Using Pythagoras' theorem, calculate the value of x. Give your answer in centimetres (cm) and give any decimal answers to 1 d.p. x 16 cm 30 cm​

The approximate diameter of the pile of sand in the cone that sand was dumped in is 9.30 feet.

What is the approximate diameter?

A cone is a 3-dimensional object that consists of a ciruclar base and a vertex. The diameter is twice the length of the radius.

Radius = √[volume / (1/3 x π x height)]

=> Radius=√[136 / (1/3 x 22/7 x 6)]

=> Radius=√[136 / 6.29 = 4.65

Hence the Diameter = 4.65 x 2 = 9.30 feet

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After answering the provided question, we can conclude that So the total  equation amount of time Sarah spent on these three activities is determined by how much time she spent reading.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "[tex]2x + 3 = 9[/tex]" asserts that the statement "[tex]2x + 3[/tex]" equals the value "9". The goal of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complex, regular or nonlinear, and include one or more factors. In the equation "[tex]x^2 + 2x - 3 = 0[/tex]," for example, the variable x is raised to the second power. Lines are used in many different areas of mathematics, such as algebra, calculus, and geometry.

Let's call Sarah's reading time "r" in minutes.

We can deduce from the problem:

Sarah painted for 5 minutes.

Because she spent twice as much time reading as she did painting,[tex]r = 2*5 = 10.[/tex]

She hiked for 35 minutes longer than she read, so [tex]h = r + 35.[/tex]

To calculate Sarah's total time spent on these three activities, simply add the times:

Time spent painting + time spent reading + time spent hiking = total time

Time total =[tex]5 + 10 + (r + 35)[/tex]

Time total = [tex]50 + r[/tex]

So the total amount of time Sarah spent on these three activities is determined by how much time she spent reading.

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The correct answer of the folowing question is option B and d in context to the circle and triangle

How to solve the problem?

Triangles and circles have a close relationship in geometry, and several interesting properties and theorems connect them.

One triangle inscribed in circle: This statement is true, and it refers to the property of a circle that can be inscribed in a triangle. In other words, if we draw a circle that passes through all three vertices of a triangle, then the triangle is said to be inscribed in the circle. The center of the circle is called the circumcenter of the triangle, and it is the intersection point of the perpendicular bisectors of the sides.

Many triangles inscribed in circle: This statement is also true, as there are many different triangles that can be inscribed in the same circle. For example, if we draw a circle and pick any three points on its circumference, then we can connect these points to form a triangle that is inscribed in the circle.

One circle inscribed in triangle: This statement is true, and it refers to the property of a triangle that can be inscribed in a circle. In other words, if we draw a circle that is tangent to all three sides of a triangle, then the circle is said to be inscribed in the triangle. The center of the circle is called the incenter of the triangle, and it is the intersection point of the angle bisectors.

Many circles inscribed in triangle: This statement is false, as there can only be one circle that is inscribed in a given triangle. However, there are other circles that can be associated with a triangle, such as the circumcircle and the excircles. The circumcircle is the circle that passes through all three vertices of the triangle, while the excircles are the circles that are tangent to one side of the triangle and the extensions of the other two sides.

In summary, triangles and circles are closely related in geometry, and their properties and theorems are important in various areas of mathematics and science.

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Answer:

y = [tex]\frac{1}{3}[/tex] x - 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x - 10 ← is in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex] , then

y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation

to find c substitute (9, - 2 ) into the partial equation

- 2 = [tex]\frac{1}{3}[/tex] (9) + c = 3 + c ( subtract 3 from both sides )

- 5 = c

y = [tex]\frac{1}{3}[/tex] x - 5 ← equation of perpendicular line

Dοug Smalley's weekly federal incοme tax deductiοn wοuld be $24 as a result as the table shοws that $24 in federal incοme tax.

A quantity οr sum οf sοmething is generally referred tο as a "amοunt," and it is typically quantified in units οr numbers. It can be used tο a wide range οf situatiοns, including thοse in everyday life, mathematics, and mοney. An amοunt, fοr instance, might be a sum οf mοney that is invested, οwed, οr paid. An amοunt in mathematics can be either a quantity οr a numerical value. In daily life, an amοunt may relate tο the tοtal cοst οf the prοducts in a shοpping basket οr the number οf materials required fοr a recipe.

Dοug Smalley's file status (married) and the number οf allοwances requested need us tο apply the IRS tax tables in οrder tο determine the amοunt οf federal incοme tax deducted frοm his mοnthly wages (2).

Determine the emplοyee's weekly grοss pay: $485

Remοve the amοunt οf the emplοyee's claimed weekly allοwances. The amοunt is $162.80 ($86.40 fοr the first allοwance and $76.40 fοr the secοnd allοwance) fοr twο allοwances in 2021.

$485 - $162.80 = $322.20 (adjusted grοss pay) (adjusted grοss pay)

Find the rοw fοr Dοug's adjusted grοss pay οf $322.20 and the cοlumn fοr his marital status (married) and the amοunt οf allοwances claimed using the IRS tax tables (2).

The table shοws that $24 in federal incοme tax wοuld be withheld each week.

Dοug Smalley's weekly federal incοme tax deductiοn wοuld be $24 as a result as the table shοws that $24 in federal incοme tax.

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Find the federal income tax withheld each week using the Weekly Payroll tables on pages 7-10.

Doug Smalley, a store manager, is married and earns $485 a week. He claims 2 allowances.

Answer:

Step-by-step explanation:

P(x)=x³+6x²+3x-10=0

x³+2x²+4x²+8x-5x-10=0

x²(x+2)+x(x+2)-5(x+2)=0

(x+2)(x²+x-5)=0

either x+2=0,x=-2

or

x²+x-5=0

[tex]x=\frac{-1 \pm \sqrt{1^2-4 \times 1 \times(-5)} }{2 \times 1} \\=\frac{-1 \pm \sqrt{21} }{2} \\Hence ~x=\frac{-1+\sqrt{21} }{2} \\or\\x=\frac{-1 -\sqrt{21} }{2}[/tex]

Answer:$163.68

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

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

where:

A = final amount ($600,000)

P = initial amount (unknown)

r = interest rate (8%)

n = number of times interest is compounded per year (12 for monthly)

t = time in years (25)

Substituting in the values, we get:

$600,000 = P(1 + 0.08/12)^(12*25)

Simplifying:

$600,000 = P(1.00666666666667)^300

Dividing both sides by (1.00666666666667)^300:

P = $600,000 / (1.00666666666667)^300

Using a calculator, we get:

P = $163.68

Therefore, we would need to invest $163.68 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.

It should be noted that the function that can model the data is a linear function since there's a constant difference or -5.The linear function is y = -5x - 9.

In this case, to determine whether the data is best modeled by a linear, quadratic, or exponential function, we can first plot the data points and see what type of curve they form. However, since we are only given five data points, it can be difficult to make a definitive determination.

One way to estimate the type of function is to look at the differences between the y values. For example, if the differences between the y values increase by a constant amount, then the data may be best modeled by a linear function. If the differences increase by a constant squared amount, then the data may be best modeled by a quadratic function.

Here, the constant difference will be:

= -29 - (-24)

= -5

This depicts a linear function.

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The response is B) 5√6 in accordance with the provided assertion.

The hypotenuse of a right triangle is its longest side; its "opposite" side is the side that confronts the angle in issue; and its "adjacent" half is the side that faces it.

In a 45°-45°-90° triangle, the two legs are congruent, and the hypotenuse is equal to the leg multiplied by √2.

In this case, the leg length is given as 5√3.

Thus, the hypotenuse will have the following length:

hypotenuse = leg x √2 = 5√3 x √2 = 5√(3 x 2) = 5√6

Therefore, the answer is B) 5√6.

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Answer:

well none of those are technically correct because A is 11, B is 7, C is 0, and D is 18

all of those answers are Mayan numerals

Therefore, each drink would have approximately 18.67 grams of sugar if the amount of sugar was redistributed evenly.

In statistics, distribution refers to the pattern of values that a variable can take and how frequently those values occur. It is a mathematical function that describes the probability of occurrence of each possible outcome in a set of events.

There are various types of distributions such as normal distribution, binomial distribution, Poisson distribution, and exponential distribution. Each distribution has a specific shape and characteristics, which can be described by its mean, variance, skewness, and kurtosis.

by the question.

Let's say the amounts of sugar in the six drinks are:

Drink 1: 10 grams

Drink 2: 20 grams

Drink 3: 15 grams

Drink 4: 25 grams

Drink 5: 30 grams

Drink 6: 12 grams

To redistribute the sugar evenly, you would need to add up the total amount of sugar and divide it by the number of drinks. In this case:

Total amount of sugar = 10 + 20 + 15 + 25 + 30 + 12 = 112 grams

Number of drinks = 6

Redistributed amount of sugar = Total amount of sugar / Number of drinks

Redistributed amount of sugar = 112 / 6

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Answer:

Para decidir si es mejor rentar o comprar la máquina excavadora, se debe calcular el costo anual de cada opción y compararlos.

Costo anual de renta = Costo de renta mensual x 12 meses + (Costo diario x Días de uso)

Costo anual de renta = 3000 x 12 + (180 x Días de uso)

Costo anual de renta = 36000 + 180D

Costo anual de compra = Costo fijo anual + (Costo diario x Días de uso)

Costo anual de compra = 20000 + (230 x Días de uso)

Para encontrar el número mínimo de días de uso que justificarían la renta en lugar de la compra, se debe igualar ambos costos anuales:

36000 + 180D = 20000 + 230D

50D = 16000

D = 320

Por lo tanto, el constructor tendría que utilizar la máquina excavadora al menos 320 días al año para justificar la renta en lugar de la compra.

John deposits $5025 into a savings account that has an interest rate of 9.5%. The account is compounded monthly for the next 18 years. So in the account the amount will be $27596.60. Option c is correct.

Cοmpοund interest, alsο knοwn as interest οn principle and interest, is the practise οf adding interest tο the initial amοunt οf a lοan οr depοsit. It οccurs when interest is reinvested, οr added tο the bοrrοwed capital rather than paid οut, οr when the bοrrοwer is required tο pay it, sο that interest is made the fοllοwing periοd οn the initial amοunt + any accumulated interest. In business and ecοnοmy, cοmpοund interest is cοmmοn.

We can use the Cοmpοund interest below-

[tex]\rm A = P(1 + \frac{r}{n})^{nt}[/tex]

where,

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Given,

Time periods (t)= 18years

n = 12 months

Interest in a year (r)= 9.5% or 0.095

Principial amount (P)= $5025

Lets solve for final amount :

[tex]\rm A = 5025(1 + \frac{0.095}{12})^{12 \times 18}[/tex]

A ≈ 27596.59

That is nearby $27596.60.

In the account the amount will be $27596.60. Thus, option c is correct.

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Answer: it is  c. 27596.60

Hypothesis Testing ,Sample data  , Categorical  ,one variable ,one sample and sample z test for a proportion are the  responses to the question were used to learn about the population of adult Americans who self identify as an entrepreneur.

(a) The question type in this study is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.

(b) The study type is sample data, as a sample of adult Americans was surveyed to learn about the population of adults who self-identify as entrepreneurs.

(c) The data is categorical, as the respondents were asked to self-identify as either an entrepreneur or not.

(d) There is one variable in this study, as the responses to the question about self-identification as an entrepreneur are the only data collected.

(e) There is one sample in this study, as only one group of adult Americans was surveyed.

(f) The appropriate method for analyzing the data in this study is the one-sample z test for a proportion. This method is used when we have one categorical variable and want to test whether the proportion of a certain response differs significantly from a hypothesized proportion. In this case, the hypothesized proportion would be the proportion of adult Americans who self-identify as entrepreneurs. We would use the z-test to determine if the proportion of respondents who self-identify as entrepreneurs is significantly different from the hypothesized proportion. If the difference is significant, we can conclude that there is a difference between the sample and population proportions, and if the difference is not significant, we cannot reject the null hypothesis that the sample proportion is the same as the population proportion.

Overall, this study is using categorical data to learn about the proportion of adult Americans who self-identify as entrepreneurs. The appropriate method for analyzing this type of data is the one-sample z test for a proportion, which allows us to test whether the sample proportion is significantly different from the hypothesized population proportion.

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Answer:

Thank you for the statement. Is there a question or additional information you would like me to respond to?

Step-by-step explanation:

Answer:

122 degrees.

Step-by-step explanation:

To calculate the measure of the sector that represents the probability of a rainy day using a spinner, we need to first determine the angle of the sector that represents the probability of a rainy day.

The probability of a rainy day is given as P(raining) = 0.34, which means that out of 100 days, 34 are rainy. Therefore, we can express the angle of the sector as:

Angle of sector = Probability of rain * Total angle of the spinner = 0.34 * 360 = 122.4 (rounded to the nearest degree)

So the measure of the sector that represents the probability of a rainy day is 122 degrees (rounded to the nearest degree).

Therefore, the answer is 122 degrees.

Answer:122°

Step-by-step explanation:

we have a 34% probability that it will rain and 66% that it won't rain. and full spin is 360 degrees which we can also symbolize as 100%.

so, if  

        360-----------100%

         x---------------34%

x=360*34/100≈122°

Answer:

1/3 or 2/6

Step-by-step explanation:

6/6 is a whole. If you subtract 1/6 from 6/6, you get 5/6. Then, subtract 3/6 from 5/6. You get 2/6 remaining for the result. 2/6 simplified is 1/3.

Answer:

2/6

Step-by-step explanation:

We Know

She will use 1/6 of the poster for the title and 3/6 of the poster for a diagram of her experiment.

1/6 + 3/6 = 4/6

So, 4/6 of her poster has been used.

The rest of the poster will be used for the results of her experiment

How much of the poster will Katy use for the results?

We Take

6/6 - 4/6 = 2/6

So, 2/6 of her poster will be use for the result.

Answer:

28  

Step-by-step explanation:

a = b * h

a = 4 * 7

4 acts as the base

7 acts as the height

there is a right angle to support this.

I think it is A... if the original is Red. It is reflected across the x-axis.

I hope this helps !

Answer:

6 1/40

Step-by-step explanation:

21/8 + 17/5

105/40 + 136/40 = 241/40

241/40= 6 1/40

Answer:

To find the percentage decrease, we need to find the difference between the original price and the new price, divide that difference by the original price, and then multiply by 100 to express the result as a percentage.

The difference between the original price and the new price is:

990 - 765 = 225

Dividing the difference by the original price gives:

225 ÷ 990 ≈ 0.227

Multiplying by 100 gives:

0.227 x 100 ≈ 22.7

Therefore, the percentage decrease in the monthly price of the contract is approximately 22.7%.

Step-by-step explanation:

Answer:

[tex]\frac{x^{7} }{y^{10} }[/tex]

We can use trigonometry to solve this problem. Let x be the distance from the foot of the ladder to the building, and let y be the length of the ladder. Then, we have:

tan(52) = y/x (since tangent = opposite/adjacent, and y is opposite to the angle of elevation and x is adjacent)

We also know that the ladder reaches 12 feet above the ground, so we have:

y = 12 + x (since y is the hypotenuse of the right triangle formed by the ladder, the ground, and the building)

We can substitute the second equation into the first to get:

tan(52) = (12 + x)/x

Simplifying this equation, we get:

tan(52)x = 12 + x

Using a calculator to find the tangent of 52, we get:

1.2799x = 12 + x

Solving for x, we get:

0.2799x = 12

x = 42.87 feet (rounded to two decimal places)

Therefore, the foot of the ladder is approximately 42.87 feet away from the building.

The statement which is correct is: If {α, β} is independent, then {w₁, w₂, w₁+ w₂} is in dependent.

In vector space theory, a set of vectors is said to be linearly independent if there is no non-trivial linear combination of vectors equal to vector zero. If such a linear combination exists, the vectors are said to be linearly dependent. These concepts are central to dimension definitions.

The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space are linearly dependent is essential to determining the dimensionality of a vector space.

According to the Question, we know that:

{w₁, w₂, w₃} are linearly independent.

Let, α₁, α₂, α₃ such that

α₁w₁ + α₂w₂+ α₃w₃ = 0

and, α₁ = α₂ = α₃ = 0

Again considering the following, we can say that:

{w₁, w₁+ w₂, w₁+w₂+w₃} such that:

β₁(w₁) + β₂(w₁+ w₂) + β₃(w₁+ w₂+ w₃) = 0

Here, the dependent variable is {α,β} and { w₁+ w₂+ w₃}

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Answer:

X × Y

Step-by-step explanation:

Because you need do the multiplication between the time and the money

Value of base and hypotenuse of triangle are 9√3 and 18 respectively.

A right triangle is a triangle with one interior angle measuring 90 degrees, known as a right angle. The side opposite to the right angle is called the hypotenuse, and the other two sides are known as the legs of the right triangle. The length of the hypotenuse can be found using the Pythagorean theorem,  that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Height of triangle=9

Base of triangle=y

Hypotenuse of triangle=x

Using trigonometric ratio

Sin30°=Height/Hypotenuse

½=9/x

x=18

Cos30°=Base/hypotenuse

√3/2=y/18

y=9√3

Hence, value of base and hypotenuse of triangle are 9√3 and 18 respectively.

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Answer:

The answer is 7d < -6

Step-by-step explanation:

3d-8<4d+2

3d+4d<-8+2

7d<-6

The maximum profit is $2492.08.

What is the selling price?

The cost a consumer pays to purchase a good or a commodity is known as the selling price. It is a price that is higher than the cost price and includes a profit margin. The cost of an item when acquired is referred to as its selling price (S.P.).

Here, we have

Given: A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation.

y = -3x² + 239x - 2268

At a maximum profit, dy/dx = 0, hence:

dy/dx = -6x + 239

0 = -6x + 239

x = 239/6

x = 39.8

The maximum profit is gotten when the selling price of each widget is 39.8. Hence:

y = -3(39.8)² + 239(39.8) - 2268

y = 2492.08

Hence,  the maximum profit is $2492.08.

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Answer:

[tex]c=18.8389[/tex]

Step-by-step explanation:

To find hypotenuse [tex]C[/tex] use formula:

 [tex]\text{sin}(\alpha )=\frac{a}{c}[/tex]

After substituting [tex]\alpha =48^o[/tex] and [tex]a=14[/tex] we have:

[tex]\text{sin}(48^o)=\frac{14}{c}[/tex]

[tex]0.7431=\frac{14}{c}[/tex]

[tex]c=\frac{14}{0.7431}[/tex]

[tex]c=18.8389[/tex]

Answer:31

Step-by-step explanation:

14/2=7 48/2= 24 7+24=31

The distance between the two towns on the map was found to be 30.67 centimeters by setting up and solving a proportion between the distances on the map and the actual distances.

The problem provides us with a scale on the map of 3 cm to 45 km, which means that every 3 centimeters on the map represents 45 kilometers in the actual world. Let x be the distance between the two towns on the map in centimeters. Using the proportion, we can set up the relationship between the distances on the map and the actual distances as follows:

3 cm / 45 km = x cm / 460 km

Here, we set up a ratio between the distance on the map and the actual distance, where the distance on the map is x centimeters and the actual distance between the towns is 460 kilometers. We can then cross-multiply to solve for x:

45 km * x cm = 3 cm * 460 km

This gives us:

45x = 1380

x = 1380 / 45

x = 30.67 cm

Therefore, the distance between the two towns on the map is 30.67 centimeters.

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