Jonny cut a plank of wood so that it is 50% shorter.

It is now 42cm long.

How long was the plank of wood before Jonny cut it?

Answer:

3.5/100*8=.28

Step-by-step explanation:

To find the difference in the number of cups of sugar used to bake 9 batches of cookies compared to 3 batches of cookies, we need to calculate the amount of sugar used for each case.

From the table, we can see that:

- For 1 batch of cookies, Sonya uses 2-7 cups of sugar.

- For 2 batches of cookies, Sonya uses 47/17 cups of sugar.

- For 3 batches of cookies, Sonya uses 6²2/2 cups of sugar.

To calculate the amount of sugar used for 9 batches of cookies, we can use the pattern observed in the given values:

- For 4 batches of cookies, Sonya uses 2-7 cups of sugar.

- For 5 batches of cookies, Sonya uses 47/17 cups of sugar.

- For 6 batches of cookies, Sonya uses 6²2/2 cups of sugar.

- For 7 batches of cookies, Sonya uses 2-7 cups of sugar.

- For 8 batches of cookies, Sonya uses 47/17 cups of sugar.

- For 9 batches of cookies, Sonya uses 6²2/2 cups of sugar.

Therefore, to find the difference in the number of cups of sugar used to bake 9 batches of cookies compared to 3 batches of cookies, we subtract the amounts:

Amount of sugar for 9 batches - Amount of sugar for 3 batches

[(2-7) + (47/17) + (6²2/2)] - [(2-7) + (47/17) + (6²2/2)]

Simplifying the expression, we get:

[(2-7) + (47/17) + (6²2/2)] - [(2-7) + (47/17) + (6²2/2)]

= 6²2/2 - 6²2/2

= 0

Therefore, the correct answer is:

d) 19 1/4

There is no difference in the number of cups of sugar used to bake 9 batches of cookies compared to 3 batches of cookies.

Answer:

False

Step-by-step explanation:

Answer:

152

Step-by-step explanation:

(x - 15) + 43 = 180

x - 15 = 180 - 43

x = 180 - 43 + 15

x = 152

its 28 hope this helped you <3

0.7 is greater than 0.07, as the decimal place value indicates. 7.52 is greater than 3 based on the decimal value comparison.

The comparison between 0.7 and 0.07 is reasonable. It is evident that 0.7 is greater than 0.07. The decimal point indicates the place value, and in this case, the difference in the tenths place (0.7) and hundredths place (0.07) clearly shows that 0.7 is a larger value.

On the other hand, the comparison between 3 and 7.52 is not reasonable. It is incorrect to claim that 3 is greater than 7.52. In the decimal system, the whole numbers are on the left side of the decimal point and the decimal fractions are on the right side. When comparing numbers, we start with the whole number part and move to the right, comparing each decimal place one by one. In this case, the digit 7 in 7.52 is greater than 3, and the decimal places further reinforce that 7.52 is a larger value than 3.

In summary, the comparison between 0.7 and 0.07 is reasonable as it aligns with the principles of decimal place value. However, the comparison between 3 and 7.52 is not reasonable, as 7.52 is greater than 3.

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Each team member should run 9073.6 miles in the race on Course B.

Let's break down the problem step by step:

1. First, we need to find the length of Course B. We know that Course B is 212 times as long as Course A, and Course A is 214 miles. So, to find the length of Course B, we multiply:
  Course B length = 212 × 214 miles

2. Calculate the length of Course B:
  Course B length = 45368 miles

3. Now, we need to determine the distance each team member should run. There are 5 members on the team, and they need to run an equal distance on Course B. To find the distance for each member, we divide the total length of Course B by the number of team members:
  Distance per member = Course B length / number of members

4. Calculate the distance per team member:
  Distance per member = 45368 miles / 5

5. Finally, we find the distance each team member should run:
  Distance per member = 9073.6 miles

So, each team member should run 9073.6 miles in the race on Course B.

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The greatest possible number of different types of this caterpillar that could exist is 120.

If we assume that the order of the parts does not matter and that all caterpillars with the same color arrangement are considered identical, we can use combinations to find the number of different types of caterpillars that could exist.

First, we need to choose 2 out of the 5 parts to be green, which can be done in 5 choose 2 ways:

5 choose 2 = (5!)/(2!(5-2)!) = 10

For each green-yellow arrangement there are;

3! ways to permute the yellow parts and

2! ways to permute the green parts.

Therefore, the total number of different types of caterpillars is:

10 × 3! × 2! = 10 × 6 × 2 = 120

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Answer:

f(8)= 113

Step-by-step explanation:

f(8)= 2(8)^2-3(8)+9

f(8)= 2(64)-3(8)+9

f(8)= 128-24+9

f(8)= 113

(USE PEMDAS)

The derivative of the function f(0) = (e^0 + e^(-0))^(-6) is f'(0) = 0. This means that the rate of change of the function at x = 0 is zero.

To find the derivative of the function f(0) = (e^0 + e^(-0))^(-6), we can apply the chain rule. The chain rule states that if we have a composition of functions, f(g(x)), then the derivative is given by f'(g(x)) * g'(x). In this case, our composition of functions is (e^x + e^(-x))^(-6), where g(x) = e^x + e^(-x) and f(g) = g^(-6).

Let's begin by finding the derivative of g(x) = e^x + e^(-x). The derivative of e^x is simply e^x, and the derivative of e^(-x) is -e^(-x) (using the chain rule). Therefore, the derivative of g(x) is:

g'(x) = e^x - e^(-x)

Next, we can find the derivative of f(g) = g^(-6). Using the power rule, the derivative of g^(-6) is:

f'(g) = -6 * g^(-7) * g'

Substituting the value of g'(x) we found earlier, we have:

f'(g) = -6 * g^(-7) * (e^x - e^(-x))

Finally, to find the derivative of f(0), we substitute g(x) = 0 into f'(g):

f'(0) = -6 * 0^(-7) * (e^0 - e^(-0))

Since 0^(-7) is undefined, we cannot evaluate f'(0) directly. However, notice that the function (e^x + e^(-x))^(-6) is an even function, meaning it is symmetric about the y-axis. Therefore, its derivative at x = 0 is 0. Hence, we can conclude that:

f'(0) = 0

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Answer:

ohk where is test

Step-by-step explanation:

and question

Step-by-step explanation:

I recommend you to use matrices for systems of equations; it's a lot faster and more expedient.

Answer:

\((2, -1)\)

Step-by-step explanation:

Given the system of equations:

\(\begin{cases}5x+7y=3,\\2x+3y=1\end{cases}\)

Multiply the first equation by -2 and the second equation by 5, then add both equations to solve for \(y\):

\(\begin{cases}-2(5x+7y)=(-2)3,\\5(2x+3y)=(5)1\end{cases},\\\begin{cases}-10x-14y=-6,\\10x+15y=5\end{cases},\\-10x+10x-14y+15y=-6+5,\\y=-1\)

Substitute \(y=-1\) into any equation to solve for \(x\):

\(2x+3y=1,\\2x+3(-1)=1,\\2x-3=1,\\2x=4,\\x=\boxed{2}\)

Therefore, the solution to this system of equations is \(\boxed{(2, -1)}\)

Answer:

A = 60 m^2

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh where b is the base and h is the height

A = 1/2 (20)*6

A = 60 m^2

The value of m by the given data is m=2

We are given that;

Number of elephants= 125000gram

The mass of african elephant= 3 x 10

Now,

To find the values of b and c, we need to write the given masses in scientific notation, which means that the coefficient must be between 1 and 10. For example, 6 x 10 grams is not in scientific notation, because 6 is not between 1 and 10. To fix this, we need to move the decimal point one place to the left and increase the exponent by one. We get:

6x106 grams=6.0x106 grams=6.0x106−1×101 grams=6.0x105×101 grams=6.0x105+1 grams=6.0x107 grams

Similarly, for the silverback gorilla, we get:

2x105 grams=2.0x105 grams=2.0x105−1×101 grams=2.0x104×101 grams=2.0x104+1 grams=2.0x105 grams

Therefore, the values of b and c are b=7,c=5

To find the value of m, we need to divide the mass of the African elephant by the mass of the silverback gorilla and write the result in scientific notation. We get:

Mass of silverback gorillaMass of African elephant​=2.0x105 grams6.0x107 grams​=2.06.0​×105107​=3.0×107−5=3.0×102

Therefore, by unitary method the answer will be m=2.

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Answer:

area:\(16x^2+24x+9\) Perimeter: 16x+12

Step-by-step explanation:

area :\((4x+3)^2\)

thats \(16x^2+24x+9\)

P: 4(4x+3)

thats 16x+12

Hope this helped you

<3

Red

Answer:

Perimeter is all sides added together, while Area is one side height times length

Step-by-step explanation:

Since your shape is a square all sides are equal so the equation is the same for all sides

Perimeter = 4z+3+4z+3+4z+3+4z+3 or (4z+3)4

14z+12 <= answer for perimeter

Area = (4z+3) (4z+3)

16z^2+12z+12z+9

16z^2+24z+9 <= answer for area

Step-by-step explanation:

Answer:

\(x + x + x = 65 \\ \\ 3x = 65 \\ \\ x = \frac{ 65}{3} \\ \\ x = 21 .66\)

it's was helpful to you

Answer: (w-8)(-4w+3)  

Step-by-step explanation:

Given:

4w(8 − w) + 3(w − 8)

Solution:

You need to make what's inside the parentheses the same so you can take it out as the GCF

let's change the look of (8-w) to look like (w-8)

Start:

8-w                >let's make w first, don't forget to carry signs

-w+8              >take out GCF -1 (opposite of distribution)

-1(w-8)           >now it looks more like the other parentheis,   Subsitiute in

8-w    is same as   -1(w-8)      from above

4w(8 − w) + 3(w − 8)                  >original question, now substitute

4w(-1)(w-8) + 3(w − 8)                 > simplify -1

-4w(w-8) + 3(w − 8)                     >take out w-8 as GCF

(w-8)(-4w+3)              

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:

y - x = 3 (Expression that represents age difference between Fatimah and Nadia)

x + 3 = y, where x, y > 0 and y > x. (1)

The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.

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Answer:

13

Step-by-step explanation:

Since Seth pays $0.50 for each check he writes, he would write (let x be how many checks Seth wrote) "x" checks for $6.50. That means;

1 = 0.50

x = 6.50

Now let us set up a fraction:

\(\frac{0.5}{1}=\frac{6.5}{x}\)

Step 1: Cross multiply

\(0.5x=1\cdot \:6.5\)

\(0.5x=6.5\)

Step 2: Divide both sides by \(0.5\)

\(\frac{0.5x}{0.5}=\frac{6.5}{0.5}\)

Simplify

\(x=13\)

Therefore, Seth will write 13 checks for $6.50

Answer:

The 6 pack

Step-by-step explanation:

i searched it up

The required option that has a lesser price per mini football is a package of 8.

Given that,
at a toy store, Colton can buy a package of 6 mini footballs for $7.50. or a package of 8 mini footballs for $9.60. wich option has the lesser price per mini football is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
For 6 package footballs the cost of a mini football = 7.50 / 6 = $1.25.
For 8 package footballs the cost of a mini football = 9.60 / 8 = $1.20.

Thus, the required option that has a lesser price per mini football is a package of 8.

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Answer:

5x+9=x-23

5x-x=-23-9

4x= -32

4x/4=-32/4

x=-8

Answer:

\(\{0, 1, 2, 3\}\) is a partition of Z

Step-by-step explanation:

Given

\($$A _ { 0 } = \{n \in \mathbf { Z } | n = 4 k$$,\) for some integer k\(\}\)

\($$A _ { 1 } = \{ n \in \mathbf { Z } | n = 4 k + 1$$,\) for some integer k},

\($$A _ { 2 } = { n \in \mathbf { Z } | n = 4 k + 2$$,\) for some integer k},

and

\($$A _ { 3 } = { n \in \mathbf { Z } | n = 4 k + 3$$,\)for some integer k}.

Required

Is \(\{0, 1, 2, 3\}\) a partition of Z

Let

\(k = 0\)

So:

\($$A _ { 0 } = 4 k\)

\($$A _ { 0 } = 4 k \to $$A _ { 0 } = 4 * 0 = 0\)

\($$A _ { 1 } = 4 k + 1$$,\)

\(A _ { 1 } = 4 *0 + 1$$ \to A_1 = 1\)

\(A _ { 2 } = 4 k + 2\)

\(A _ { 2} = 4 *0 + 2$$ \to A_2 = 2\)

\(A _ { 3 } = 4 k + 3\)

\(A _ { 3 } = 4 *0 + 3$$ \to A_3 = 3\)

So, we have:

\(\{A_0,A_1,A_2,A_3\} = \{0,1,2,3\}\)

Hence:

\(\{0, 1, 2, 3\}\) is a partition of Z

Approximately 68% of the area under the normal distribution curve falls within 1 standard deviation above and below the mean. This is known as the empirical rule, also called the 68-95-99.7 rule.

Approximately 95% of the area under the normal distribution curve falls within 2 standard deviations above and below the mean.

Approximately 99.7% of the area under the normal distribution curve falls within 3 standard deviations above and below the mean.

It's important to note that these values apply to a standard normal distribution (mean = 0, standard deviation = 1). For any normal distribution with a different mean and standard deviation, you can use the standard score (z-score) to transform the data into the standard normal distribution, and then use the standard normal distribution to find probabilities.

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Given:

Vertex at (-1,-2)

Goes through point (0,1)

The vertex form of a quadratic equation is defined as

Substitute (h,k) with the vertex (-1,-2)

Now we solve for a, by substituting (x,y) with (0,1) to the vertex form of the previous equation.

Putting it together with the vertex form we have

Expand the equation, and change it into standard form

Simplify further, and the equation of the parabola in standard form is

Answer:  y=1.6552x

Step-by-step explanation:

Determine the coordinates of the two points, C and D.

C (0,0)

D (7.25, 12)  [Hard to read the graph.  Use the values you judge to be correct]

We want a straight line to go through C and D.  It should have the form y = mx + b, where m is the slope and b is the y-intercept (the value of y when x=0).  The slope is the rise/run of the line, so we'll use the two given points to determine slope.  Rise = (12-0)=12.  Run = (7.25-0) = 7.75.  Rise/Run = 12/7.25, or 1.6552.  The equation becomes y = 1.6552x + b.

Find b by using one of the given points.  I'll use (0,0) because it is easy:

y = 1.6552x + b for (0,0):  0 = 1.6552(0) + b;  b = 0

The equation is thus y=1.6552x

The correct option is B. Famous and well-known.

A person who is widely known is said to be famous, renowned, celebrated, noteworthy, notorious, distinguished, prominent, or illustrious. Being extensively and well known, even for a little period of time, is all that being famous really means. A known actress suggests greater honor and acclaim.

Celebrated, distinguished, eminent, illustrious, notable, notorious, and renowned are some popular synonyms for famous. All of these phrases refer to being "known far and wide," while "famous" only refers to the reality of having a large and widespread following.

Disclaimer

8 famous images showed Tweed with a bag of money in place of his

A) NO CHANGE

B) famous and well-known

C) famous and commonly known

D) famous, commonly known

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Answer:

x=5.657 y=5.657

Step-by-step explanation:

Answer:

AB=5

Step-by-step explanation:

Triangle TAB is similar to triangle TWE. This can be proven through AA congruency. Because line AB is parallel to line segment WE, angle TAB is congruent to angle TWE (corresponding angles) and angle TEW is congruent to angle TEW(corresponding angles). Now, having proved that triangle TAB is similar to triangle TWE, we know that similar triangles have proportional sides. We can do \(\frac{TB}{AB} = \frac{TE}{WE}\), plug in values for \(\frac{4}{AB} = \frac{16}{20}\)  , simplify   \(\frac{4}{AB} = \frac{4}{5}\), both fractions have a four in the numerator and must be equal to each other so AB=5.

Answer:

Step-by-step explanation:

soory

The fractions of the hole above that are the standard 4 patterns blocks are as follows:Standard pattern block hexagon: 1/1 or 1Trapezoid: 0/1 or 0Parallelogram: 0/1 or 0Rhombus: 0/1 or 0

To find the fractions of the hole above that are the standard 4 patterns blocks, we need to analyze the given figures. The figures are as follows:

Figure 1: The standard pattern block hexagon

Figure 2: A trapezoid

Figure 3: A parallelogram

Figure 4: A rhombus

Now, we need to identify which of these figures fit into the given hole. Looking at the hole, we can see that it is in the shape of a hexagon. Therefore, the only pattern block that can fit into this hole is the standard pattern block hexagon. Hence, the fraction of the hole above that is the standard pattern block hexagon is 1/1 or simply 1. No other pattern blocks fit into the given hole. Therefore, the fractions of the hole above that are the standard 4 patterns blocks are as follows:

Standard pattern block hexagon: 1/1 or 1

Trapezoid: 0/1 or 0

Parallelogram: 0/1 or 0

Rhombus: 0/1 or 0

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