-Exponential and Logarithmic Functions- Solve the following, round the answer to the nearest hundredth.

Answer:

is = c⁸d⁹/c²d³

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Given:

Speed of current (y)= 6 km/hour

Distance = d km

Speed of boat in still water = x km/hour

Speed of the cruiser with the current= (x+6) km/hour

Speed of the cruiser against the current= (x-6) km/hour

From equation (1) and (2)

Therefore the speed of the without a current is 15km/hour.

The diameter of the cylinder is 24 mm.

Therefore, the radius is given by:

The height of the cylinder is given as 5 mm.

The formula for the volume V of a cylinder with radius r and height h is given by:

Substitute r = 12mm and h = 5 mm into the formula for volume:

Therefore, the volume of the cylinder is approximately 2261.9 mm².

.

The values of f(0), f(2) and f(-2) for the polynomial f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex] are 12, 28 and 52 respectively.

According to the question,

We have the following function:

f(x) = [tex]-x^{3} +7x^{2} -2x+12[/tex]

Now, in order to find the value of f(0), we will put 0 in place of x.

f(0) = [tex]-0^{3} +7(0)^{2} -2(0)+12[/tex]

f(0) = 0+7*0-0+12

(More to know: when a number is multiplied with 0 then the result is always 0 even the number being multiplied with zero is in lakhs.)

f(0) = 0+0-0+12

f(0) = 12

Now, in order to find the value of f(2), we will put 1 in place of x:

f(2) = [tex]-2^{3} +7(2)^{2} -2(2)+12[/tex]

f(2) = -8+7*4-4+12

f(2) = -8+28-4+12

f(2) = 40 -12

f(2) = 28

Now, in order to find the value of f(2), we will put -2 in place of x:

f(-2) = [tex]-(-2)^{3} +7(-2)^{2} -2(-2)+12[/tex]

f(-2) = -(-8) + 7*4+4+12

f(-2) = 8+28+4+12

f(-2) = 52

Hence, the value of f(0) is 12, f(2) is 28 and f(-2) is 52.

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Answer:

Son's age (y) = 14 years

Step-by-step explanation:

According to the question,

Father's age = 42 years

Son's age = y years

Difference between father's & son's age is 28 years. i.e.

Father's age - son's age = 28

42 - y = 28

42 - 28 = y

y = 42 - 28

y = 14

Take into account that there are 7 chices for the first course, and there are 10 choices for the entree.

The total number of choices is given bye:

total_choices = Choices_for_first_course x choices_fro_entree

Then, by replacing the values of the previous parameters you get:

total_choices = 7 x 10 = 70

There are 70 ways a person can order a two-course meal

First, let's calculate the number of different hands of 5 cards that can be made, using a combination of 52 choose 5:

(a standard deck card has 52 cards)

Now, let's calculate the number of hands that have 4 aces. Since the fifth card can be any of the remaining 48 cards after picking the 4 aces, there are 48 possible hands that have 4 aces.

Then, the probability of having a hand with 4 aces is given by the division of these 48 possible hands over the total number of possible hands of 5 cards:

The probability is 1/54145.

Answer:

Step-by-step explanation:

We're going to use length DC and ML, along with DA and MJ

[tex]\frac{DC}{ML} = \frac{5}{6}[/tex] which is 0.833333333

now for

[tex]\frac{DA}{MJ} =\frac{7}{8.4}[/tex] which is 0.833333333 (again)

as you can see since the shapes ABCD and JKLM are similar, they have a relationship which in this case is 0.833333333

and we can use this 0.833333333 to help us find the length of KL

knowing that any length for ABCD divided by JKLM is 0.833333333

we can do

[tex]\frac{CB}{LK}=0.833333333[/tex]

since we don't know what KL is, we can switch the spots and enlongate it, to become:

[tex]\frac{CB}{0.833333333} =LK[/tex]

put in the value for CB

[tex]\frac{3}{0.833333333} =LK[/tex]

and we get 3.6

The length of x of KL is...

The increase in number will be 1,478,400.

The projected number of students in an associate degree program in 2024-2025 is 7878400.

The the number of students enrolled in an associate degree program is projected to increase by 23.1 % and the enrollment in associate degree programs in 2014-2015 is 6,400,000.

The increase will be:

= Percentage increase × Enrollment

= 23.1% × 6,400,000

= 1,478,400

The projected number will be:

= Original number + Increase

= 6400000 + 1478400

= 7878400

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the figure below to better undesrtand the problem

Applying proportion

h/17.35=1.55/(17.35-12.70)

solve for h

h=17.35*1.55/4.65

Solution:

Given:

Two parallel lines have identical slopes.

Hence, the slope of line 1 is gotten by comparing the equation given to the equation of a line in the slope-intercept form.

Thus,

Since both lines are parallel, then the slopes are equal.

To get the equation of line 2 through the point (2,11), the formula below is used;

Therefore, the equation of the line that is parallel to y = 3x - 2 passing through the point (2,11) is;

Answer:

15

Step-by-step explanation:

5x + 9 and 84 are alternate interior angles.

Since,

lines l and m are parallel, alternate interior angles are equal.

So,

5x + 9 = 84

Step 1 : Subtract 9 on both sides.

5x = 84 - 9

5x = 75

Step 2 : Divide 5 on both sides.

x = 75/5

x = 15

Hence,

The value of x is 15.

The value of the bill was $58. The tip was $8.7. Percentage is expressed in terms of 100. To determine the percentage of the bill that was the tip, we would find the ratio of the tip to the bill and multiply by 100. It becomes

8.7/58 * 100

= 15%

The tip was 15% of the bill

Answer:

2.3

Explanation:

The formula for calulating mean deviation is expressed as:

where;

m is the mean of the data set

Xi are individual values

n is the total sample space

Get the mean;

n = 7

mean = (10+12+11+15+9+8+5)/7

mean = 70/7

mean = 10

Get the mean deviation:

Mean deviation = (10-10)+(12-10)+(11-10)+(15-10)+(9-10)+(8-10)+(5-10)/7

Since the values is in modulus |xi - m| will give a positive value, hence;

Mean deviation = (0+2+1+5+1+2+5)/7

Mean deviation = 16/7

Mean deviation = 2.28

Mean deviation = 2.3 (to the nearest tenth)

We will solve as follows:

Methjod th find the asnswer to thsi question.

First of mark a point on the line segment CD. Then, draw a perpendicular from that point to the a point to the line segment MN.

Then, mesure the length of the line segment.

Thus, the value of k is obtained.

ANSWER

5 pairs

EXPLANATION

We have that:

- one pair of pants cost $24.95

- one t-shirt costs $22.50

- one pair of socks cost $5.95

You want to buy one pair of pants, one t-shirt and several pairs of socks and you don't want to spend more than $80.

This means that everything you spend must be less than or equal to $80.

Let the number of pairs of socks you can buy be x.

This therefore means that:

Because we know that the number of pairs of socks must be a whole number, we have to approximiate to whole number, which will be:

x = 5

Therefore, you can buy at most 5 pairs of socks.

Since he has the same number of nickels as dimes.

x = nickels

x = dimes

500 - 2x = quarters

the total value of the coins is $72.50

5x + 10x + 25(500-2x) = 7250

Solve for x

15x + 25(500) + 25(-2x) = 7250

15x + 12,500 - 50x = 7250

Combine like terms

15x - 50x = 7250 - 12500

-35x = -5250

Divide both sides of the equation by -35

-35x/-35 = -5250/-35

x = 150

150 quarters

we have

step 1

Adds 1 both sides

step 2

Divide by 16 both sides

step 3

Applying square root both sides

Step-by-step explanation:

9)

it is not linear, because while x is increasing with every data point by 1, y is decreasing and increasing again, and the differences from one point to the other vary.

for a linear relationship also y has to change in a constant way, and the difference from one point to the next would be the same for all points.

10)

so, since it is not linear, it is quadratic then (since that was our only given alternative).

y = ax² + bx + c

we know c from point (0, -6). c = -6.

for a and b we need to use 2 data points with their x and y coordinates.

let's start with the first (-2, 14)

14 = a×(-2)² + b×-2 - 6 = 4a - 2b - 6

we can simplify that

7 = 2a - b - 3

and then

10 = 2a - b

the next point is (-1, -1)

-1 = a×(-1)² + b×-1 - 6 = a - b - 6

5 = a - b

so, we have the 2 equations

10 = 2a - b

5 = a - b

from the second we get

a = 5 + b

and that we can use in the first equation

10 = 2×(5 + b) - b = 10 + 2b - b

0 = b

therefore

5 = a - b = a - 0 = a

a = 5

and the equation is

y = 5x² - 6

11)

f(-7) = 5×(-7)² - 6 = 5×49 - 6 = 245 - 6 = 239

Answer:

5

Step-by-step explanation:

put it in order

6056605570546055

and the one that appears the most is the mode

We need to find the equation of the new function g(x) obtained by vertically stretching the function:

Vertically stretching a function by a factor of k corresponds to multiplying the whole expression of function by k:

In this problem, we have k = 18. Thus, we obtain:

Answer: C. g(x) = 18x²

Answer:

C(2,-2), D(-1,-2)

Explanation:

The area of a rectangle is calculated using the formula:

• From the graph, AB = 3 units.

• Given that the area = 12 square units

This means that the distance from B to C and A to D must be 4 units each.

Count 4 units vertically downwards from A and B.

The coordinates of C and D are:

• C(2,-2)

• D(-1,-2)

The first option is correct.

Answer:

Yes.  r = 3 + 3sin θ is symmetrical along the y axis

Step-by-step explanation:

Original polar equation is

r = 3 + 3sinθ

If this plot is to be symmetrical about the y axis then replacing Θ with (π-θ) in the original equation should not change the equation and thereby should not change the plot

r = 3 + 3sinθ

Replace θ with π-θ:

==>  3 + 3sin(π-θ)

But sin(π-θ) = sinθ

So the equation is unchanged at 3 + 3sin(π-θ) from the original equation r = 3 + 3sinθ

Hence the equation is symmetrical along the y-axis

This can be also be clearly seen if you plot both the equations, you will see the plot does not change

Given the functions:

By definition, (f+g)(x) is equivalent to:

Finally, using the expressions for f and g:

Answer:

45

scalene

acute

Step-by-step explanation:

Answer: The triangle classified by the sides is 59 degrees.  The triangle is classified by the angel is 1

Step-by-step explanation:

1) Using the data from the table, we plot the following segmented bard chart for the relationship between age and behaviour toward humans.

2) From the graph we see that for each behaviour towards humans, we have approximately the same percentage of juveniles (around 10%) and adults (around 90%), that's because the blue and green portions are proportionally the same for each bar. Based on what we see from the graph, we conclude that there is no association between age and behaviour towards humans.

The number of rolls divided in the two groups so that the ratio is 3 to 5 is 27 and 45 respectively.

According to the question,

We have the following information:

Rolls are being prepared to go to grocery stores.

Now, we have to divide 72 rolls into 2 groups so the ratio is 3 to 5.

Now, let's take the number of rolls given to the first group to be 3x and the number of rolls given to the second group to be 5x.

So, we have the following expression:

3x+5x = 72

8x = 72

x = 72/8

x = 9

So, the number of rolls for the first group:

3x

3*9

27

Now, the number of rolls for the second group:

5x

5*9

45

Hence, the number of rolls divided in the given two group is 27 and 45.

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Answer:

C

Explanation:

Given:

Volume of a cylinder (V) = 4pi cubic units

To find:

Base area(A) and height(h)

Recall that the volume of a cylinder(A) is usually given as;

So let's go ahead and try each of the options and see which gives us 4pi on the left-hand side as we have on the right-hand side for Volume.

For option A;

We have that A = 1 and h = 2, so we'll have;

For option B;

We have A = 2pi and h = 1, so we'll have;

For option C;

We have A = 2pi and h = 2, so we'll have;

We can see from the above that option C is the right option.

-2/5t - 6 + 2/3t + 15​

Combining similar terms

(-2/5t + 2/3t) + (-6 + 15)

4/15t + 9