An AP has first term 7 and common difference 4. If the sum of all it's terms is 900,how many term are there?

The area of the right triangular puppy pen found using the formula 1/2(b.h²) is 4900.90 feet².

What is a triangle?

A polygon with three edges and three vertices is called a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A right triangle is a specific kind of triangle that has one angle that is exactly 90 degrees.

Given,

 The length of OY = 12 feet

The length of DY = 31 feet

m∠OYD = 65°

Since SDOG is a rectangle, m∠DOY = 90°.

So the ΔDOY is a right triangle.

Area of right triangle = 1/2 * b * h²

where b = base length

          h = height

From the given figure,

b = OY = 12

h = OD

h can be found using Pythagoras' theorem.

DY² = OD² + OY²

OD² = DY² - OY² = 31² - 12²  = 817

OD = √817 = 28.58 feet = h

Therefore the area of the right triangle ΔDOY is

area =  1/2 * b * h² = 0.5 * 12 *28.58² = 4900.90 feet².  

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The required formula that describes the given variation is F = 1.6d².

The general formula to describe the variation that F is directly proportional to the square of d is F = kd²,

where k is a constant of proportionality.

To determine the value of k, we can use the given information that F = 40 when d = 5:

40 = k(5)²

40 = 25k

k = 40/25

k = 1.6

Substituting this value of k into the general formula, we get:

F = 1.6d²

Therefore, the formula that describes the variation is F = 1.6d².

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The missing number in the sequence is 64

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

1, 4, 16, ____, 256, 1024, ...​

Using the above as a guide, we have the following:

To obtain the next term, we can multiply the previous term by 4:

So, we have

Next term = 16 * 4

Next term = 64

Therefore, the next term in the sequence is 64.

The completed sequence is: 1, 4, 16, 64, 256, 1024, ...

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Answer:

Step-by-step explanation:

well if there are 5 pepperoni pizzas that means that he eats 2 meaning he has 3 pepperoni slices of pizza.

The algebraic expression is h - 21 = 62

If we let "h" be Holly's original height,

The phrase "Holly's height decreased by 21 is 62" can be translated into an algebraic expression as:

h - 21 = 62

This equation represents the relationship between Holly's original height and her current height, after a decrease of 21 units.

We can solve for h by adding 21 to both sides of the equation:

h - 21 + 21 = 62 + 21

h = 83

Hence, Holly's original height was 83 units.

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In geometry, two triangles are said to be congruent if they are the same size and shape. This means that all corresponding angles and sides are equal.

To prove that two triangles are congruent, we must use one of the five congruency tests: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL).The SSS test states that if all three sides of two triangles are equal, then the triangles are congruent. The SAS test states that if two sides and the included angle of two triangles are equal, then the triangles are congruent. The ASA test states that if two angles and the included side of two triangles are equal, then the triangles are congruent. The AAS test states that if two angles and a non-included side of two triangles are equal, then the triangles are congruent. Lastly, the HL test states that if the hypotenuse and a leg of a right triangle are equal to the hypotenuse and a leg of another right triangle, then the triangles are congruent.In order to prove that two triangles are congruent, we must show that one of the five congruency tests is true. To do this, we can use techniques such as the Reflexive Property, the Symmetric Property, and the Transitive Property. We can also use logical reasoning, such as if two angles are equal and their corresponding sides are proportional, then the triangles must be congruent.

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What is the definition of congruent triangles?

The number of possible requests for free samples is 5^1 = 5. This means that the customer has 5 different requests that they can make for free samples.

The number of possible requests for free samples can be calculated using the combination formula. The combination formula is used to calculate the number of combinations with repetitions of size “n” taken from a set of “r” elements . The formula is: [tex]C(n,r) = n^r[/tex] In this case, n = number of requests (1 request) and r = number of free samples offered (let’s say, 5). Therefore, the number of possible requests for free samples is[tex]5^1 = 5.[/tex]This means that the customer has 5 different requests that they can make for free samples.

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As per unitary method, you'll earn $9.50 by selling five magazine subscriptions.

The unitary method is a method of finding a single value of a quantity or unit, given the value of a unit of the same quantity. In this case, we need to find out how much money you'll earn by selling magazine subscriptions.

We know that for selling the first subscription, the magazine company will pay you $1.50. For each additional subscription sold, the magazine company will pay 20 cents more than what was paid for the previous subscription.

Let's use the unitary method to find out how much you'll earn by selling the second subscription.

The magazine company pays 20 cents more than $1.50 for the second subscription. Therefore, the payment for the second subscription is

=> $1.50 + $0.20 = $1.70.

Using the same method, we can calculate the payment for the third subscription, which is

=> $1.70 + $0.20 = $1.90.

Similarly, we can use the unitary method to calculate the payment for the fourth, fifth, and so on, subscriptions.

By adding up the payments for each subscription, we can calculate your total earnings. Let's assume you sold five subscriptions.

The payment for the first subscription is $1.50, for the second subscription, it's $1.70, for the third subscription, it's $1.90, for the fourth subscription, it's $2.10, and for the fifth subscription, it's $2.30.

Total earnings = $1.50 + $1.70 + $1.90 + $2.10 + $2.30 = $9.50.

Therefore, you'll earn $9.50 by selling five magazine subscriptions.

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The unknown number's variable w is equal to -10.

In mathematics, a variable is an alphabet or phrase that represents an unknown quantity, unknown value, or unknown number. The variables are used, particularly when dealing with algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.

The following information can be written as an equation to express it:

4 + w/5 = 2

By deducting 4 from both sides of the equation, we may isolate the variable on one side and solve for w:

w/5 = -2

Then, to find w, we can multiply both sides by 5.

w = -10

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Answer:

The radical approximations of 7.07, 7.21, and 7.93 to the nearest whole number are:

2.65

2.68

2.82

Step-by-step explanation:

Sure, here's a step-by-step explanation of finding the approximate square root of 7.07, 7.21, and 7.93 to the nearest whole number:

Start by finding an approximate square root by making an educated guess or by using a calculator.

Use the initial guess to determine if the number is closer to the actual square root or to a smaller or larger value.

Refine the estimate by averaging the guess and the number divided by the guess.

Repeat the process of refining the estimate until a satisfactory level of accuracy is reached.

Here's an example for 7.07:

An educated guess for the square root of 7.07 could be 2.7

Dividing 7.07 by 2.7 gives an estimated value of 2.61, which is closer to the actual value.

To get a more accurate estimate, the average of 2.7 and 2.61 (2.655) is taken as the new estimate.

Repeat steps 2 and 3 until the desired level of accuracy is achieved.

After several iterations, the square root of 7.07 is approximately equal to 2.65.

Similarly, you can find the approximate square roots of 7.21 and 7.93.

Work Shown:

48w+23

48*3+23

144+23

167

It takes 167 minutes to cook 3 kg of meat.

Convert this to hours+minutes format.

167 min = 120 min + 47 min

167 min = 120/60 hr + 47 min

167 min = 2 hr + 47 min

Answer:

(36 - 18x) / x√(36x^2)

Step-by-step explanation:

I assume that the expression is:

1/x - 3/6

To simplify the expression and put it in the simplest radical form, we need to find a common denominator for the two terms. In this case, the least common multiple (LCM) of the denominators is 6x. Thus, we can rewrite the expression as:

(6/x) / (6x/6) - (3/6) / (6x/6)

Simplifying the above expression gives:

(6/x) / (x/6) - (3/6) / (x/6)

(6/x) * (6/x-3) / (x/6)

Simplifying the expression further gives:

(36/x^2 - 18/x) / (x/6)

We can simplify this expression by multiplying the numerator and denominator by 6x^2, which gives:

(36 - 18x) / x√(36x^2)

Therefore, the expression in the simplest radical form is:

(36 - 18x) / x√(36x^2)

Answer:

just 150x2 = 300 minutes or just 150 minutes to cook

Step-by-step explanation:

The cooking time of a turkey depends on its weight, so a 16-pound turkey will take longer to cook than an 8-pound turkey. However, without additional information such as the cooking method, temperature, and the shape and size of the turkeys, it's not possible to determine the exact cooking time for the 16-pound turkey.

Kathy should take 4 trips if the price of a round-trip ticket is 230.

Point A on the graph would be placed at (230, 4). This demonstrates that Kathy should take 4 trips if the price of a round-trip ticket is 230. This can be calculated as follows:

Kathy has a budget of 1,000. Therefore, she can afford 4 round-trip tickets at the price of 230 each. This can be calculated by dividing 1000 by 230, which gives 4. Therefore, Kathy should take 4 trips if the price of a round-trip ticket is 230.

It is important to note that Kathy should also consider other factors such as the cost of other expenses, such as accommodation and food, when deciding how many trips to take. Additionally, Kathy may also want to consider whether the benefits of taking more trips are worth the additional cost.

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The simplified product of the ^3sqrt2x^5 x ^3sqrt64x^9 is [tex]24\sqrt{2} x^{17}[/tex]

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

For finding the simplified product we will first remove the squareroot possible and simplify the value in a simplest way as possible. In the given question, first we will simplifying [tex]\sqrt{64}[/tex] and after simplifying it we will then apply [tex]a^{n} . a^{m} = a^{n+m}[/tex], and lastly we will multiply the two numbers i.e., 3 and 8.

[tex]3\sqrt{2}x^5x^3\sqrt{64}x^9[/tex]

[tex]3\sqrt{2}x^5x^3\sqrt{8^{2} }x^9[/tex]

[tex]3.8\sqrt{2}x^{5+3+9}[/tex]

[tex]3.8\sqrt{2}x^{17}[/tex]

[tex]24\sqrt{2}x^{17}[/tex]

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The correct order of the ratios from the least to the greatest is given below:

4/2, 11 to 2, 22:3, 30/4, 36:5

Least to greatest: 4/2 = 2, 11:2 = 5.5, 22:3 = 7.33, 30:4 = 7.5, 36:5 = 7.2

15/4, 19 to 5, 53/15, 4:1, 18 to 6

Least to greatest: 15/4 = 3.75, 19:5 = 3.8, 53:15 = 3.53, 4:1 = 4, 18:6 = 3

7:11, 8:12, 6:10, 1/2, 7:4

Least to greatest: 7:11 = 0.6364, 6:10 = 0.6, 8:12 = 0.6667, 1/2 = 0.5, 7:4 = 1.75

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

Therefore,

The ratios listed in the question are ordered from least to greatest by converting each ratio into a decimal and comparing the values.

In each case, the fraction is divided, the ratio of two numbers is expressed as a decimal, and then the decimals are ordered from least to greatest.

For example, in the first list, the ratio "11 to 2" is expressed as the decimal 11/2, which is equal to 5.5. The other ratios are similarly expressed as decimals and then ordered to get the final answer.

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The equation can be written in slope-intercept form as y = -43x - 250. This equation has a slope of -43 and a y-intercept of -250.

Subtract 2 from both sides:

y - 2 - 2 = -43(x + 6) - 2

y - 4 = -43(x + 6)

Divide both sides by -43:

(-1/43) * (y - 4) = x + 6

(-1/43)y - (-4/43) = x + 6

x = (-1/43)y + (-38/43)

Add 6 to both sides:

x + 6 = (-1/43)y + (-32/43)

Subtract (-1/43)y from both sides:

x + 6 - (-1/43)y = (-32/43) - (-1/43)y

x + 6 + (1/43)y = (-32/43)

Multiply both sides by -43:

(-43)(x + 6 + (1/43)y) = (-43)(-32/43)

-43x - 250 = -32

Add 250 to both sides:

-43x - 250 + 250 = -32 + 250

-43x = 218

Divide both sides by -43:

x = (-218)/(-43)

x = 5

The equation can be written in slope-intercept form as y = -43x - 250. This equation has a slope of -43 and a y-intercept of -250.

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Two events that are disjoint are not independent. This is because that disjoint events do not overlap, which means that if one event occurs, the other cannot. So, the occurrence of one event provides information about the absence of the other, which violates the definition of independence.

Two events A and B are considered independent if the occurrence of A has no effect on the likelihood of B occurring, and vice versa.

In other words, the probability of both events happening at the same time is equal to the product of their individual probabilities:

[tex]P(A and B) = P(A) * P(B) (B).[/tex]

This formula cannot be satisfied when two events are disjoint because if one event occurs, the other cannot occur. As a result, two disjoint events are not independent.

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Answer:

1. 285 centiliters

2. yards-->inches-->centimeters

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

3+3 = 6 which is not more than 6 hours

3 x $25 = $75

3 x $15 = $45

$75 + $45 = $120

The expression is a summation formula, representing the sum of a series of values. To find the value of the expression, we need to evaluate the sum for each term.

The general formula for each term is:

900(1.04)^n

where n is the term number and 1.04 is the common ratio.

For the first term (n = 1), the formula is:

900(1.04)^1 = 900 * 1.04 = 937.6

For the second term (n = 2), the formula is:

900(1.04)^2 = 900 * 1.04^2 = 976.9792

And so on, for each term. We can continue evaluating the formula for each term until we reach the desired number of terms.

Let's evaluate the expression for n = 10 terms.

The sum of the first 10 terms is:

937.6 + 976.9792 + 1018.057312 + ... + 1412.14803883

The value of the expression is approximately 1412.15.

Rounding to the nearest integer, the answer is 1412.

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Answer:

48

Step-by-step explanation:

the sequence of numbers alternates between adding 6 and 8.

6 + 6 = 12

12 + 8 = 20

20 + 6 = 26

26 + 8 = 34

34 + 6 = 40

40 + 8 = 48!

i hope this helps :)

Answer:48

Step-by-step explanation:The sequence adds 6 first then adds 8

The amount of money that the items will cost you to send through United States Postal Service would be = $13.3

The dimensions of the first envelope = 20 L, 10°H and 4"W

The weight of the first envelope = 10 ounce.

The first envelope is a parcel because the dimensions are larger than 11.5 L, 6.125" H, 0.25"W.

The price per ounce = $1.22

10 ounce = 1.22×10 = $12.2

The dimensions of the second envelope = 8 L, 5" H and 0.20 W.

The weight of the second envelope = 2.5 ounce.

The second letter is of normal letter size because of the dimensions (min. dimension: 5" L, 3.5" H, 0.007" W; max. dimension: 11.5 L, 6.125" H, 0.25 W, max. weight 3.5 oz)

The price per ounce = $0.44

2.5 ounce = 2.5× 0.44 = $1.1

The total price = 12.2+1.1 = $13.3

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The value of the equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex] after taking the integral is  [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].

What is meant by the integral of an equation?

Calculating areas, volumes, and their extensions require the use of integrals, which are the continuous equivalent of sums. One of calculus' two fundamental operations is integration, which involves computing integrals. The other essential operation is differentiation. The area under the graph of a function for some interval can be expressed numerically as the integral (definite integral), or a new function can be created whose derivative is the original function (indefinite integral).

Given equation [tex]\frac{x+1}{x(1+x.e^x)}dx[/tex]

Multiply and divide the equation by eˣ

The equation becomes [tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx[/tex]

Now substitute eˣx = a

Differentiating both sides

[eˣ + xeˣ]dx = da

eˣ[1+x]dx = da

Substituting the above in the equation

[tex]\frac{e^x(x+1)}{e^xx(1+x.e^x)}dx = \frac{da}{a(1+a)}[/tex]

Now add and subtract a in the numerator

[tex]\frac{1 da}{a(1+a)} = \frac{a-a+1}{a(1+a)} da = \frac{a+1-a}{a(1+a)} da = \frac{1}{a} da - \frac{1}{a+1} da[/tex]

Now taking integral

[tex]\int \frac{1}{a} da -\int \frac{1}{a+1} da = ln(a) - ln(a+1) + c = ln ( \frac{a}{a+1} ) + c[/tex]

Now substituting back the value of a = eˣx

Therefore the value of the equation after taking the integral is  [tex]ln ( \frac{x.e^x}{x.e^x+1} ) + c[/tex].

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The slope-intercept equation of this linear function is y = -3x + 5.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Based on the information provided, we can logically deduce the following data points on the line:

At point (0, 5), a linear equation of this line can be calculated in slope-intercept form as follows:

y - 5 = (2 - 5)/(1 - 0)(x - 0)

y - 5 = -3(x - 0)

y = -3x + 5

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Answer: x=8

Step-by-step explanation: since we know 2 sides of both quadrilaterals and they are similar,

just put 32/40 = 24/3x+6 ,

cross multiply ( 32 x 3x+6   and 40 x 24),

they become 96x +192 = 960.

move 192 to the other side and divide both sides by 96

She travel  31.25 miles we calculate it by multiply by speed and time

Speed indicates how quickly something or someone is moving. If you know how far something has travelled and how long it took to get there, you can calculate its average speed. Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example because the distance is measured in metres (m) and the time is measured in seconds (s).The formula can be rearranged in three ways:

speed = distance ÷ time

distance = speed × time

time = distance ÷ speed

To calculate one of the variables (speed, distance or time) we need the other two.

As given in Question she cycled at speed 12 1/2 miles per hours

12 1/2  can be written as 12.5 miles per hours

and she cycled for 2 1/2 hours which can be written as 2.5 hours

and to find the distance how much she total travel we have to multiply the speed and time

distance = 12.5x2.5 = 31.25 miles

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Answer: To determine the amount in Heidi's 401(k) account after 15 years, we need to calculate her total contribution each month and the interest earned on that contribution over the 15-year period.

First, let's calculate Heidi's contribution each month:

11% of $3,250 = $357.50

Next, let's calculate her employer's contribution each month:

6% of $3,250 = $195

Since Heidi's contribution is $357.50, and her employer matches her contribution up to 6% of her salary, her employer will contribute $195 each month.

So, Heidi's total contribution each month is $357.50 + $195 = $552.50

Next, we can use the formula for compound interest to calculate the balance in her 401(k) account after 15 years:

A = P * (1 + r/n)^(nt)

where:

A is the balance in the account after t years

P is the principal (initial deposit)

r is the interest rate

n is the number of times the interest is compounded in a year

t is the number of years

In this case, n = 12 (because interest is compounded monthly) and t = 15 (because the calculation is for 15 years). The principal P is $552.50 (Heidi's total contribution each month). The interest rate r is 6.25%.

Plugging in the values, we get:

A = $552.50 * (1 + 0.0625/12)^(12 * 15) = $552.50 * (1.00520833)^180

Using a calculator or spreadsheet software, we can calculate this value to be approximately $27,973.81.

So, the amount in Heidi's 401(k) account after 15 years, rounded to the nearest cent, is $27,973.81.

Step-by-step explanation:

The sequence is a geometric sequence with a common ratio of 4.

What is a geometric sequence?

A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a fixed non-zero number called the common ratio (r).

To determine whether the sequence is arithmetic or geometric, we can look at the differences between consecutive terms.

The difference between the second and first terms is 2 - 0.5 = 1.5.

The difference between the third and second terms is 8 - 2 = 6.

The difference between the fourth and third terms is 32 - 8 = 24.

The difference between the fifth and fourth terms is 148 - 32 = 116.

Since the differences are not constant, the sequence is not arithmetic.

To determine if it is a geometric sequence, we can look at the ratios of consecutive terms.

The ratio of the second and first terms is 2/0.5 = 4.

The ratio of the third and second terms is 8/2 = 4.

The ratio of the fourth and third terms is 32/8 = 4.

The ratio of the fifth and fourth terms is 148/32 = 4.

Since the ratios are constant, the sequence is geometric with a common ratio of 4.

Therefore, the sequence is a geometric sequence with a common ratio of 4.

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Gold costs less than platinum per ounce because the slope of the graph for gold is less than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars per ounce.

In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Mathematically, the slope (rate of change) can be calculated by using this mathematical expression;

Rate of change (slope), m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change (slope), m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph of the weight of gold and platinum, we can reasonably infer and logically deduce that the slope (unit rate) of the graph for gold is less than the slope (unit rate) of the graph for platinum.

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Complete Question:

Use the drop-down menus to complete the statements to match the information shown by the graph.

A graph has weight (ounces) on the x-axis, and cost (dollars) on the y-axis. A line labeled gold starts at (0, 0) and has a positive slope. A line marked platinum starts at (0, 0) and has a greater positive slope than gold.

Gold costs ---------------- platinum per ounce because the ----------- of the graph for gold is -------------that of the chart for platinum. The --------of the graph tells you the unit rate in _____.