probability is defined as the ratio of favorable outcomes to all other possible outcomes of an event. The symbol x can be used to express the quantity of successful outcomes for an experiment with 'n' outcomes. The probability of an event can be calculated using the following formula.

Probability of an event = Number of favourable outcomes/Total number of outcomes = x/n.

In the given question,

If the first card drawn is a 10, then there are

\(P_9^2=\frac{9!}{(9-2)!} =9*8=72 hands\)

There are 9 possible numbers if the second card is a 10, and there are 8 possible numbers if the third card, giving us,

\(9*8= 72 hands\)

If the third card is 10 then there are 9 possible numbers for the first card and 8 possible numbers for

second card, it gives us

\(9*8= 72 hands\)

And there are 5 odd cards, and it gives us:

\(P_5^3=\frac{5!}{(5-3)!} =5*4*3=60 hands\)

So, we have that in total we have

72+72+72+60=276 winning hands.

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Answer:

biosphere then ecosystem then community populations then organisms

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

The answer will be A

Step-by-step explanation:

have a nice day/night

Answer: 0.02655

Step-by-step explanation:

Explanation: The formula for finding the probability of no successes in a binomial experiment is given by (1 - p)^n, where p is the probability of success in a single trial and n is the number of trials. In this case, p = 0.30 and n = 6. So, the probability of no successes is (1 - 0.30)^6 = 0.02655.

Answer:

D

Step-by-step explanation:

D represents a function because the input (x) is not repeating itself.

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Answer:

12% increase

Step-by-step explanation:

First, find the difference between 18.48 and 16.50:

18.48 - 16.50 = 1.98

Now, what percent of 16.50 is 1.98?:

1.98 / 16.50 = 0.12

0.12 * 100% =   ==> 100% = 1. Anything multiplied by 1 is itself ( 1 * 3 = 3 )

0.12 * 100% = 12%

Hence, $16.50 to $18.48 is an increase of $1.98 or 12%.

Answer:

12% increase

Step-by-step explanation:

(V2−V1)|V1|×100

=(18.48−16.5)|16.5|×100

=1.9816.5×100

=0.12×100

=12%change

=12%increase

According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

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