Brandon made a model of a tower as shown below. It is composed of a square, prism, and a square pyramid. The height of the pyramid is 2 inches while The height of the prism 3 feet and the base of the prism is 8 inches long. What is the volume, to the nearest cubic inch, of the tower?

The slope of line h that is perpendicular to line g is: -4/3.

The slope values of any two lines that are perpendicular to each other are values that are negative reciprocals to each other.

The equation of of line g is given as y = 3/4x + 3/4, it is expressed in slope-intercept form as y = mx + b. This means that the value of the slope of line g is 3/4.

The negative reciprocal of 3/4 is -4/3. Therefore, the slope of line h that is perpendicular to line g would be -4/3.

The slope of line h is: -4/3.

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From trigonometric ratio, we used the tangent of the angle to determine that the flagpole is leaning by an angle of 47.12°

The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.

In the question, we can assume the point of view and the flagpole makes a right angle triangle.

Since we have the opposite and adjacent, we can find the acute angle by using the tangent of the angle

tanθ = opposite / adjacent

tan θ = 14 / 13

θ = tan⁻¹(14/13)

θ = 47.12°

The flagpole is leaning with an acute angle of 47.12 degrees

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Answer: (1,4)

Step-by-step explanation:

The system of equations:

y=5x-1       (1)

y=x+3       (2)

Hence,

5x-1=x+3

5x-1-x=x+3-x

4x-1=3

4x-1+1=3+1

4x=4

Divide both parts of the equation by 4:

x=1

Substitute the value of x=1 into equation (2):

y=1+3

y=4

Thus, (1,4)

The following are needed to find p-value for hypothesis test:

The p value is a number calculated from a statistical test that describes the likelihood of finding a specific set of observations if the null hypothesis is true. P values are used in hypothesis testing to help determine whether the null hypothesis should be rejected.

Given the probability distribution of the statistic, p-values are calculated as the difference between the observed value and a chosen reference value, with a greater difference between the two values corresponding to a lower p-value.

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This is the way to find the p value that is required in a hypothesis test:

The likelihood of receiving outcomes from a statistical hypothesis test that are at least as extreme as the actual results, assuming the null hypothesis is true, is known as the p-value in statistics.

The p-value provides the minimal level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by stronger evidence when the p-value is lower.

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Answer:

B.  37 cm²

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a square}\\\\$A=s^2$\\\\where $s$ is the side length.\\\end{minipage}}[/tex]

Given the side length of the square is 4 cm:

[tex]\begin{aligned}\implies \sf Area\;of\;the\;square&=4^2\\&=\sf 16\;cm^2\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a semicircle}\\\\$A=\dfrac{1}{2}\pi r^2$\\\\where $r$ is the radius. \\\end{minipage}}[/tex]

The radius of a circle is half its diameter.

Given the diameter of the semicircles is 2 cm, then their radius is 1 cm.

[tex]\begin{aligned}\implies \textsf{Area of one semicircle}&= \sf \dfrac{1}{2} \pi (1)^2\\& = \sf \dfrac{1}{2} \pi \; cm^2\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{4.5 cm}\underline{Area of a trapezoid}\\\\$A=\dfrac{1}{2}(a+b)h$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the bases. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given the bases of the trapezoids are 2 cm and 4 cm, and their height is 3 cm:

[tex]\begin{aligned}\implies \textsf{Area of one trapezoid}&= \sf \dfrac{1}{2} (2+4)(3)\\&= \sf \dfrac{1}{2} (6)(3)\\&= \sf (3)(3)\\&=\sf 9\;cm^2\end{aligned}[/tex]

Given the figure is made up of a square, two congruent trapezoids and two congruent semicircles:

[tex]\begin{aligned}\implies\textsf{Area of the figure}&= \sf square+2\;trapezoids+2\; semicircles\\&= \sf 16+2(9)+2\left(\dfrac{1}{2} \pi\right)\\& = \sf 16 + 18 + \pi \\& = \sf 34 + \pi \\& = \sf 37.14159...\; cm^2\end{aligned}[/tex]

Therefore, the measurement that is closest to the area of the figure in square centimeters is 37 cm².

Tanya's earnings for the last week of August is  $455.40.

Tanya's earnings for the last week of August is the sum of the amount earned for working regular hours and overtime.

Earnings = amount earned working regular hours + amount earned for working overtime

Amount earned working regular hours = number of hours worked x wage rate

Amount earned working regular hours =37.5 x 9.20 = $345

Amount earned for working overtime = wage per hour worked overtime x number of hours worked overtime

Wage rate for overtime = 1.5 x $9.20 = $13.80

Amount earned for working overtime = $13.80 x 8 = $110.40

Total earnings = $110.40 + 345 = $455.40

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The time taken for the rocket to reach its maximum height is; 2.25 seconds.

The maximum height reached by the toy rocket as evaluated from the given parameters is; 88 feet.

It follows from the task content that the maximum height reached by the rocket is to be determined.

The given function is; h (t) = -16 t² + 72t + 7.

Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.

Therefore; at maximum height;

h'(t) = 0

h'(t) = -32t + 72 = 0

-32t = -72

t = -72/-32

t = 2.25 seconds.

Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.

Also, the maximum height reached by the rocket is at; h (2.25);

h(2.25) = -16(2.25)² + 72 (2.25) + 7

= -81 + 162 + 7

= 88.

The maximum height reached is; 88 feet.

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The amount of time spent on bicycle by Jim =6.5 hours

The amount of time spent on walking by Jim =2.5 hours

To calculate speed, divide the distance travelled by the time it took to complete the voyage, so speed = distance divided by time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.

Distance divided by time equals speed. Distance = time * speed

To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.

Given,

Distance=270miles

Time=9 hours

Speed by walk=4 miles/hour

Speed by cycle=40 miles/ hour

t= time for riding a bicycle

9-t= time for walking

Distance= Speed ×Time

270=40t+4(9-t)

40t+36-4t=270

36t=234

t=6.5

Time spent on bicycle = 6.5 hours

Time spent on walking = 9-6.5

=2.5 hours

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△MPQ: M(-4,3), P(-5,8), Q(-1,6). Translation: along (-4,-4) Reflection: in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).

Here we need to find translation along (-4,-4) and reflection in y=x.

First we will find translation,

⇒ (x,y)→ (x-4,y-4)

M(-4,3 )→ M'(-8,-1) ,  

P(-5,8) → P'(-9,4)

Q(-1,6) → Q'(-5,2)  

now we will do reflection,

⇒(x,y) → (y,x)

M'(-8,-1) →  M''(-1.-8)

P'(-9,4) →  P''(4,-9)

Q'(-5,2) → Q''(2.-5).

Therefore translation along (-4,-4) and reflection in y=x is M''(-1,-8), P''(4,-9), Q''(2,-5).

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The given two triangles ΔQRS and ΔTUV are similar.

What is similar figures?

The same shape between two figures is referred to as similarity. If two figures have congruent corresponding angles and equivalent length ratios on their corresponding sides, they are said to be similar mathematically. The scale factor is the name of this often used ratio.

Given: Two triangles ΔQRS and ΔTUV.

The angles of ΔQRS  are 28°, 76° and 76°.

The angles of ΔTUV are 28°, 76° and 76°.

So, the angles of given two triangles are congruent.

Now consider, the sides of the triangle.

The sides of ΔQRS are, 4, 4, 2 and

The sides of  ΔTUV are 12, 12, 6.

It seems that the sides of the triangle are in proportion.

Therefore, the given two triangles ΔQRS and ΔTUV are similar.

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Answer: M = -11/3

Step-by-step explanation:

Answer:

last dagre would be 3

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

The degree of a polynomial will be no less than one more than the number of turning points of its graph.

From inspection of the given graph, there are 3 turning points.  

Therefore, the least degree is 4.

Answer:

-10

-7

-4

Step-by-step explanation:

287 = [tex]a_{1[/tex] + (n-1)3

287 = [tex]a_{1}[/tex]+ (100-1)3

287 = [tex]a_{1}[/tex] + 99(3)

287 = [tex]a_{1}[/tex] + 297  Subtract 297 from both sides

-10 = [tex]a_{1}[/tex]

If the first term is -10  The second term is 3 greater -7 and the third terms is 3 greater than that. -4

Answer:we need a better picture

Step-by-step explanation:I cant since my eyes are bad

Step-by-step explanation:

the Hypotenuse (the inclined length of the staircase) of the right-angled triangle is the radius of an imaginary circle with the center at the vertex with the 64°.

then

11 = cos(64) × r

r = 11/cos(64) = 25.09289236...

and

x = sin(64) × r = sin(64) × 11/cos(64) = 11 × tan(64) =

= 22.55334226... ≈ 22.55

If ST = QR, then QR = ST by the symmetric property of congruence.

The symmetric property states that -

For all real numbers [x] and [y] , if x = y , then y = x .

Given is if ST =QR, then QR=ST.

If ST = QR, then QR = ST by the symmetric property of congruence. If ST = QR, then we can say that ST is congruent to QR.

Therefore, if ST = QR, then QR = ST by the symmetric property of congruence.

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The profit when producing 204 units is $1,560.6

Cost of producing 200 units = $2958

Cost of producing 1 unit = $2958 / 200

= $ 14.79

Marginal cost of production = $9.2

Total cost per unit = cost of producing unit + Marginal cost

= $(14.79+9.2)

= $23.99

Cost incurred in producing 204 units = $(23.99 * 204)

= $4,893.96

Revenue from producing 200 unit,

R(q) = 6868

For each units, Revenue = R(q) / q

= 6868 / 200

= 34.34 dollars per cent

Revenue per unit is decreasing by $2.7

i.e., Final revenue = $(34.34 - 2.7)

= 31.64 dollars per cent

Final revenue for 204 units

= $(31.61 * 204)

= $ 6454.56

∴ Total profit from 204 units = R(q) - C(q)

= $(6454.56 - 4,893.96)

=$1,560.6

Hence, the profit when producing 204 units is $1,560.6

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The value of 199.65 rand was worth $24 and $29.11 was worth 243 rand with rounding off.

What is foreign currency exchange?

A global decentralized or over-the-counter market for trading currencies is known as the foreign exchange market. For every currency, exchange rates are set by this market.

Main body:

Given: 1 rand = $0.12

a) According to question ,

199.65 rand = 0.12* 199.65

                    = 23.948

Now rounding off to nearest hundred , we get

199.65 rand = $24

b) According to question,

$1 = 1/ 0.12

$29.11 = 29.11/ 0.12

          =242.5833333

Now rounding off to nearest hundred , we get

$29.11 = 243 rand.

Hence answer are $24 and 243 rand.

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His percentage of change in the amount of quarts is 82.22%.

Initial amount of lemonade = 45 quart

End amount of lemonade = 8 quart

Change in amount = 45 - 8

                               = 36

Percent = [tex]\frac{change in value}{initial value}*100[/tex]

             = [tex]\frac{37}{45}*100[/tex]

             = 0.8222 * 100

             = 82.22%

Hence, his percentage of change is 82.22%.

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The percentage of last​ semester's college costs was spent on​ books is 10 %

A percentage is a ratio out of 100.

Since a student's cost for last semester at her community college was ​$2900 and she spent ​$290 of that on books.

The percentage spent on books is given by x = amount spent on books/student cost × 100 %

Given that

Substituting the values of the variables into the equation, we have

percentage spent on books x = amount spent on books/student cost × 100 %

= $290/$2900 × 100 %

= 1/10 × 100 %

= 10%

So, thus we see that the percentage that was spent is 0 %

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The cups of red paints for 1 yellow cup is 4/9 cups

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

Red paint = 1/3 cups

Yellow paint = 3/4 cups

When these parameters are represented as ratio, we have the following expression

Ratio = Red : Yellow

This is then represented as

Red : Yellow = 1/3 : 3/4

When the number of yellow cups is 1, we have

Red = 1/3/3/4

Express as products

Red = 1/3 * 4/3

Evaluate

Red = 4/9

Hence, the red cups is 4/9 cups

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Answer:

0.33=0.33

Step-by-step explanation:

it is answer 0.33=0.33

The convertion 40 square inches to square meters is  0.0258064 square meters.

You can convert a square inch measurement to a square metre measurement by multiplying the square inch measurement by 0.00064516. (the conversion factor). Here is the equation:

Square inch value divided by square metre value is 0.00064516.

Consider converting 40 square inches to square metres. Using the above conversion formula, you will obtain:

= 40 sq in * ( 2.54 cm / 1 in)² * (1 m/100cm)²

= 40 × 0.00064516

= 0.0258064 square meter.

Hence, convert 40 square inches to square meters is  0.0258064 square meters.

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Answer:

The 3rd answer.

Step-by-step explanation:

2(pi)10 is the equation.

You're question should be deleted soon probably 10-15 minutes.

↑ My opinion not answer by a admin/moderator.

Step-by-step explanation:

x = number of dimes

y = number of quarters

x + y = 100

x = 100 - y

0.1x + 0.25y = 19

0.1(100 - y) + 0.25y = 19

10 - 0.1y + 0.25y = 19

10 + 0.15y = 19

0.15y = 9

y = 9/0.15 = 60

x = 100 - y = 100 - 60 = 40

there were 60 quarters and 40 dimes.

Answer:$110

Step-by-step explanation:

$100x0.01x10

Answer:

44

Step-by-step explanation:

Answer:

Answer:

We use the formula:

y2 - y1 / x2 - x1

-2 - 1 / -7 - (-3)  ---> this gives us -3 / -4 or simply 3/4. So our slope for line 1 is 3/4.

Now using the formula, (y - y1) = m (x - x1) we find the line.

(y - 1) = 3/4 (x - (-3)) ---> (y - 1) = 3/4x + 9/4.

Now we add one to each side to get y = 3/4x + 13/4.

Now for line 2, we use the same process and formulas.

Find the slope of line 2.

4 - (-1) / 8 - 2 gives us 5/6. Our slope for line 2 is 5/6.

(y - (-1)) = 5/6 (x - 2).

(y + 1) = 5/6x - 5/3 ---> now subtract one from both sides to get...

y = 5/6x - 8/3.

Since the two lines do not have the same slope or the negative reciprocal of one slope being the other, the two lines through the given points are neither parallel nor are they perpendicular

There is 1/6 gallon of milk left in Leo's jug.

The step by step fraction subtraction are as follows:

The first step would be to deduct the 3/4 gallon of milk with 1/3 he uses to make the soup.

3/4 - 1/3 = (3x3)/(4x3) - (1x4)/(3x4) = 9/12 - 4/12 = 5/12

Then out of 5/12 gallon of milk left in the jug, he pours 1/4 of the remaining milk into a glass.

5/12 - 1/4 = 5/12 - (1x3)/(4x3) = 5/12 - 3/12 = 2/12 = (2÷2)/(12÷2) = 1/6

So Leo has 1/6 gallon of milk left in the jug.

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