9. The functions f and g are such that
f(x) = 3(x – 4) and g(x) = x/5+1
a) Find the value of f(10)
b) Find g-'(x)
c) Show that ff(x) = 9x - 48​

Answer:

c=35 + 25m

Step-by-step explanation:

Sorry, that's all I got

Answer:

she gets home at 2:30

Step-by-step explanation:

Answer:

1/105

Step-by-step explanation:

First, the probability that Joe chooses a grand prize bag is 2/15 because there are 2 grand prize bags out of 15 total bags.

Next, the probability that Devon chooses a grand prize bag is 1/14 because if Joe already chose one of the grand prize bags, there is only 1 left out of a total of 14 bags left.

The last step is to multiply those two bags, so \(\frac{2}{15} * \frac{1}{14}\) = \(\frac{1}{105}\)

The probability the coin comes up all heads or all tails after 4 tosses is 12.5%.

Probability refers to the ratio, chance, likelihood, or odds that an expected outcome is achieved when there are many possible outcomes.

Probability is a fractional value, especially when the odds of the occurrence of the expected event are not 100% uncertain or certain.

In this case, probability lies between zero and one.

Odds of a coin coming up either heads or tails every time = 1:7

The sum of ratios = 8 (1 + 7)

Thus, the probability of the coin coming up with all heads or all tails = 12.5% (1/8 x 100)

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Answer:

A

Step-by-step explanation:

sorry if its wrong but i think its right

The probability that at least 6 of these will have a mechanical defect is 0.1612.

For the given question;

At least six of the seven chosen has to have a mechanical defect.

So we add this same cases with exactly 6 mechanical defects and the cases with exactly 7 mechanical defects.

Number of possible approaches = ⁶C₂ + ¹⁹C₇ = 6!/2!4! + 19!/7!2!

= 27132 + 50388

= 77, 520

Calculated the total number of options to pick the seven keyboards as;

²⁵C₇ = 25!/7!18!

²⁵C₇ = 480,700.

As a result, the necessary probability = 77, 520/480,700 = 0.1612.

Thus, the probability that at least 6 of these will have a mechanical defect is 0.1612.

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The complete question is-

Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 6 of which have electrical defects and 19 of which have mechanical defects.

If a sample of 7 keyboards is randomly selected, what is the probability that at least 6 of these will have a mechanical defect? (Round the answer to four decimal places.)

JK is perpendicular to a line that has a slope

What is Slope?

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).

Two lines, L1 and L2, with slopes m1 and m2 are perpendicular if

m1 x m2 = -1.

In our case m1 = 1

1 x m2 = -1

m2 = -2

so the slope of the perpendicular line is -2.

( -2 x (1) = -1).

As x increases, the line with a slope of -2 increases. Line JK is the only line displayed that fits this. Line AB cannot be the solution because it is "falling" as x grows.

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There is insufficient evidence to suggest that there are differences in the frequency of blood types by location.

Yes, there may be differences in the frequency of blood types in different locations (states). to test this hypothesis.

Null hypothesis:

There is no difference in blood type frequency by location (state).

Alternative hypothesis:

There are differences in the frequency of blood types depending on the location (state).

The degrees of freedom for this test are (r - 1)(c - 1). where r = number of rows and c = the number of columns. In this case, we have 4 rows and 3 columns, so  (4 - 1)(3 - 1) = 6 degrees of freedom.

Using a chi-square table or calculator, you'll discover that the basic value for a chi-square dispersion with 6 degrees of freedom and an importance level of 0.05 is 12.592.

 The chi-square value calculated from the given data is 5.65.

The p-value can be decided to employ a chi-square dispersion table or a calculator with 6 degrees of flexibility and a chi-square value of 5.65.

The p-value is the likelihood of obtaining a chi-square value that's more extreme than or greater than the computed value, given the invalid theory is true.

Employing a chi-square table or calculator, we are able to discover that for a chi-square value of 5.65 and 6 degrees of freedom, the p-value is roughly 0.578.

The calculated chi-square esteem of 5.65 is less than the basic value of 12.592 and the p-value of 0.578 is more prominent than the centrality level of 0.05, so the invalid theory isn't rejected.

 Therefore, there is insufficient evidence to suggest that there are differences in the frequency of blood types by location .

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The penguin swims half the circumference of the circular island, which is equivalent to half the distance around the circle.

The circumference of a circle can be calculated using the formula:

C = πd,

where C is the circumference and d is the diameter of the circle.

Given that the diameter of the island is 20 meters, the radius (r) of the island is half the diameter, which is 10 meters.

Substituting the value of the radius into the formula, we have:

C = π * 10 meters = 10π meters.

To find half the circumference, we divide the total circumference by 2:

Half circumference = (10π meters) / 2 = 5π meters.

Therefore, the penguin swims a distance of 5π meters.

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If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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Answer:

Options (1), (2) and (5) are true.

Step-by-step explanation:

Option (1). m∠1 = (2x + 10)°

lines c and d are the parallel lines and t is a transverse.

Therefore, m∠1 = (2x + 10)° [corresponding angles]

This option is true.

Option (2). m∠3 = 87°

Since ∠3 and angle having measure equal to 87° are the vertical angles therefore, both the angles will be equal in measure.

This option is true.

Option (3). m∠2 = (2x + 10 + 5x - 1)°

m∠2 = (5x - 1)° [Since both the angles are interior alternate angles]

Therefore, this option is not true.  

Option (4). m∠1 + m∠2 = m∠3

(5x - 1) + (2x + 10) + 87 = 180° [Sum of liner angles at a point is 180°]

7x + 96 = 180

7x = 180 - 96

x = \(\frac{84}{7}\)

x = 12

Therefore, m∠1 = (2x + 10) = 34°

                 m∠2 = (5x - 1) = 59°

                 m∠3 = 87°

For the given relation,

m∠1 + m∠2 = m∠3

34 + 59 = 87

93 = 87

Not true.

Therefore, this option is not correct.

Option (5). 87 + 2x + 10 + 5x - 1 = 180°

True.

Since these angles are the linear angles so the sum of all angles = 180°

Therefore, the given option is correct.

Options (1), (2) and (5) are the true.

Answer:

answer 1 2 and 5

Step-by-step explanation:

right on edge

Slope:-

\(\\ \rm\rightarrowtail m=\dfrac{5-2}{2-1}\)

\(\\ \rm\rightarrowtail m=\dfrac{3}{1}\)

\(\\ \rm\rightarrowtail m=3\)

Answer:

Angle 2 = 75 degrees, Angle 1 = 105 degrees

Step-by-step explanation:

Step 1:

Angle 8 = Angle 2  Alt. Int.

Step 2:

180 degrees - Angle 2 = 105 degrees

Step 3:

Angle 1 = 105 degrees

Answer:

Angle 1 = 105 degrees, Angle 2 = 75 degrees

Hope This Helps :)

Answer:

  ∠2 = 75°

  ∠1 = 105°

Step-by-step explanation:

∠2 is an "alternate interior" angle with respect to the one marked 75°, so is congruent to that:

  ∠2 = 75°

__

∠1 and ∠2 form a linear pair, so ∠1 is supplementary to ∠2:

  ∠1 = 180° -75°

  ∠1 = 105°

Answer:
A part to part ratio is the porportion if the diff parts in relation to each other

Step-by-step explanation:

Answer:

for the 1st one, m=10 and b=2 because from the word problem it says it starts at 10 which would be 10 on the y axis being where the line would pass through and spending 2 a week would be the slope because he is losing 2 per week its a negative slope so y=10x-2.

for the second one m=48 and b=44 its just like the last one but with different numbers but comment if you want me to explain it but the answer is y=48x-44.

Answer:

A.  180°

Step-by-step explanation:

This is a simple subtraction problem.

212° - 32° =  180°

Using the critical value, we should reject the null.

So,

Therefore, using the critical value, we should reject the null.

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Answer:

NO

Step-by-step explanation:

25 hours is 5 days is the same as 5 hours per day.  25 ÷ 5 = 5

8 hours in 2 days is the same as 4 hours per day.   8 ÷ 2 = 4

Answer:

Step-by-step explanation:

For angle C,

cos(∠C) = \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\) = 0.97

sin(∠C) = \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\) = 0.26

tan(∠C) = \(\frac{\text{Adjacent side}}{\text{Adjacent side}}\) = 0.27

Therefore, from the triangle ABC,

cos(∠A) = cos(90° - ∠C)

             = sin(∠C)

             = 0.26

sin(∠A) = sin(90 - ∠A)

            = cos(∠A)

            = 0.97

tan(∠A) = \(\frac{\text{sinA}}{\text{cosA}}=\frac{0.97}{0.26}\)

            = 3.73

Angle        \(\frac{\text{Adjacent side}}{\text{Hypotenuse}}\)                 \(\frac{\text{Opposite side}}{\text{Hypotenuse}}\)                    \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

  A                    0.26                       0.97                             3.73

Answer:

2079 divided by 27 is the answer to the question

The expression "2,079 divided by 27" has the same solution as "3,157 divided by 41".

To find the expression that has the same solution as the division of 3,157 by 41, you need to divide each of the given numbers by their respective divisors and see which one matches the quotient of 3,157 divided by 41.

Let's calculate the values of the given expressions:

a) 1852 divided by 24 = 77.166...

b) 1928 divided by 25 = 77.12

c) 2079 divided by 27 = 77

d) 2184 divided by 28 = 78

The closest value to the quotient of 3,157 divided by 41 (which is approximately 77) is option c) 2,079 divided by 27. So, the expression "2,079 divided by 27" has the same solution as "3,157 divided by 41".

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The descriptive statistics of the variables tota The mean of total_cases represents the average number of reported COVID-19 cases, while the mean of total_deaths represents the average number of reported COVID-19 deaths.

The measures of dispersion, such as standard deviation, indicate the spread or variability of the data points around the mean.

The mean of total_cases reveals the average magnitude of the spread of COVID-19 cases. A higher mean suggests a larger overall impact of the virus. The standard deviation quantifies the degree of variation in the total_cases data. A higher standard deviation indicates a wider range of reported cases, implying greater heterogeneity or inconsistency in the number of cases across different regions or time periods.

Skewness measures the asymmetry of the distribution. Positive skewness indicates a longer right tail, suggesting that there may be a few regions or time periods with exceptionally high case numbers. Kurtosis measures the shape of the distribution. Positive kurtosis indicates a distribution with heavier tails and a sharper peak, which implies the presence of outliers or extreme values in the data.

Similarly, the mean of total_deaths provides an average estimate of the severity of the COVID-19 outbreak. A higher mean indicates a greater number of deaths attributed to the virus. The standard deviation of total_deaths indicates the variability or dispersion of the death toll across different regions or time periods. Skewness and kurtosis for total_deaths provide insights into the shape and potential outliers in the distribution of death counts.

The means of total_cases and total_deaths offer average estimates of the impact and severity of COVID-19. The standard deviations indicate the variability or spread of the data, while skewness and kurtosis provide information about the shape and potential outliers in the distributions of the variables. These descriptive statistics help us understand the overall patterns and characteristics of COVID-19 cases and deaths.

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The solution of the given equation \(y=6x+20\) is \(x = \frac{y + 20}{6}\)

What is linear equation?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

We have,

                        \(y = 6x + 20\)

Arrange the equation both sides so that all variable terms are on the left hand side.

                        \(6x - 20 = y\)

Add 20 to both sides of the equation.

                   \((6x - 20) + 20 = y + 20\)

                        \(6x = y + 20\)

Divide both sides by 6 we get,

                          \(\frac{6x}{6} = \frac{y + 20}{6}\)

                      ∴   \(x = \frac{y + 20}{6}\)

Hence, final solution is \(x = \frac{y + 20}{6}\) .

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With these base cases and the defined recurrence relation, you can recursively calculate the number of ways to deposit any given amount of dollars, considering the order of coins and bills.

To formulate a recurrence relation for the number of ways to deposit n dollars in a vending machine, where the order of coins and bills matters, we can break it down into smaller subproblems.

Let's define a function, denoted as F(n), which represents the number of ways to deposit n dollars. We can consider the possible options for the first coin or bill deposited and analyze the remaining amount to be deposited.

1. If the first deposit is a coin of value d, where d is a positive integer less than or equal to n, the remaining amount to be deposited will be (n - d) dollars. Therefore, the number of ways to deposit the remaining amount, considering the order, would be F(n - d).

2. If the first deposit is a bill of value b, where b is a positive integer less than or equal to n, the remaining amount to be deposited will be (n - b) dollars. Similar to the coin scenario, the number of ways to deposit the remaining amount, considering the order, would be F(n - b).

To obtain the total number of ways to deposit n dollars, we sum up the results from both scenarios:

F(n) = F(n - 1) + F(n - 2) + F(n - 3) + ... + F(1) + F(n - b)

Here, b represents the largest bill denomination available in the vending machine. You can adjust the range of values for d and b based on the available denominations of coins and bills.

It's important to establish base cases to define the initial conditions for the recurrence relation. For example:

F(0) = 1   (There is only one way to deposit zero dollars, which is to deposit nothing)
F(1) = 1   (There is only one way to deposit one dollar, either as a coin or a bill)

With these base cases and the defined recurrence relation, you can recursively calculate the number of ways to deposit any given amount of dollars, considering the order of coins and bills.

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If linear function is  y=145+30x

Part A

y is the cost of airline tickets in dollars

x is the checked bags

30 is the cost of the each bag

145 is the fixed cost of airline tickets without including the cost of bags

Part B

The domain = {0, 1, 2, 3, 4, 5} and it is a discrete domain

Part C

The graph of the function has been plotted

The linear function is

y = 145 + 30x

Part A

The linear function is

y = 145 + 30x

Where y is the cost airline tickets in dollars

x is the checked bags

30 is the cost of the each bag

145 is the fixed cost of airline tickets without including the cost of bags

Part B

Here at most 5 bags can be checked.

Therefore the domain = {0, 1, 2, 3, 4, 5}

It is a discrete domain, because values of the domain that can be counted, like the integers

Part C

Plot the graph using the linear function and domain

Hence, If linear function is  y=145+30x

Part A

y is the cost airline tickets in dollars

x is the checked bags

30 is the cost of the each bag

145 is the fixed cost of airline tickets without including the cost of bags

Part B

The domain = {0, 1, 2, 3, 4, 5}

Part C

The graph of the function has been plotted

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An expression that represents the measure of the third side is 4x.

A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.

Given:

The perimeter of the triangle is 3x² - 7x + 2.

And the measures of the two sides are x² - x - 4 and 2x² - 10x + 6.

The measure of the third side = the perimeter of the triangle - (the total measure of the two sides)

The measure of the third side = 3x² - 7x + 2 - (x² - x - 4 + 2x² - 10x + 6)

The measure of the third side = 3x² - 7x + 2 - (3x² - 11x +2)

The measure of the third side = 4x

Therefore, the measure of the third side = 4x.

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The number of different letter arrangements for the given words are:

"fluke": 120

"propose": 3,360

"mississippi": 34,650

"arrange": 840

Here, we have,

To calculate the number of different letter arrangements for a given word, you can use the formula for permutations.

The formula is:

n! / (n1! * n2! * n3! * ... * nk!)

Where:

n is the total number of letters in the word.

n1, n2, n3, ..., nk represent the frequencies of each distinct letter in the word.

Let's calculate the number of different letter arrangements for the words you provided:

Word: "fluke"

Number of letters (n): 5

Number of distinct letters: 4 (f, l, u, k)

Frequency of each letter: f-1, l-1, u-1, k-1

Number of different arrangements: 5! / (1! * 1! * 1! * 1!) = 5! = 120

Word: "propose"

Number of letters (n): 7

Number of distinct letters: 5 (p, r, o, s, e)

Frequency of each letter: p-1, r-1, o-2, s-1, e-1

Number of different arrangements: 7! / (1! * 1! * 2! * 1! * 1!) = 7! / 2 = 3,360

Word: "mississippi"

Number of letters (n): 11

Number of distinct letters: 4 (m, i, s, p)

Frequency of each letter: m-1, i-4, s-4, p-2

Number of different arrangements: 11! / (1! * 4! * 4! * 2!) = 11! / (4! * 4! * 2!) = 34,650

Word: "arrange"

Number of letters (n): 7

Number of distinct letters: 6 (a, r, n, g, e)

Frequency of each letter: a-2, r-2, n-1, g-1, e-1

Number of different arrangements: 7! / (2! * 2! * 1! * 1! * 1!) = 7! / 4 = 840

Therefore, the number of different letter arrangements for the given words are:

"fluke": 120

"propose": 3,360

"mississippi": 34,650

"arrange": 840

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Answer:

72.34

Step-by-step explanation:

Calculated the value

936.24 cm

Step-by-step explanation:

First of all find the cm or m value of that inches value as it'll become harder to tackle with inches... then find the radius in inches... then find the area