A ladder that is 55 meters in length is resting on a branch of a tree, and the base of the ladder is 33 meters from the tree on the level ground. How high up is the branch on which the ladder is resting?

Given:

The total amount is P = $10,000.

The rate of interest is r(1) = 10% 0.10.

The other rate of interest is r(2) = 8%=0.08.

The number of years for both accounts is n = 1 year.

The total interest earned is A = $820.

The objective is to find the amount invested in each account.

Explanation:

Consider the amount invested for r(1) as P(1), and the interest earned as A(1).

The equation for the amount obtained for r(1) can be calculated as,

Consider the amount invested for r(2) as P(2), and the interest earned as A(2).

The equation for the amount obtained for r(2) can be calculated as,

Since, it is given that the total interest earned is A=$820. Then, it can be represented as,

On plugging the obtained values in equation (3),

Also, it is given that the total amount is P = $10,000. Then, it can be represented as,

Substitute the equation (3) in equation (4).

Remember that we can get the mean of a dataset by adding up each datum and dividing such sum by the number of data.

Now, let's call the number of puppets Marco made M

This way, we would have that:

Solving for M :

Therefore, we can conclude that Marco made 4 puppets.

Distributive property

In this property, multiplying the sum of two or more terms in that add up in a bracket by a number outside the bracket will be equal to multiplying each term in the bracket individually and then followed by sum of the product. In this question:

2x + 22 = 2(x + 11 ) in that when you perform product on the right side of the equation, the result is the same i.e 2x + 2*11 = 2x + 22

the statement given 1/3 of the sum of 45 and a number is 16

In order to find the value of x, w

we have that

In a rhombus the length sides are congruent

the diagonals bisect each other and are perpendicular

so

If mmIn the right triangle IFJ

mtan(30)=FJ/IJ

Remember that

FJ=4

substitute the given values

Find the length side IF

Applying Pythagorean Theorem

IF^2=4^2+IJ^2

IJ^2=48

IF^2=16+48

IF^2=64

IF=8 units

that means

side GH=8 units

side JG=side IJ=4√3 units

side FH=2*side FJ=2*4=8 units

Answer:

Julie can run 12 laps

Step-by-step explanation:

9 min = 3 laps

9 x 2 = 18 = 6 laps

9 cant fit into 24 again

24 - 18 = 6

6 + 6 = 12 laps

Answer:

11.796

Step-by-step explanation:

2nd term

[tex] {1.3}^{2} = 1.3 + \frac{1.3}{ \frac{10}{3} } [/tex]

[tex] {1.3}^{2} = 1.69[/tex]

add first term

[tex]27.8 + 1.69 = 29.49[/tex]

times by 0.4 or ×2/5

[tex]29.49 \times \frac{2}{5} = \frac{58.98}{5} [/tex]

[tex] = 11.796[/tex]

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

The formula for calculating slope is expressed as

m = (y2 - y1)/(x2 - x1)

where

x1 and y1 are the x and y coordinates of the initial point

x2 and y2 are the x and y coordinates of the final point

From the information given, the initial point is (- 2, - 4) and final point is (2, 8)

Thus,

x1 = - 2, y1 = - 4

x2 = 2, y2 = 8

By substituting these values into the slope formula,

m = (8 - - 4)/(2 - - 2) = (8 + 4)/(2 + 2) = 12/4 = 3

We would find the y intercept, c by substituting m = 3, x = - 2 and y = - 4 into the slope intercept equation. We have

- 4 = 3 * - 2 + c

- 4 = - 6 + c

Adding 6 to both sides of the equation,

- 4 + 6 = - 6 + 6 + c

c = 2

By substituting m = 3 and c = 2 into the slope intercept equation, the equation of the line is

C) y = 3x + 2

Given

3 different waters: tap, bottled in glass, and bottled in plastic.

Find

probability that Adina's friend correctly identifies each of the 3 cups of water

Explanation

As we have given three different waters : tap , bottled in glass and bottled in plastic.

number of ways in which the person can make guesses about the 3 cups of water =

number of ways in which person identifies correctly the 3 cups of water = 1

so , probability that Adina's friend correctly identifies each of the 3 cups of water =

so , P = 1/6

Final Answer

Therefore , the probability that adina's friend correctly identifies each of the cup of water = 1/6

From the recursive formula:

we notice that the common difference of the sequence is -pi. Now we know that the first term is 7, then the explicit formula is:

when

We can relabel this sequence if we assume we start at zero, in this case the sequence will be:

when:

A rhombus is a quadrilateral with 4 congruent sides.

For the Rhombus ABCD given

Also,

Also,

To solve this problem we need to find the fraction of a fraction, for that we just have to multiply them. This is done below:

The section is 16/35 of a mile long.

Answer:

Explanation: Axis of symmetry is a vertical line that makes function symmetrical along either side:

In case of parabla function or:

We get axial symmetry where the first derivate is zero, and in fact, that is the x value for vertex:

Therefore:

And the corresponding y-value is:

Therefore vertex is at the point:

The volume of the pyramid is 144 cm³

The volume of a prism is given by the formula:

V = BH

where B is the base area

and H is the height

The base of the the pyramid is the lateral triangle, and the area is given by the formula:

B = 0.5 x b x h

b = 8 cm

h = 6 cm

B = 0.5 x 8 x 6

B = 24 cm²

The volume is then:

V = BH, where H = 6 cm

V = 24 x 6

V = 144 cm³

Given:

The rent for trucks is $3750.

The additional charge per ton of sugar is $150.

To write: The equation relating the total cost C and amount of sugar S.

Explanation:

The equation represents the total cost C and the amount of sugar S is given by,

Let us find the three coordinates to plot the graph.

When

Then,

When

Then,

When

Then,

So, the coordinates are,

The equation represents the total cost C and the amount of sugar S is given by,

The graph is,

As observed from the graph, the curve is a straight line from point (-2,-1) to (-5,2).

Consider that the equation of a straight line passing through two points is given by,

So the equation of the line passing through (-2,-1) and (-5,2) is given by,

Note that this function is only for the interval [-2, -5].

Now, the value of 'y' corresponding to the input x=-4 is calculated as,

Thus, the required output is y = 1 .

The match was Hornet's vs Panthers

Hornets's scored 5 goals

Panthers won by 3 goals, this means that the panters scored 3 more goals than the Hornets.

That would be +3 goals.

Given:

The given information is the shape is a rectangle.

About the diagonals of rectangles, there are two known properties:

- The diagonals of a rectangle bisect each other

- Both diagonals have the same length

Then, the answer is option C. They have the same length

First, we need to identify the square root of the fisrt squared numbers:

Since 40 is a number between 36 and 49, we can say that the square root of 40 is between 6 and 7. So:

First, we are going to divide the figure and named new points X and Y as:

Now, we know that TS is the sum of TX and XS.

TS = TX + XS

Adittionally, TX has the same length of HJ, so:

TX = HJ = 14

Now, we want to know the length of YK, and we can calculate it using the following equation:

LK = LY + YK LY is also equal to HJ, so LY = 14

42 = 14 + YK

42 - 14 = YK

28 = YK

Finally, since T and S are midpoints, the length of XS is the half of the length of YK. It means that XS is:

XS = YK/2

XS = 28/2

XS = 14

Therefore, TS is equal to:

TS = TX + XS

TS = 14 + 14

TS = 28

Answer: TS = 28

In a linear relationship, each step of x modifies the y value in the same way.

In the first table, when x = 1, y = 3 and when x = 2, y = 6. This is an increment of 3. If this is a linear relationship, we expect the next value of y to be the previous value plus 3, thus y = 9. But in the table shows x =3 and y = 12. We can rule out the first table.

With similar reasoning, in the second table, we see (1, 2) and (2, 5). This is an increase of the y value of 3. We expect the next value to be y = 8, but we see (3, 9). The second table is not a linear relationship.

In the third table, we see (1, -3) and (2, -5). This is a decrease of -2. We expect the next value of y to be y = -7, and we do see (3, -7). The next value should be y = -9, and the table shows (4, -9). Table 3 shows a linear relationship.

To be sure, let's see the 4th table. We see (1, -2) and (2, -4). This is a decrease of -2. The expected next value is y = -6, but the next point is (3, -2). Fourth table is not a linear relationship.

Thus, the correct answer is the top-right table.

Let x be a random variable representing the blood pressures of adults in the USA. Since it is normally distributed, we would apply the formula for determining z score which is expressed as

z = (mean - population mean)/standard deviation

From the information given,

population mean = 121

Standard deviation = 16

For stage 2 high blood pressure, the probability is

P(x greater than or equal to 160). It is also equal to 1 - P(x < 160)

Thus, for x = 160, we have

z = (160 - 121)/16 = 2.4375

From the standard normal distribution table, the probability value corresponding to a z score of 2.4375 is 0.9927

P(x < 160) = 0.9927

P(x greater than or equal to 160) = 1 - 0.9927 = 0.0073

Converting to percentage, it is 0.0073 * 100 = 0.73%

b) If 2000 peaople were sampled, the number of people with stage 2 high blood pressure would be

0.73/100 * 2000 14.6

To the nearest person, it is 15 people

c) For stage 1, the probability is

P(140 < x < 160)

For x = 140,

z = (140 - 121)/16 = 1.1875

From the standard normal distribution table, the probability value corresponding to a z score of 1.1875 is 0.883

Recall, for x = 160, the probaility is 0.9927

Thus,

P(140 < x < 160) = 0.9927 - 0.883 = 0.1097

Converting to percentage, it is

0.1097 * 100 = 10.97%

d) The 30th percentile refers to all values of blood pressure below k, where k is the 30th percentile. This means that we would find

P(x < k) = 0.3

The z score corresponding to a probability value of 0.3 is - 0.52

Thus,

(k - 121)/16 = - 0.52

k - 121 = - 0.52 * 16 = - 8.32

k = - 8.32 + 121

k = 112.68

The pressure for the 30th percentile is 112.68

ANSWER

EXPLANATION

Initial amount is $8800

percentage decrease is 6.5%

Decrease amount (in dollars );

The amount of money in the account at the end of last year= Initial amount - decrease

Decrease in amount: $572

Year-end amount: $8228

Solution

- The amount Michael withdraws every day is $40.

- The number of days it takes to withdraw $680 is given by:

- Using the formula above, we have:

Final Answer

The answer is 17 days

You have the following fraction:

180000/120000

First of all you cancel zeros:

180000/120000 = 18/12

next, you can simplify

18/12 = 9/6 = 3/2

finally 3/2 is:

3/2 = 1.5

Hence: 180000/120000 = 1.5

Furthermore, for the following fraction:

0.11/0.08

Here, you can use a calculator. The result is:

0.11/0.08 = 1.375

that is approximately

1.375 ≈ 1.4

For other fractions:

350/10,000 = 35/1,000 = 0.035

which is approximately

0.035 ≈ 0.04

6.01/7.2 = 0.834 ≈ 0.83

To solve this, we will need to convert all values to decimal.

First convert 1/4 to decimal:

Now convert 43% to decimal:

Simplify 5/9:

0.15 is already a decimal value.

Simplify 1/12:

1.4 is already a decimal.

After simplifying, we have the following values:

0.25

0.43

0.56

0.15

0.083

1.4

We can see the values greater than 0.25 are:

0

we have the fractions

1/4 and 3/4

Remember that

If the denominators are the same, then the fraction with the greater numerator is the greater fraction

3/4 > 1/4

use the number line

Divide number 1 into 4 parts

ANSWER

Rectangle

EXPLANATION

If we take a cross-section perpendicular to the base of a cylinder,

We get a rectangle.

The base of the cylinder is circular and the

Answer: Rectangle

Step-by-step explanation:

I got it right on the test

Given a parallelogram as shown below:

The formula to calculate the area of the parallelogram is given to be:

From the question provided, we have the following parameters:

Therefore, we can use the formula to calculate the area as shown below:

The area of the parallelogram is 99 squared yards (99 yd²).