Use the diagram to answer each part of the question. The image is not drawn to scale.

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In the afternoon, the person (who is 1.6 m tall) casts a shadow that is 8 m. The distance along the ground from the person (H) to the tree (G) is 30 m, and the distance from the tree (G) to the building (F) is 105 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.

Answer:

382 cm²

Step-by-step explanation:

Front face + Back face:

A = 2(a + b)h/2

A = 2(14 cm + 8 cm)(7 cm)/2

A = 154 cm²

Left face:

A = 7 cm × 6 cm = 42 cm²

Right face:

A = 9 cm × 6 cm = 54 cm²

Bottom face:

A = 14 cm × 6 cm = 84 cm²

Top face:

A = 6 cm × 8 cm = 48 cm²

Total surface area =

= (154 + 42 + 54 + 84 + 40) cm²

= 382 cm²

The frequency of the periodic function is given by: 0.0796.

From the graph, we have that the period is of 4pi hours, hence the frequency is:

f = 1/4pi = 0.0796.

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Answer:

The value of x will be 2.5cm.

Step-by-step explanation:

Volume = Length*Width*Height

where,

[tex]v = l \times w \times h \: ...substitute \: values \\ 120cm {}^{3} = 12cm \times w \times 4cm \\ 120cm {}^{3} = 48cm {}^{2} \times w \: ...divide \: both \: \\ sides \:by \: 48cm {}^{2} \\ \frac{120cm {}^{3} }{48cm {}^{2} } = w \\ w = 2.5cm[/tex]

Answer:

17, 5

Step-by-step explanation:

Let the width be x

width = x

length = x + 12

length x width = x(x + 12)

length x width = x² + 12x

x² + 12x = 85

x² + 12x - 85 = 0

Now it is just a quadratic:

The 2 numbers we need are 17 and -5

(x + 17)(x - 5) = 0

x = -17 or x = 5.

Since width and length cannot be negative, x must equal 5.

Width = 5

length = 17

The answer is 17, 5.

We are given two things :

We can represent the length and width as x + 12 and x respectively.

Now, the formula for the area of a rectangle is :

Area = Length x width

Now, let's substitute the values for length and width in the formula along with the area.

We now have a quadratic equation, which can either be solved by splitting the middle term, or by using the quadratic formula. For convenience purposes, we'll go with the first one.

Answer:

1/36

Step-by-step explanation:

Assuming the dice has 6 sides in total, we can set up a probability for each scenario.

The chances of the dice landing on 1 will be 1/6, since there are 6 total faces. Same goes for the second die and landing on 4.

Now that we have our 2 probabilities, we multiply them to get the final probability. 1/6 x 1/6 = 1/36.

Answer:

Step-by-step explanation:

You can only multiply matrices if the number of columns in the matrix on the left is the same exact number as the number of rows in the matrix to the right of that other matrix.

The matrix on the left, |5 -2  4| has the dimensions

                                      1 x 3 (1 row, 3 columns)

The matrix to its right, |2  7  -3| has the dimensions

                                      1 x 3 (1 row, 3 columns).

Putting those dimensions next to each other in that order:

                  1 x 3     1 x 3

The bold print 3 and 1 have to be the same number (both 3's or both 1's) in order for the multiplication to work. This doesn't work; it's impossible.

Answer: -16

Step-by-step explanation:

i was on a unit exam typing in random numbers since i didn't know it and -16 is the right answer.

Answer:

sorry I don't know please forgive because I can't copy the question

The probability of Maria selecting 2 questions on Science is 1/ 5

From the information given, we have that there are;

The total questions = 2 + 4 + 4 = 10 questions

We have that Maria picks two questions at random

The probability of her selecting two questions on Science is given as

P(2 science) = number of Science questions/ total number of questions

P(2 science) = 2/ 10

P(2 science) = 1/ 5

The probability of picking two questions on Science is 1/5

Thus, the probability of Maria selecting 2 questions on Science is 1/ 5

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Answer:

1/45

Step-by-step explanation:

Using proportions, Nelly's total pay for last week was of £220.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From Monday to Friday, she worked 17 hours, hence:

On Saturday, she worked 5 hours, and was paid £16 per hour.

Hence her total payment is found as follows:

15 x 8 + 2 x 10 + 5 x 16 = £220.

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Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

The body temperature is simply a measure of how well a human body can produce and get rid of heat. the normal body temperature is or 37 degrees Celsius or 98.6 degrees Fahrenheit.

Given the data in the question;

To get Aakash body temperature in the evening, we simply add the initial body temperature and the the temperature increase.

Temperature in the evening = 99.2° Fahrenheit + 3.4° Fahrenheit

Temperature in the evening = 102.6° Fahrenheit

Given that, Aakash has a fever, if  his body temperature during the day was 99.2°F and by evening his body temperature has increased by 3.4°F, Aakash's body temperature in the evening is 102.6° Fahrenheit.

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Answer:

B. the second graph.

Step-by-step explanation:

Literally the photo is on the question.

Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2. Therefore, the correct option is option B.

The study of graphs, that are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. In this sense, a network consists of vertices, also known as nodes or points, linked by edges, also known as links or lines.

Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics that are investigated in discrete mathematics is graphs. Second graph represents (y-3)²/25 + (x+1)²/4 > 1 and y <= square root{x+5}+2.

Therefore, the correct option is option B.

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By finding some points on the curve and then connecting them.

Here we have the rational function:

t = d/s

Where t represents time, d distance, and s speed.

We assume that d is a fixed value, then our variables are time and speed.

On the examples, you can see that the value of d is:

d = 616.5km, then we just need to graph the equation:

t = (616.5km)/s

To do so, you can evaluate the function in different values of s, like the points the problem asks to graph, and then connect all these points with a curve.

Doing that, you should get a graph like the one below:

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After 16 days, the total homework questions that have been assigned would be 80 questions.

Ratio expresses the equivalent relationship between two numbers. It shows the frequency of the number of times that one value is contained within other value(s).

A ratio table can be described as table that shows equivalent values between two numbers.

The first step is to determine the ratio between the number of days and the total number of questions.

Ratio = money saved / money earned

8/10 =  total number of questions / number of days

55 / 11 = 5

Now, multiply the ratio gotten in the previous step by the number of days

Total number of homework questions = number of x ratio

5 x 16 = 80 questions

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GH 13000 is the amount of his sales for that month.

how to find sales of the month?

total income = salary + commission

total income = GH530 (given)

salary = GH200 (given)

Commission is 3% on the sales above Gh2000 (given)

Let sales be x

total income = salary + commission

530 = 200+3%(x-2000)

530-200=0.03(x-2000)

330/.03=x-2000

11000=x-2000

x= 13000

total sales = GH13000

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Step-by-step explanation:

g(x) is also called y. the functional result value for an input value x is shown in the y direction above or below that x value on the x axis.

so, when it says g(x) = c, the solution is to find the values of x for which b the function g delivers c as result.

now, we look at the graphic.

for example, g(x) = 0 (c = 0) has actually 3 solutions, as the function crosses the x-axis (and that means y or g(x) = 0) 3 times. so, there are 3 different values of x that create g(x) = 0.

but we are looking for a c that has only one solution (one value of x to create that result).

c = 1 ?

let's imagine a horizontal line through y = 1.

we see, it cuts the function also 3 times. 3 solutions.

c = -1 ?

a similar horizontal line through y = -1 cuts the function also 3 times. 3 solutions

but c = 3 !

a horizontal line through y = 3 stays above all the waves of the function and then cuts the function only one time at the very right. 1 solution !

and that is therefore our answer.

The sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

Given that average rate of deposition is  per 1000 years of 1 centimeter.

We are required to find the type of sediment deposit that has an average rate of deposition (per 1000 years) of 1 centimeter.

Biogenic ooze, which is also called biogenic sediment, is any pelagic segment that contains more than 30 percent skeletal material. These sediments can be made up of either carbonate ooze or siliceous ooze.

In plagic sediments feldspar is obtained from local volcanic sources, whereas quartz may be introduced from the continents by wind,upsetting simple patterns.A large number of accessory minerals occur in shales.

Hence if the sediment deposit that has an average rate of deposition

(per 1000 years) of 1 centimeter is bigenous ooze,pelagic deposit.

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The Probability that the total showing is either even or less than five = 5/6

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

The example space for rolling two dice is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

36 events total.

Events that have a sum that is even or less than Five .

Total instances when the aggregate is even or less than Five equals 30.

P(sum is even or less than 5)

= (Total no of favorable event)/(Total no of event)

= 30/36

=5/6

probability that the total showing is either even or less than five = 5/6

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[tex]direct \: variation \: lines \: pass \: through \: the \: origin[/tex]

Assuming you mean [tex]f(x,y) = xy^2[/tex] over the domain

[tex]D = \left\{(x,y) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } x^2 + y^2 \le 3\right\}[/tex]

we first observe that [tex]f(x,y) = 0[/tex] for all [tex](x,y)[/tex] on the coordinate axes.

There are no critical points elsewhere in the interior of [tex]D[/tex], since

[tex]\dfrac{\partial f}{\partial x} = y^2 = 0 \implies y=0[/tex]

[tex]\dfrac{\partial f}{\partial y} = 2xy = 0 \implies x = 0 \text{ or } y = 0[/tex]

Parameterize the circular arc boundary by [tex]x=\sqrt3\cos(t)[/tex] and [tex]y=\sqrt3\sin(t)[/tex], where [tex]0\le t\le\frac\pi2[/tex]. Then

[tex]f(x(t), y(t)) = g(t) = 3\sqrt3 \cos(t) \sin^2(t) = 3\sqrt 3 (\cos(t) - \cos^3(t))[/tex]

Find the critical points of [tex]g[/tex].

[tex]g'(t) = -3\sqrt3 \sin(t) + 9\sqrt3 \cos^2(t) \sin(t) = 0[/tex]

[tex]-3 \sin(t) (1 - 3 \cos^2(t)) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } 1 - 3 \cos^2(t) = 0[/tex]

[tex]\sin(t) = 0 \text{ or } \cos^2(t) = \dfrac13[/tex]

[tex]\sin(t) = 0 \text{ or } \cos(t) = \pm\dfrac1{\sqrt3}[/tex]

In the first case, we get

[tex]t = \sin^{-1}(0) + 2n\pi \text{ or } t = \pi - \sin^{-1}(0) + 2n\pi[/tex]

where [tex]n[/tex] is an integer; the only solution on the boundary of [tex]D[/tex] is [tex]t=0[/tex] corresponding to the point [tex](\sqrt3,0)[/tex].

In the second case, we get

[tex]t = \cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

with only one relevant solution at [tex]t=\cos^{-1}\left(\frac1{\sqrt3}\right)[/tex]  corresponding to [tex](1,\sqrt2)[/tex].

In the third case, we get

[tex]t = \cos^{-1}\left(-\dfrac1{\sqrt3}\right) + 2n\pi \text{ or } t = -\cos^{-1}\left(\dfrac1{\sqrt3}\right) + 2n\pi[/tex]

but there is no [tex]t[/tex] in this family of solutions such that [tex]0\le t\le\frac\pi2[/tex].

So, we find

[tex]\min\left\{xy^2 \mid (x,y) \in D\right\} = 0 \text{ at } (0,0)[/tex]

(but really any point on either axis works)

[tex]\max \left\{xy^2 \mid (x,y) \in D\right\} = 2 \text{ at } (1,\sqrt2)[/tex]

When searching for the value 10 in the array [2, 3, 5, 6, 9, 13, 16, 19], a recursive binary search algorithm will return false since the element is not found in the array.

About Binary Search Algorithm

The binary search algorithm, applied on arrays are of recursive type. The broad strategy is to look at the middle item on the list. The procedure of the binary search algorithm is either terminated (key found), the left half of the list is searched recursively, or the right half of the list is searched recursively, depending on the value of the middle element.

The function carrying out the binary search algorithm in a code returns true if the desired element is found in the array, else returns false. Since the element 10 is not present in the given array: [2, 3, 5, 6, 9, 13, 16, 19], the binary search algorithm will return false.

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Values of c and d make the equation true are c=6, d=2

Equations

                                [tex]\sqrt[3]{162x^{c}y^{5} } = 3x^{2} y^{3} \sqrt[3]{6y^{d} }[/tex]

                               [tex](\sqrt[3]{162x^{c}y^{5} })^{3} = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]

                                 [tex]{162x^{c}y^{5} } = (3x^{2} y^{3} \sqrt[3]{6y^{d} })^{3}[/tex]

                                  [tex]{162x^{c}y^{5} } = 27x^{6} y^{3} ({6y^{d})[/tex]

                                     [tex]{x^{c}y^{5} } = x^{6} y^{3} ({y^{d})[/tex]

                                     [tex]{x^{c}y^{5} } = x^{6} y^{3+d}[/tex]

                                   c = 6

                                   d = 2

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Answer:

4.25 × 10^-4

Step-by-step explanation:

0.00045-2.5x10^-5

= (4.5 × 10^-4) - (0.25 × 10¹ × 10^-5)

= (4.5 × 10^-4) - (0.25 × 10^{1-5} )

= (4.5 × 10^-4) - (0.25 × 10^-4)

= (4.5 - 0.25) × 10^-4

= 4.25 × 10^-4

The mean of the data set A is 4.58 while the mean of data set B is 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

The mean of a set of numbers is the average of that group of number. It is the ratio of the sum of the data to the total number of data.

Mean of data set A = [(3 * 1) + (4 * 3) + (5 * 2) + (6 * 2) + (7 * 3) + (8 * 1)] / (1 + 3 + 2 + 2 + 3 + 1) = 4.58

Mean of data set B = [(4 * 2) + (5 * 2) + (6 * 2)] / ( 2 + 2 + 2) = 5

The mean of the data set A is 4.58 while the mean of data set B is 5.

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The distance from Humood's house to the school is 500m

The given parameters are:

Humood's house is (-5,7)

The school is (3,1)

The distance between both points is calculated using

[tex]d = \sqrt{(x_2- x_1)^2 + (y_2 - y_1)^2[/tex]

Substitute the known values in the above equation

[tex]d = \sqrt{(-5 - 3)^2 + (7 - 1)^2[/tex]

Evaluate

d = 10

Each unit in the graph is 50m.

So, we have

Distance =10 * 50m

Evaluate the product

Distance = 500m

Hence, the distance from Humood's house to the school is 500m

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In the hypothesis, based on the 90% confidence interval, (0.02, 0.12), there is convincing evidence that the new formula of laundry detergent is better because the interval is entirely above 0

Let's define the null hypothesis and alternative hypothesis first.

H0:p1-p2=0

Ha:p1-p2>0

Also, 90% CI is (0.02,0.12), we know that if the 0 of the null hypothesis is not in the confidence interval then we reject the null hypothesis.

In the given scenario 0 is not within the given interval, hence we reject the null hypothesis and accept the claim that new detergent A cleans better.

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The given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

An expression can be defined as a type of mathematical equation which is used to show the relationship that is existing between two or more variables and numerical quantities (integers).

In this exercise, you're required to fully simplify the given expression in the lowest terms. Thus, we would simplify the given expression completely by collecting like terms and performing the necessary arithmetic operations (addition and subtraction) as follows:

Collecting like terms, we have:

8h - 5h + 3w + 2w

Subtracting and adding the like terms respectively, we have:

3h + 5w.

In conclusion, we can logically deduce that the given expression (8h + 2w - 5h + 3w) can fully be simplified as 3h + 5w.

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Complete Question:

Fully simplify 8h + 2w - 5h + 3w.

Answer:

Step-by-step explanation:

x+3y=1

Answer:

  (-∞, ∞)

Step-by-step explanation:

Unless there are restrictions on the domain, the range of any odd-degree polynomial function is "all real numbers."

The given function is a linear function, degree 1. This is an odd degree, so the range of the function is "all real numbers."

  -∞ < f(x) < ∞

  (-∞, ∞) . . . . . in interval notation