- Higher Order Thinking
Simone built the same number of toy
cars and toy airplanes.
Show how Simone could have built
14 toys. Explain how you know.

The length of AC in this right-angled triangular prism is approximately 60.66 cm.

What is Pythagoras theorem?

For right angle triangle,

Hypotenuse² = Height²+Base²

However, we can use the Pythagorean theorem to find the length of AC if we know the lengths of AE and EC and ED.

If we assume that face AEC is the base of the prism and the right angle is at vertex E, then we can use the Pythagorean theorem to find the length of AC:

AC² = AE²+ EC²

We are given that AE = 43 cm, but we don't know the length of EC. However, we can use the fact that the base of the prism is a rectangle to find EC. Since opposite sides of a rectangle are equal, we have:

EC = 51 cm and ED = 45 cm

Substituting this into the equation above, we get:

AC² = 43² + 51²

AC² = 3680

AC ≈ 60.66 cm (to 1 decimal place)

Therefore, the length of AC in this right-angled triangular prism is approximately 60.66 cm.

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Correct question is "Find the length of AC in this right-angled triangular prism. Give your answer in centimetres (cm) to 1 d.p.

Base is ED 51 cm and height is AE 43 cm of the prism."

By evaluating and simplifying f(x)=3x2 +3x+8, we get  f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8 and  (f(x + h) - f(x))/h = 6x + 3h + 3.

Given function is, f(x) = 3x² + 3x + 8

Evaluate f(x + h)

Expanding f(x + h) => f(x) + hf′(x) + h²/2f″(x)

Applying formulae in the given function f(x + h) = 3(x + h)² + 3(x + h) + 8=> 3x² + 6xh + 3h² + 3x + 3h + 8Now, f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8

Evaluate (f(x + h) - f(x))/h

Expanding both the terms f(x + h) and f(x) and simplifying, (f(x + h) - f(x))/h = [3x² + 6xh + 3h² + 3x + 3h + 8 - (3x² + 3x + 8)]/h=> [3x² + 6xh + 3h² + 3x + 3h + 8 - 3x² - 3x - 8]/h=> [6xh + 3h² + 3h]/h=> 6x + 3h + 3

Therefore, the required value is f(x + h) = 3x² + 6xh + 3h² + 3x + 3h + 8and (f(x + h) - f(x))/h = 6x + 3h + 3.

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Translate: Knowing that sen alpha = 0. 6 and that a is an acute angle, calculates the rest of trigonometric ratios

Rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.

If we know that sin(alpha) = 0.6, we can use the Pythagorean identity to find cos(alpha) and tan(alpha). Here's how:

Since sin(alpha) = opposite/hypotenuse, we can represent sin(alpha) as the ratio of the length of the side opposite the acute angle alpha to the length of the hypotenuse of the right triangle. Let's assume that the length of the opposite side is a and the length of the hypotenuse is h. Then we have:

sin(alpha) = a/h = 0.6

Solving for a, we get:

a = 0.6h

Using the Pythagorean theorem:

[tex]a^2 + b^2 = h^2[/tex]

Since a and h are related by a = 0.6h, put 0.6h for a to get:

[tex](0.6h)^2 + b^2 = h^2[/tex]

Simplifying:

[tex]0.36h^2 + b^2 = h^2[/tex]

[tex]b^2 = h^2 - 0.36h^2 = 0.64h^2[/tex]

[tex]b = \sqrt{0.64h^2} = 0.8h[/tex]

So now we know that b = 0.8h and a = 0.6h. Using these values, we can find cos(alpha) and tan(alpha) as follows:

[tex]cos(alpha) = adjacent/hypotenuse = b/h = 0.8h/h = 0.8tan(alpha) = opposite/adjacent = a/b = 0.6h/0.8h = 0.75[/tex]

Therefore, the rest of the trigonometric ratios for the acute angle alpha are cos(alpha) = 0.8 and tan(alpha) = 0.75.

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Answer:15

Step-by-step explanation:

Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, 6 divided by 2/5 is the same as multiplying 6 by 5/2, which equals 15.

The expression 6 divided by 2/5 is equivalent to 6 multiplied by 5/2. This is because dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/5 is 5/2. Therefore, 6 divided by 2/5 is the same as 6 multiplied by 5/2, which gives you the result 15.

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The first step in evaluating the expression 6 - (4/2 x 5)² is to simplify the expression inside the parentheses first.

An expression is a mathematical phrase that consists of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that are combined according to certain rules to represent a mathematical calculation.

Following the order of operations or PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), as shown below:

4/2 = 2, so we can replace 4/2 with 2:

6 - (2 x 5)²

2 x 5 = 10, so we can replace 2 x 5 with 10:

6 - 10²

10² means 10 multiplied by itself, which equals 100:

6 - 100

Therefore, the expression simplifies to -94.

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Accοrding tο given cοnditiοns, 250 hamburgers were sοld οn Tuesday.

Algebra is a branch οf mathematics that deals with symbοls and the rules fοr manipulating thοse symbοls. It invοlves sοlving equatiοns and manipulating variables tο find unknοwn values.

Let's use algebra tο sοlve the prοblem.

Let x be the number οf hamburgers sοld.

Then the number οf cheeseburgers sοld is x - 59.

The tοtal number οf hamburgers and cheeseburgers sοld is 441, sο we can write an equatiοn:

x + (x - 59) = 441

Simplifying the left side, we get:

2x - 59 = 441

Adding 59 tο bοth sides, we get:

2x = 500

Dividing by 2, we get:

x = 250

Therefοre, accοrding tο given cοnditiοns, 250 hamburgers were sοld οn Tuesday.

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[tex]\qquad \qquad \textit{combined proportional variation} \\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with }\underline{z^5} \end{array} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}x}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{llll} \textit{"y" varies}\\ \textit{directly with "x"}\\ \textit{inversely with "z"} \end{array}\qquad y=\cfrac{kx}{z}\hspace{5em}\textit{we also know that} \begin{cases} x=10\\ z=4\\ y=15 \end{cases} \\\\\\ 15=\cfrac{k(10)}{4}\implies \cfrac{4}{10}\cdot 15=k\implies 6=k\hspace{8em}\boxed{y=\cfrac{6x}{z}} \\\\\\ \textit{when x = 20 and z = 6, what's "y"?}\qquad y=\cfrac{6(20)}{6}\implies y=20[/tex]

Answer:

I think is 500 hope it helps

Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

The probability of picking a medal won by Sam in the years 2009 or 2012 is 5/6.

The probability of picking a medal won by Sam in the years 2009 or 2012 can be calculated using the formula P(A∪B) = P(A) + P(B) - P(A∩B). In this case, P(A) equals the probability of picking a medal won by Sam in 2009, which is 1/3, and P(B) equals the probability of picking a medal won by Sam in 2012, which is 1/2. P(A∩B) would be the probability of picking a medal won by Sam in both years, which is 0, since he did not win a medal in both years. Therefore, the probability of picking a medal won by Sam in the years 2009 or 2012 is P(A∪B) = P(A) + P(B) - P(A∩B) = 1/3 + 1/2 - 0 = 5/6.

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If locked out of an account due to forgotten password and invalid email, try password recovery options or contact customer support, or create a new account.

If you've been locked out of your account. If you've forgotten your password and the email you used to sign up is not valid, it can be difficult to regain access to your account. Few steps you can try to recover your account:

It's important to note that in some cases, it may not be possible to regain access to your account. Always be cautious about the information you provide when signing up for online services and make sure to keep your login credentials in a safe and secure location.

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The work required to move q from the other vertex to the center of the line joining the fixed charges is (1/4π ε0) x 2 x q 2/a.

To solve this problem, we can use the principle of superposition to calculate the potential at the center of the equilateral triangle due to each of the two fixed charges, and then add them up to get the total potential.

Let's first find the potential due to one of the fixed charges at the center of the triangle. We can use the formula for the electric potential due to a point charge q at a distance r from it, which is given by:

V = k x q/r

In this case, the distance from one of the fixed charges to the center of the triangle is: r = a/2

So the potential due to one fixed charge at the center of the triangle is:

V1 = kq/r = kq/(a/2)

Next, let's find the potential due to the other fixed charge at the center of the triangle. Since the triangle is equilateral, the distance from the other fixed charge to the center of the triangle is also a/2. So the potential due to the other fixed charge at the center of the triangle is:

V2 = k x q/(a/2)

Now, the total potential at the center of the triangle due to the two fixed charges is simply the sum of the individual potentials:

V_total = V1 + V2 = kq/(a/2) + kq/(a/2) = 2kq/a

The work required to move a charge q from infinity to the center of the triangle is equal to the change in potential energy of the charge, which is given by:

W = q x (V_final - V_initial)

In this case, the initial potential is zero (since the charge is at infinity), and the final potential is 2kq/a (which we just calculated). So the work required is:

W = q x (2kq/a - 0) = 2kq 2/a

Substituting the given value of k, we get:

W = (1/4π ε0) x 2 x q2/a

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Based on the information, the only prediction that is justified is that the speed of the fish will be greater than 40 mph, and the speed of the mammal will be less than 50 mph.

Therefore option B  is  correct.

Based on the given information above, we were able to deduct that about 75% of the fish were faster than 40 mph and about 75% of the mammals were slower than 50 mph.

We can go ahead and use this information to make predictions about the speeds of one additional fish and one additional mammal.

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Answer:

2

Step-by-step explanation:

John had 10 and he gave Janet 8, which means that he remained with 2

2 kilometers per hour

The position of a car driving along a straight road at time t in minutes is given by the function y = f(t).

The function y represents the position of the car in thousands of feet, while the variable t represents the time in minutes.

To find the position of the car at any given time, you simply need to plug in the value of t into the function and solve for y. For example, if you wanted to find the position of the car at 2 minutes, you would plug in 2 for t and solve for y:

y = f(2)

Once you have solved for y, you will have the position of the car in thousands of feet at 2 minutes. You can repeat this process for any value of t to find the position of the car at any given time.

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The solution set of the given system of linear equations can be expressed as a line in R^3 vector as r = (6, -2) + x_3(3, -5).

To express the solution set of the given system of linear equations as a line in R^3, we first need to express the solution set as a vector equation. We can do this by expressing the equations in terms of x_3 as follows:

x_1 = 6 + 3x_3,

x_2 = -2 - 5x_3

Therefore, the solution set of the given system of linear equations can be expressed as a line in R^3 as follows:

r = (6, -2) + x_3(3, -5).

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Answer:

3069 windows on the side of the apartment building if it has 10 columns.

Step-by-step explanation:

We can notice that the number of windows in each column is double the number of windows in the previous column. So, we can write down the number of windows in each column as a sequence of powers of 2:

3, 6, 12, 24, 48, 96, 192, 384, 768, 1536

We can see that this is a geometric sequence with a common ratio of 2. We can use the formula for the sum of a geometric sequence to find the total number of windows:

Sn = a(1 - r^n)/(1 - r)

where

a = 3 (the first term)

r = 2 (the common ratio)

n = 10 (the number of terms we want to sum)

Substituting these values into the formula, we get:

Sn = 3(1 - 2^10)/(1 - 2)

= 3(1 - 1024)/(-1)

= 3(1023)

= 3069

Therefore, there are 3069 windows on the side of the apartment building if it has 10 columns.

The inflation rate in 2020, given the CPI in 2020 and the price in both years, would be 95. 5 %.

To find the inflation rate from the CPI (Consumer Price Index), subtract the beginning CPI from the end CPI. This gives you the increase in the price level over the time period.

Divide the increase in the price level by the beginning CPI. Multiply the result by 100 to get the inflation rate as a percentage. Basically, the formula is:

= (CPI in 2020 - CPI in 2019 ) / CPI in 2019

= ( 195.5 - 100 ) / 100

= 95. 5 %

Note : The CPI for 2020 is 195.5 and the assumed CPI for 2019 would be 100 as a base year.

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Answer:

Step-by-step explanation:

we should do multiplications first:

1)

[tex]1)12a^{2}*3ba=12a^{3}b\\2)2ab*3ab^{2}=6a^{2}b^{3}\\3)11aba=11a^{2}b\\4)12a^{3}b+6a^{2}b^{3}+11a^{2}b=a^{2}b(12a+6ab^{2}+11)[/tex]

2)

[tex]1)1.5xy^{2}*(-4)xyz=-6x^{2}y^{3}z\\2)-4mnk*5m^{2}n^{3}k=-20m^{3}n^{4}k^{2}\\3)-6x^{2}y^{3}z-20m^{3}n^{4}k^{2}[/tex]

Answer:

Binomial

Step-by-step explanation:

A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials.

a) The continuous rate of growth of this bacterium population is 45%

b) Initial population of culture at t = 0 is 950 bacteria

c) number of bacterial cultures contain at t = 5 is 9013 bacteria

The number of bacteria in a culture is given by the function n(t) =950[tex]e^{0.450t}[/tex] Where t is measured in hours

what is the continuous rate of growth of this bacterium population

The number of bacteria in a culture is given by

n(t) = 950[tex]e^{0.45t}[/tex]

a) rate of growth is

Bacteria growth model N(t) = no[tex]e^{rt[/tex]

Where r is the growth rate

hence r = 0.45

             = 45%

b) Initial population of culture at t = 0

n(0) = 950[tex]e^0[/tex]

      = 950

      = 950 bacteria

c) number of bacterial culture contain at t = 5  

n(5)      = 950[tex]e^{0.45*5}[/tex]

     = 9013.35

     = 9013 bacteria

the complete question is-

The number of bacteria in a culture is given by the function n(t) =950e^0.45t Where t is measured in hours A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent B) what is the initial population of the culture (at t=0) your answer is __ C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria

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Answer:

-7

Step-by-step explanation:

A negative number times a negative number is positive. Because -5 is negative and 35 is positive the other factor must be negative as well.

5 x 7 = 35

So, -5 x -7 also equals 35

Answer: 11 in the 5th picture

Step-by-step explanation:

or if you add 5 more then it would be 17

add 2

Answer:

40Km

Step-by-step explanation:

Total Distance of Journey  = 140KM

5/7 of the journey:
[tex]\frac{5}{7 } * 140 = 100km[/tex]

Distance travelled before stopping: Total Distance - 5/7 of Total Distance

= 140 - 100KM = 40KM

Gloria traveled a distance of 7.5 miles on the bus.

The process of translating a measurement from one unit to another is known as unit conversion. Since multiple units are frequently used to measure the same quantity and because unit conversion is required to carry out calculations and solve issues, it is significant in problem solving. Moreover, unit conversion is crucial since it enables us to compare measurements and present them in a uniform manner. For instance, measurements in science and engineering are frequently stated in SI units.

Given that, Gloria traveled a total of 8 miles.

8 x 1760 = 14080 yards.

The distance walked is 880 yards.

So the distance she traveled on the bus is:

14080 - 880 = 13200 yards

13200 / 1760 = 7.5 miles

Hence, Gloria traveled 7.5 miles on the bus.

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The complete question is:

Each piece of the rope is 247.76 meters long, approximately.

To find the length of each piece, we need to divide the total length of the rope by the number of pieces it is cut into:

Length of each piece = Total length of the rope / Number of pieces

Length of each piece = 4212 meters / 17

Length of each piece = 247.76 meters (rounded to two decimal places)

The method used to find the length of each piece of rope is division. We divided the total length of the rope by the number of pieces it was cut into, which gives us the length of each piece. This method is based on the fact that the length of each piece is the same, so we can divide the total length equally among the pieces.

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The 12  mutual funds in the simple randοm samples are

714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488

A simple randοm sample is a subset οf persοns picked at randοm, all with the same prοbability, frοm a larger set οf individuals. It is a methοd οf chοοsing a sample at randοm.

Here, we have

Given: a certain newspaper prοvides the net asset value, the year-tο-date percent return, and the three-year percent return fοr 882 mutual funds at the end οf 2017. assume that a simple randοm sample οf 12 οf the 882 mutual funds will be selected fοr a fοllοw-up study οn the size and perfοrmance οf mutual funds. use the third cοlumn οf the table οf randοm numbers, beginning with 71744, tο select the simple randοm sample οf 12 mutual funds.

The last three digits in each rοw οf cοlumn 6 less than 882 are

714, 041, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488

Hence, The 12  mutual funds in the simple randοm samples are

714, 41, 535, 358, 191, 378, 290, 518, 520, 421, 240, 488.

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Answer:

  996,250,626,076

Step-by-step explanation:

You want the value of the numerical expression 251^5+8-(9×20+3).

Your calculator will evaluate this properly if you enter it as shown. See the attachment.

If you're doing this in parts, the Order of Operations tells you to start with the parentheses, then do the exponentiation.

  251^5 +8 -(9·20 +3)

  = 251^5 +8 -183

  = 996,250,626,251 +8 -183 = 996,250,626,076

__

Additional comment

You can use a spreadsheet (or an on-line calculator) if your calculator only displays 10 digits.

Answer:

5.1, 5 1/10

Step-by-step explanation:

(3.5 − 2/3) ⋅ (−2.8 + 4 3/5) =

= (7/2 - 2/3)(-14/5 + 23/5)

= (21/6 - 4/6)(9/5)

= (17/6)(9/5)

= (17 × 9)/(6 × 5)

= 51/10

= 5.1 = 5 1/10