Using these estimated values, the mass of the African elephant is about 3 × 1 0 � 3×10 m times the mass of the silverback gorilla, where � m is an integer.

a) The way to get the number after 15 is by finding the fourth term

b) The general term of the given sequence in the form of Tₙ = 2 + 6n

c) The term in the sequence equal to 45 is; The 8th term

The formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

d is common ratio

The sequence is given as:

3, 9, 15,....,57

Thus:

a = 3

d = 9 - 3 = 6

aₙ = 3 + (n - 1)6

aₙ = 3 + 6n - 1

aₙ = 2 + 6n

The term after 15 is the fourth term. Thus:

a₄ = 3 + (4 - 1)6

a₄ = 21

The term that is equal to 45 is:

3 + (n - 1)6 = 45

(n - 1)6 = 42

n - 1 = 7

n = 8

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The height of the ball after 4 seconds if it was kicked from the top of a 25 foot tall hill at 72 feet per second is 57 feet.

We are given that the height of the ball after t seconds is given by the polynomial −16[tex]t^{2}[/tex] + vt + h. We need to find the height of the ball after 4 seconds if it was kicked from the top of a 25 foot tall hill at 72 feet per second.

Substituting v = 72 and h = 25 in the given polynomial, we get:

-16[tex]t^{2}[/tex] + 72t + 25

To find the height of the ball after 4 seconds, we substitute t = 4 in the above polynomial:

-16[tex](4)^{2}[/tex] + 72(4) + 25 = -256 + 288 + 25 = 57

Therefore, the height of the ball after 4 seconds is 57 feet.

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Answer: B

Step-by-step explanation:

If you do the vertical line test, which means if you drew a vertical line(straight up and down line) anywhere on the graph and there should never be more than 1 point.  A, C, D all have multiple points that touch more than once.

answer B

Answer:

More cows

Step-by-step explanation:

more cows because:

8*1/4=2

12*1/4=3

The statement that is NOT true about infants' approximate number system is option (b) Infants can only discriminate approximate numbers when there is a large difference between the numbers.

Infants possess an innate sense of quantity that enables them to discriminate between different numerical magnitudes. This sense of quantity, also known as the approximate number system, is present in infants as young as 6 months old. Infants are able to discriminate between numerical quantities even when the difference between them is small, and their ability to do so improves with age.

However, their ability to discriminate between numerical quantities can be affected by various factors, including the numerical ratio between the stimuli, the duration of the presentation, and the task demands. Overall, the approximate number system is an important precursor to the development of more advanced mathematical skills.

Therefore, the correct option is (b) Infants can only discriminate approximate numbers when there is a large difference between the numbers.

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The given question is incomplete, the complete question is:

Which of the following is NOT true about infants' approximate number system?

Select one: a. Infants are able to discriminate approximate numbers by 6 months of age.

b. Infants can only discriminate approximate numbers when there is a large difference between the numbers.

c. Infants are unable to discriminate approximate numbers when dots change in both size and position simultaneously.

d. Infants' ability to discriminate approximate numbers is not dependent on non-numeric perceptual properties.

The original amount is 6200, which is obtained by dividing 837 by 0.135.

To find the original amount, we can use the formula for finding the percentage of a number

percentage = (part / whole) x 100%

where "part" is the given number (837 in this case), "percentage" is the given percentage (13.5%), and "whole" is the original amount we are trying to find.

Let's plug in the given values and solve for "whole"

13.5% = (837 / whole) x 100%

Divide both sides by 100% to get

0.135 = 837 / whole

Multiply both sides by "whole" to get

0.135 x whole = 837

Divide both sides by 0.135 to get

whole = 837 / 0.135

Simplifying, we get

whole = 6200

Therefore, the original amount is 6200.

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The expression is written as 2x - 9 = 17 and x = 13

Algebraic expressions are simply defined as expressions that are known to consist of terms, variables, constants, coefficients and factors.

These expressions are also seen as expressions containing mathematical or arithmetic operations.

These operations are listed as;

From the information given, we have that;

the difference between twice a number and nine is 17.

Let the number be x, we get;

2x - 9 = 17

collect the like terms

2x = 17 + 9

add the values

2x = 26

Divide the values

x = 13

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The complete question:

Write an equation for the following verbal expression: the difference between twice a number and nine is 17. Find the number

The differences between the exponential functions y = 3(2)^x and y = -3(0.5)^x is given as follows:

An exponential function is defined as follows:

y = ab^x.

In which:

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The relation between g(x) and g(x) is  a vertical dilation of scale factor of 0.5

So here we have two exponential functions:

g(x)= 200*(1.015)^x

f(x) =400*(1.015)^x

You can see that the only different thing between the two functions is the initial value. Then we can see that g(x) is a vertical dilation of f(x), such that if the scale factor is k, we can write:

g(x) = k*f(x)

Now let's find the value of k:

200*(1.015)^x = k*400*(1.015)^x

(200*(1.015)^x )/(400*(1.015)^x) = k

200/400 = k

0.5 = k

We have a vertical dilation of scale factor of 0.5

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The day when the sun is highest in the sky varies depending on the location within the United States. However, generally speaking, the highest point of the sun is reached on the summer solstice, which falls around June 20-21 each year.

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The pairings of equivalent expresions are:

To do it we just need to simplify the 3 expressions.

The first one is:

2(m + 3) + m - 2

2m + 6 + m - 2

3m + 4   this is equivalent to the first one.

5(m + 1) - 1 =

5m + 5 - 1

5m + 4   this is equivalent to the second one.

m + m + m + 1 + 3

= 3m + 4   this is equivalent to the first one.

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Answer:

The marginal cost is the additional cost added by increasing the quantity. This is also known as the additional cost “at the margin.” The marginal revenue is the additional revenue added by increasing the quantity. This is also known as the additional revenue “at the margin.”

Step-by-step explanation:

Please mark as brainlist

Answer:

Step-by-step explanation:

A) For a loan amount of $280,000, one point would cost $2,800 (1% of $280,000). With one point, the interest rate would be reduced by 0.2%, so the new interest rate would be:

4.18% - 0.2% = 3.98%

B) For a loan amount of $350,000, two points would cost $7,000 (2 x 1% of $350,000). With two points, the interest rate would be reduced by 0.275% per point, so the new interest rate would be:

2 x 0.275% = 0.55%

2.95% - 0.55% = 2.40%

C) For a loan amount of $600,000, three points would cost $18,000 (3 x 1% of $600,000). With three points, the interest rate would be reduced by 0.225% per point, so the new interest rate would be:

3 x 0.225% = 0.675%

4.6% - 0.675% = 3.925%

D) For a loan amount of $450,000, one point would cost $4,500 (1% of $450,000). With one point, the interest rate would be reduced by 0.3%, so the new interest rate would be:

3.75% - 0.3% = 3.45%

E) For a loan amount of $2,000,000, two points would cost $40,000 (2 x 1% of $2,000,000). With two points, the interest rate would be reduced by 0.235% per point, so the new interest rate would be:

2 x 0.235% = 0.47%

3.55% - 0.47% = 3.08%

Therefore, the cost of the points and the new interest rate for each loan amount and interest rate are as follows:

A) Cost of point: $2,800; New interest rate: 3.98%

B) Cost of points: $7,000; New interest rate: 2.40%

C) Cost of points: $18,000; New interest rate: 3.925%

D) Cost of point: $4,500; New interest rate: 3.45%

E) Cost of points: $40,000; New interest rate: 3.08%

The cross sectional area from the sphere will be greater (option c).

Let's start with the sphere. When a sphere is cut by a plane along a diameter, the resulting shape is a circle. The diameter of the sphere is 10 inches (twice the radius), so the circle that is created has a diameter of 10 inches. We can use the formula for the area of a circle (A = πr²) to determine its area. Since the radius is 5 inches, the area of the circle is:

A = π(5²) = 25π square inches

Now, let's move on to the cube. When a cube is cut vertically, we are essentially cutting through one of its faces. The resulting shape is a square with a side length of 10 inches (since the length of the cube is 10 inches).

We can use the formula for the area of a square (A = s²) to determine its area. Since the side length is 10 inches, the area of the square is:

A = 10² = 100 square inches

Hence the correct option is (c).

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Complete Question:

A sphere of radius 5 in is cut by a plane along a diameter and a cube of length 10 in is cut vertically. Which is true about their resulting cross-sectional areas?

(a) The cross sectional areas will be equal

(b) The answer cannot be determined

(c) The cross sectional area from the cube will greater

(d) The cross sectional area from the sphere will be greater

The approximate solution of t is 0.052 and the expression is t = log(20/11)/5

From the question, we have the following parameters that can be used in our computation:

11•10⁵ⁿ = 20

Divide both sides of the equation by 11

So, we have

10⁵ⁿ = 20/11

Take the logarithm to the base 10 of both sides

This gives

5t = log(20/11)

So, we have

t = log(20/11)/5

Evaluate

t = 0.052

Hence, the approximate solution of t is 0.052

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Answer:

Angles of:

1 = 87 degree, 2= 62 degree

Step-by-step explanation:

Here, we have a Vertically opposite angle so equate both the equations and get the value of x. then substitute the value of x in both equations.

hope it helps!

Answer:

y= -6

x= -7

Step-by-step explanation:

6x+7y= -42

7y= -6x-42

y=-6/7x -6

y-intercept is -6

0= -6/7-6

6=-6/7 x

x=-7

To find the x-intercept of the line, we need to set y to zero and solve for x:

6x + 7(0) = -42

6x = -42

x = -7

Therefore, the x-intercept will be  (-7, 0).

To find the y-intercept of the line, we need to set x to zero and solve for y:

6(0) + 7y = -42

7y = -42

y = -6

Therefore, the y-intercept is (0, -6).

Hence, the x-intercept is (-7, 0) and the y-intercept will be  (0, -6)

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The boys sold 200 tickets and the girls sold 230 tickets.

Let's represent the number of tickets boys sold as x.

Then, the number of tickets girls sold would be 15% more than the number of tickets boys sold, which is 1.15x.

As per the percent rule:

Together, the total number of tickets sold is given as 430:

x + 1.15x = 430

Combining like terms, we get:

2.15x = 430

Solving for x, we get:

x = 200

So the boys sold 200 tickets, and the girls sold 1.15x = 1.15(200) = 230 tickets.

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To find the limit of (1 - sin(θ))/(1 + cos(6θ)) as θ approaches π/2, we can apply a trigonometric identity:

1 - sin(θ) = cos(θ)

1 + cos(6θ) = 2cos^2(3θ)

Substituting these expressions into the original limit, we have:

lim (1 - sin(θ))/(1 + cos(6θ)) = lim cos(θ)/(2cos^2(3θ))

Now, as θ approaches π/2, the denominator 2cos^2(3θ) approaches 0, so we can apply L'Hospital's rule to the limit:

lim cos(θ)/(2cos^2(3θ)) = lim -sin(θ)/(12cos(θ)sin(3θ))

Applying L'Hospital's rule again, we take the derivative of the numerator and denominator separately with respect to θ:

= lim -cos(θ)/(12cos(θ)cos(3θ) + 3sin(θ)sin(3θ))

= lim -1/(12cos(3θ) + 3tan(θ))

Substituting θ = π/2, we have:

lim -1/(12cos(3π/2) + 3tan(π/2)) = lim -1/0

Since the denominator approaches 0 and the numerator is negative, the limit approaches negative infinity.

Therefore, the limit of (1 - sin(θ))/(1 + cos(6θ)) as θ approaches π/2 is negative infinity.

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Therefore, the value in today's dollars of what the account grows to is approximately $187,675.13.

Interest is the cost of borrowing money or the compensation paid by a financial institution to an individual or entity for depositing money. When someone borrows money, they are typically charged interest by the lender in addition to repaying the principal amount of the loan. The interest rate is expressed as a percentage of the principal and is typically calculated on an annual basis, although it can be calculated over shorter or longer periods depending on the terms of the loan or investment. Interest can be simple, where it is calculated only on the principal amount, or compound, where it is calculated on both the principal and any accumulated interest. In addition to loans and investments, interest can also be applied to credit card balances, mortgages, and other financial transactions.

Here,

To find the future value of the account, we can use the formula:

FV = Pmt x (((1 + r)ⁿ⁻¹) / r) + PV x (1 + r)ⁿ

where:

Pmt = annual payment or deposit

= $3,250

r = annual interest rate

= 10%

n = number of years

= 30

PV = present value

= 0 (assuming the account has no initial balance)

Using this formula, we get:

FV = $3,250 x (((1 + 0.10)³⁰ - 1) / 0.10) + 0 x (1 + 0.10)³⁰

= $405,093.35

This is the future value of the account in nominal dollars.

To find the value in today's dollars, we need to adjust for inflation. We can use the formula:

PV = FV / (1 + i)ⁿ

where:

i = inflation rate = 3%

Using this formula, we get:

PV = $405,093.35 / (1 + 0.03)³⁰

= $187,675.13

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The unknown are heights are shown in the complete table:

Person/Item            Shadow length(ft)            Height (ft)

Terrace                             7.5                                  5

Bird feeder                         9                                   6

Swing set                           12                                  8

Maple tree                        91.5                                61

From the question, we are to determine the value of the unknown heights in the given table.

The given table is:

Person/Item            Shadow length(ft)            Height (ft)

Terrace                             7.5                               5

Bird feeder                         9

Swing set                           12

Maple tree                        91.5

From the first item in the table, the ratio of Height to Shadow length is

5/ 7.5 = 2/3

We can multiply the shadow lengths with this ratio to get the corresponding heights

9 × 2/3 = 6

12 × 2/3 = 8

9 × 2/3 = 61

Thus,

The complete table is:

Person/Item            Shadow length(ft)            Height (ft)

Terrace                             7.5                                  5

Bird feeder                         9                                   6

Swing set                           12                                  8

Maple tree                        91.5                                61

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The functions of fat cells are:

Store energy

Hold body heat

Absorb shocks.

Adipocytes, sometimes referred to as fat cells, are specialized cells that serve as major sources of fat-based energy storage. They are essential to maintaining the equilibrium between energy intake and energy expenditure, which is known as energy homeostasis. Triglycerides, the primary building block of body fat, is accumulated in the adipose tissue when we consume more energy (calories) than we expend.

Leptin and adiponectin are two hormones secreted by fat cells that control insulin sensitivity, metabolism, and hunger. For instance, leptin helps to control body weight by alerting the brain when we've eaten enough to eat. Contrarily, adiponectin enhances insulin sensitivity and possesses anti-inflammatory properties.

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The yearly rate of the given simple interest $150 for time period of 4 years is equal to 41.67%.

Principal amount 'P' = $90.00

Simple interest 'S.I.' = $150.00

Time period 't' = 4 years

Use the formula for simple interest ,

Simple interest = P × r × t

where P is the principal 'initial amount',

r is the annual interest rate as a decimal,

and t is the time in years.

Substitute these values into the formula and solve for the interest rate 'r' ,

⇒ $150.00 = $90.00 × r × 4 years

⇒ $150.00 = $360.00 × r

Dividing both sides by $360.00 we get,

⇒0.4167 = r

Multiplying by 100 to convert to a percentage,

⇒ r = 41.67%

Therefore, the yearly rate of simple interest is equal to 41.67%.

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Answer:

SAS (Side-Angle-Side)

An appropriate label for the horizontal axis of the given populations graph of the six most populous countries in the world in 2015 is "Countries".

Based on the given graph, the appropriate label for the horizontal axis would be the names of the six most populous countries. This is because the horizontal axis in a graph typically represents the categories or groups being compared.

In this case, the six countries are being compared based on their population size. Therefore, the horizontal axis should identify each of the six countries separately, allowing the viewer to compare their population sizes. The total population of the six countries is provided as additional information.

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--The given question is incomplete, the complete question is given

" the populations of the six most populous countries in the world in 2015 are shown in the graph below. if the total population of the six countries shown is 3,489,000,000, what is an appropriate label for the horizontal axis? "--

Correct statement is,

No, because (2, 2) is a solution to neither equation.

We have to given that;

Equations are,

y - x = - 4  .. (i)

- 3x - 2y = - 10   .. (ii)

Now, Plug x = - 2 and y = 2 into above equations as;

y - x = - 4

2 - (- 2) = - 4

2 + 2 = - 4

4 ≠ - 4

- 3x - 2y = - 10

- 3 × - 2 - 2 × 2 = - 10

6 - 4 = - 10

2 ≠ - 10

Thus, Correct statement is,

No, because (2, 2) is a solution to neither equation.

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When we interchange the digits, we get the new number 43, which is 9 greater than 34.

Let's assume that the digit is x and the 2-digit number is y. Therefore, the original number is 10y + x (since y is the tens digit and x is the ones digit).

According to the given information, when the digit and the 2-digit number are added, the result is 7:

x + y = 7

When the digit is interchanged with the tens digit, the new number is 10x + y. According to the second piece of information, this new number is 9 greater than the original number (10y + x):

10x + y = 10y + x + 9

Simplifying the equation, we get:

9x - 9y = 9

Dividing both sides by 9, we get:

x - y = 1

We now have two equations:

x + y = 7

x - y = 1

We can solve this system of equations using substitution or elimination. For simplicity, we'll use elimination. Adding the two equations, we get:

2x = 8

Dividing both sides by 2, we get:

x = 4

Therefore, the digit is 4. We can substitute this value into one of the equations to find the value of y:

4 + y = 7

y = 3

Therefore, the 2-digit number is 37. The original number is 10y + x = 10(3) + 4 = 34. When we interchange the digits, we get the new number 43, which is 9 greater than 34. Hence, the solution is x = 4.

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The number of blankets Daniel can make with 15 yards of fabric will be; 10.

We are Given that Daniel has 15 yards of fabric to make baby blankets,

It will takes 1 and 1/2 yards of fabric to make each blanket,

To Calculate the total fabric required to make a blanket;

The total fabric required to make a blanket=  1 and 1/2

The total fabric required to make a blanket = 1 + 2 / 2

The total fabric required to make a blanket = 3 / 2 yards

To Calculate the number of the blanket

The number of blankets = The total fabric/fabric required to make a blanket

number of blankets = 15 / 3 / 2

number of blankets = 30 / 3

number of blankets = 10

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The complete question is

Daniel has 15 yards of fabric to make baby blankets. It takes 1 and 1/2 yards of fabric to make each blanket, and the expression that models the situation is 15-3/2y Which of the following are possible numbers of blankets that Daniel could make? Select all that apply.

Answer:  [tex]k^4[/tex] - 2k

Step-by-step explanation:

k(k³-2)

distribute

k multiply by    [tex]k^3[/tex] = [tex]k^4[/tex]

k multiply by -2 = -2k

 [tex]k^4[/tex] - 2k

You should examine the data provided in the article and follow these steps to determine if U.S. households in early 2016 indeed worked fewer hours and took more leisure time.

To determine if U.S. households in early 2016 worked fewer hours and took more leisure time, you would need to analyze the data provided in the article. Here are the steps you should take:
1. Identify the relevant data: Look for statistics or figures related to working hours and leisure time in early 2016.
2. Compare the data: Compare the early 2016 data to data from previous years or periods to see if there is a noticeable change in working hours and leisure time.
3. Analyze trends: Observe any trends or patterns that emerge from the data comparison. This will help you understand if U.S. households worked fewer hours and took more leisure time during the specified period.
4. Interpret the results: Based on the data analysis, draw a conclusion about whether or not U.S. households worked fewer hours and took more leisure time in early 2016.

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Complete question:

Corporate spending on equipment, structures and intellectual property, decreased an annualized 2.2 percent after a 3.4 percent fall in the first quarter. Outlays for equipment dropped for the fourth time in the past five quarters. Spending on structures -- everything from factories to shops to oil rigs -- have increased in just one quarter since the end of 2014. Inventories and the trade gap are two of the most volatile components in GDP calculations. To get a better sense of demand in the U.S., economists look at final sales to domestic purchasers, or GDP excluding inventories and net exports. That measure increased 2.1 percent last quarter after a 1.2 percent gain. Also holding back economic growth in the second quarter was a decrease in residential investment, which fell at a 6.1 percent pace. That was the most since the third quarter of 2010 and marked the first decrease in two years. Government spending also shrank last quarter, declining 0.9 percent, the most in more than two years as outlays for the military fell. States and municipalities also cut back. The GDP report also showed price pressures remain limited. A measure of inflation, which is tied to consumer spending and strips out food and energy costs, climbed at a 1.7 percent annualized pace compared with 2.1 percent in the prior quarter. Fed policy makers, who left interest rates unchanged this week, said risks to the U.S. outlook have “diminished” and the labor market is getting tighter, suggesting conditions are turning more favorable for an increase in borrowing costs. U.S. Economy Grew Less-Than-Forecast 1.2% in Second QuarterSho ChandraIf

U.S. households decide to work fewer hours and take more leisure time, which component of GDP is most likely to decrease as a result? Choose one: A. net exports B. investment C. consumption D. government spending

Part 2 (2.5 points) Based on the information in the article, does it appear that in early 2016 U.S. households in fact worked fewer hours and took more leisure time? What do the data suggest? According to the article (household consumption,hoisehold incomes, or unemployment) grew at an annualized rate of ( what?) percent, a ( drop or jump ?) compared to the recent past. This suggests that households worked (fewer or mre?) hours and took (less or more?) leisure time. 2 OF 19 QUESTIONS COMPLETED