Clarise evaluated this expression.

(66.3 – 14.62) ÷ 0.6 – 0.22

(51.68) ÷ 0.6 – 0.22

(51.68) ÷ 0.42

51.68 ÷ 0.16

32.3

Which errors did Clarise make?

Question:

Find the value of the letter in each of the following and give reasons for the steps involved:

1 2 A

+ 6 A B =

A 0 9

Answer:

128 + 681 =  809

Step-by-step explanation:

Here, let's use the general form of numbers where any  letter must represent one value and each digit must be represented by just one letter.

Take the following:

A = 8

B = 1

Thus, A +B = 8 + 1 = 9

Also add:

8 + 2 = 10

In general form, tens digit is zero and the 1 is carried over.

I.e, A = 1 + 6 + 1 = 8

We can now see that,

A = 8

B = 1

Therefore,

1 2 A

+ 6 A B =

A 0 9

Will be written as:

128 + 681 =  809

Answer:

C. Rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.

Step-by-step explanation:

See figure for intermediate steps.

The transformed rectangle ABCD was dilated with center (0, 0) and a scale factor of 1/2 followed by a translation right 3.5 units and down 8 units.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the rectangle be represented as ABCD

Now , the coordinates of the rectangle are

A ( 1 , 9 ) , B ( 1 , 6 ) , C ( 7 , 6 ) and D ( 7 , 9 )

Now , the rectangle is dilated with scale factor of 1/2 , we get

A ( 0.5 , 4.5 ) , B ( 0.5 , 3 ) , C ( 3.5 , 3 ) and D ( 3.5 , 4.5 )

And , the rectangle is translated right 3.5 units and down 8 units.

So , the new coordinates of the rectangle is

E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )

Hence , the transformed rectangle is E ( 4 , -3.5 ) , F ( 4 , -5 ) , G ( 7 , -5 ) and H ( 7 , -3.5 )

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Answer:

A, E, F, G

Step-by-step explanation:

The picture below represents a parabolic arc.

An example can be an object being thrown up in the air then then coming back down.

Answer:

x = -5.

Step-by-step explanation:

The solutions of the equation is when the two functions intersect. That is at (-5, 5.5), so where x = -5.

Hope this helps!

Answer:

x = -5

Step-by-step explanation:

f(x) = g(x) has more than one solution, because they intersect at two points.

The question asks for one solution of f(x) = g(x).

One point where they intersect is at (-5, 5.5), as shown in the graph.

(x , y)

x = -5, y = 5.5

Answer: the answer would be 24

Step-by-step explanation: just did the assignment

Answer:

24

Step-by-step explanation:

Just got it right on edge 2020

Answer:

C. The hypotenuse is [tex]\sqrt{2}[/tex] times as long as either leg.

Step-by-step explanation:

The hypotenuse is square root 2 times as long as the sides is a true statement.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We have to find the true statement about an isosceles right triangle.

Let us use pythagoras theorem to find this

h²=a²+b²

In this case since its an isosceles right triangle, a and b most be the same.

Let's say that the measure of the sides that are equal is x and the hypotenuse is h.

Pythagoras tells us the following:

h²=x²+x²

h²=2x²

Take square root on both sides

h=√2x

Hence, the hypotenuse is square root 2 times as long as the sides

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Answer:

La respuesta es 7+6 ó 6+7 que es 13

Answer:

1) 3x + 44

2) 2y - 8

3) x - 6

15) 5 7/8

16) 6 1/3

17) 3 7/9

Step-by-step explanation:

1) 49 + 4 - 5 - 4 + 3x = 3x + 44

2) -y - 5 + y + 2(y) - 3 = 2y - 8

3) 4x - 3 - 3(x + 1) = 4x - 3 - 3x - 3 = x - 6

15) 7 1/4 - 1 3/8 = 7 2/8 - 1 3/8 = 6 10/8 - 1 3/8 = 5 7/8

16) 9 - 2 2/3 = 8 3/3 - 2 2/3 = 6 1/3

17) 10 1/3 - 6 5/9 = 10 3/9 - 6 5/9 = 9 12/9 - 6 5/9 = 3 7/9

Answer:

The answer is

Step-by-step explanation:

The distance between two points is found by using the formula

[tex] \sqrt{ {(x1 - x2)}^{2} + {(y1 - y2)}^{2} } [/tex]

Where (x1 , y1) and ( x2 , y2) are the points

The distance between (-6, -2) and (0, -1) is

[tex] \sqrt{ {( - 6 - 0)}^{2} + {( - 2 + 1)}^{2} } \\ \\ = \sqrt{ {( - 6})^{2} + {( - 1)}^{2} } \\ \\ = \sqrt{36 + 1} \\ \\ = \sqrt{37} \: units[/tex]

Hope this helps you

Answer: √37 units

hope that helped!

Answer:

C.  6√5

Step-by-step explanation:

√20 +√80= √4*5 + √16*5 = 2√5 + 4√5 = 6√5

Answer:

140 poles

Step-by-step explanation:

1. Convert to the same unit. Either meters to kilometers or kilometers to meters, so you can complete the computation.

2. Divide 0.06 by 8.4 (8.4/0.06 = 140).

3. 140 poles can be placed on the 8.4 km road when separated by 60 m or 0.06 km.

Answer:

The answer is A.

Step-by-step explanation:

So we have the two equations:

[tex]3x+y=1\\y+4=5x[/tex]

To make a substitution of the second equation into the first equation, we need to isolate the y variable in the second equation. Thus:

[tex]y+4=5x\\y=5x-4[/tex]

Now, we can substitute this into the first equation. Therefore:

[tex]3x+y=1\\3x+(5x-4)=1\\3x+5x-4=1[/tex]

Answer: $10,000

Step-by-step explanation:

Given the following :

Profit if economy remains strong = $30,000

Profit if economy grows at moderate pace = $10, 000

Loss if economy goes into recession = $30,000

Probability that economy will remain strong = 20% = 0.2

probability the economy will grow at a moderate pace = 70% = 0.7

probability the economy will slip into recession = 10% = 0.1

Expected value = sum of (x * p(x))

Here expected value equals;

Strong economy profit = $30,000 * 0.2 = $6000

Moderate economy profit = $10,000 * 0.7 = $7000

Loss on Recession = $30,000 * 0.1 = $3000

Expected profit = $(6000 + 7000 - 3000)

Expected profit = $10,000

Step-by-step explanation:

Given:

x = 26214.47

s = 5969.25

n = 15

t = 2.046

The confidence interval is:

CI = x ± t (s / √n)

CI = 26214.47 ± 2.046 (5969.25 / √15)

CI = (23061.06, 29367.88)

Answer:

125 : 729

Step-by-step explanation:

Given the ratio of the radii of 2 similar spheres = a : b , then

ratio of volumes = a³ : b³

Here the ratio of radii = 5 : 9 , thus

ratio of volumes = 5³ : 9³ = 125 : 729

Answer:

false!

Step-by-step explanation:

i just answered true and it was false. so false is correct!

The statement that the horizontal cross-sectional shapes of the given prism are all congruent is false.

Prisms are three-dimensional shapes that have its two ends to be parallel and congruent

The given prism is a trapezoidal prism.

For the horizontal sectional shapes given prism to be congruent, the prism must be cut through the middle

Since the prism can be divided at any point, then the given statement is false

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Answer:

2 ¹/12

Step-by-step explanation:

convert 1 4/12 to an improper fraction

(1×12+4)=16/12

16/12+9/12=25/12

convert 25/12 to a mixed fraction

=2 ¹/12

Answer:

[tex]Volume = 1017.36\ in^3[/tex] -- Cone

[tex]Volume = 3052.08\ in^3[/tex] -- Cylinder

[tex]Volume = 3052.08\ in^3[/tex] -- Sphere

Best Buy: Sphere Clay

Step-by-step explanation:

Given

Solid Shapes: Cone, Cylinder, Sphere

Cost of Cone Clay = $12

Cost of Cylinder Clay = $30

Cost of Sphere Clay = $28

Required

Determine the volume of each shape

Which is the best buy

The volume of a cone is calculated as thus;

[tex]Volume = \frac{1}{3}\pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{1}{3} * 3.14 * 9^2 * 12[/tex]

[tex]Volume = \frac{3052.08}{3}[/tex]

[tex]Volume = 1017.36\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 1017.36\ in^3[/tex]

[tex]Total\ Cost = \$12[/tex] (Given)

[tex]Volume:Price = \frac{1017.36\ in^3}{\$ 12}[/tex]

[tex]Volume:Price = 84.78 in^3/\$[/tex]

[tex]Volume:Price = 84.78 in^3:\$1[/tex]

The volume of a cylinder is calculated as thus;

[tex]Volume = \pi r^2h[/tex]

From the attached diagram

Radius, r = 9 inches; Height, h = 12 inches and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = 3.14 * 9^2 * 12[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$30[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 30}[/tex]

[tex]Volume:Price = 101.736\ in^3/\$[/tex]

[tex]Volume:Price = 101.736\ in^3:\$1[/tex]

The volume of a sphereis calculated as thus;

[tex]Volume = \frac{4}{3}\pi r^3[/tex]

From the attached diagram

Radius, r = 9 inches; and [tex]\pi = 3.14[/tex]

Substitute these values in the above formula;

[tex]Volume = \frac{4}{3} * 3.14 * 9^3[/tex]

[tex]Volume = \frac{9156.24}{3}[/tex]

[tex]Volume = 3052.08\ in^3[/tex]

The unit cost of the cone is calculated as thus;

[tex]Volume:Price = \frac{Volume}{Total\ Cost}[/tex]

Where

[tex]Volume = 3052.08\ in^3[/tex]

[tex]Total\ Cost = \$28[/tex] (Given)

[tex]Volume:Price = \frac{3052.08\ in^3}{\$ 28}[/tex]

[tex]Volume:Price = 109.003\ in^3/\$[/tex]

[tex]Volume:Price = 109.003\ in^3:\$1[/tex]

Comparing the Volume:Price ratio of the three clay;

The best buy is the sphere because it has the highest volume:price ratio.

Having the highest volume:price ratio means that with $1, one can get more clay from the sphere compared to other types of clay

Divide the largest one by the smallest one : for example, the number 4 is 42=2× larger than the number 2.

Indeed, If you multiply 2 by 42 you'll get 4.

Of course, if a number is n× larger than another, then this other is n× smaller than the first one.

It will of course work with floating point : 0.6×10.6≈0.6×1.6667=1 so 1 is ~1.6667 times larger than 0.6 while 0.6 is ~1.6667 smaller than 1.

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Answer:

(-3, 3.25)

Step-by-step explanation:

Answer: No solution

Step-by-step explanation: If you are doing the Unit Test on edge2020 then D No solution is the answer.

Answer:

the answer is no "solution"

Unit Test on Edge 2023

Answer:

241 mm^2.

Step-by-step explanation:

There are 10 mm in a cm so there are 10*10 = 100 mm^2 in  a cm^2.

So the answer is 2.41 * 100 = 241 mm^2.

Answer:

241mm²

Step-by-step explanation:

If 10mm = 1cm,

then 100mm² = 1cm²

2.41 × 100 = 241mm²

Answer:

16

Step-by-step explanation:

Well first we need to plug in 10 for g and 6 for h.

2/5(10) + 3(6) - 6

4 + 18 - 6

22 - 6

16

Thus,

the answer is 16.

Hipe this helps :)

Answer:

16

Step-by-step explanation:

We are given the expression:

2/5g+ 3h - 6

We know that g=10 and h=6. Therefore, we can substitute 10 and 6 into the expression and solve according to PEMDAS( Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

2/5(10)+3(6)-6

First, multiply 2/5 and 10

4+ 3(6)-6

Next, multiply 3 and 6

4+18-6

Next, add 4 and 18

22-6

Finally, subtract 6 from 22

16

2/5g + 3h - 6 when g=10 and h= 6 is 16.

Step-by-step explanation:

Notice how you get the same value each time when you divide the cost by the number of downhill rides

Moreover when the downhill rides grow by 2 the total cost grows by 5

so we can state :

To complet the chart we can use the proportionaliyu relation:

so 20 goes with 50

same method:

so 25 goes with 62.5

Answer:

The first way to prove that the diagonals of a rectangle are congruent is to show that triangle ABC is congruent to triangle DCB

Here is what is given: Rectangle ABCD

Here is what you need to prove: segment AC ≅ segment BD

Since ABCD is a rectangle, it is also a parallelogram.

Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent.

Answer:

[tex] csc (R) = \frac{13}{12} [/tex]

Step-by-step explanation:

Formula for any given angle (Ѳ) is given as csc Ѳ = length of hypotenuse side//length of opposite side. It is the inverse of sin Ѳ.

In the right triangle given above, the opposite length = 24, while the length of the hypotenuse = 26

Thus,

[tex] csc (R) = \frac{hypotenuse}{opposite} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{26}{24} [/tex]

[tex] csc (R) = \frac{13}{12} [/tex]

Answer:

See below.

Step-by-step explanation:

To find the equation, we need to find the slope and the y-intercept. Afterwards, we can put the numbers into the slope-intercept form:

[tex]y=mx+b[/tex]

From the graph, we can see that the line crosses the y-intercept at y=-6. Thus, the y-intercept (b) is -6.

Now we need to find the slope. Pick any two points where the line crosses. I'm going to pick (0,-6) and (4,-7).

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-6)}{4-0}= -1/4[/tex]

Therefore, the equation of the line would be:

[tex]y=mx+b\\y=-1/4x-6[/tex]

Answer:

24

Step-by-step explanation:

30/100=x/80

cross multiply:

100x=2400

divide by 100:

x=24

Not quite sure how you want me to explain the other way step by step... Hope this helps!

80*.3=24

Answer:

3/8

Step-by-step explanation:

If 5/8 of the staff is male, then 8/8 is the total number of staff.

8/8 - 5/8 = 3/8

3/8 of the staff is female.

Hope this has helped. If the question has more to it, then please specify.

Answer:

[tex]\large \boxed{\sf \ \ 70\% \ \ }[/tex]

Step-by-step explanation:

Hello,

We assume that the year is 52 weeks, and we note r the interest rate we are looking for. The rate is expressed in percent and is annually, meaning that the investment is, after the first week :

   [tex]1000\cdot (1+\dfrac{r\%}{52})=1000\cdot (1+\dfrac{r}{5200})[/tex]

For the second week

   [tex]1000\cdot (1+\dfrac{r}{5200})^2[/tex]

After 52 weeks

   [tex]1000\cdot (1+\dfrac{r}{5200})^{52}[/tex]

and we want to be equal to 2000 so we need to solve:

[tex]1000\cdot (1+\dfrac{r}{5200})^{52}=2000\\\\\text{*** divide by 1000 both sides ***}\\\\(1+\dfrac{r}{5200})^{52}=\dfrac{2000}{1000}=2\\\\\text{*** take the ln **}\\\\52\cdot ln(1+\dfrac{r}{5200})=ln(2)\\\\\text{*** divide by 52 ***}\\\\ln(1+\dfrac{r}{5200})=\dfrac{ln(2)}{52}\\\\\text{*** take the exp ***}\\\\\displaystyle 1+\dfrac{r}{5200}=exp(\dfrac{ln(2)}{52})=2^{(\dfrac{1}{52})}=\sqrt[52]{2}\\\\r = 5200\cdot (\sqrt[52]{2}-1)=69.77875...[/tex]

Rounded to the nearest percent, the solution is 70%.

If you want to double your capital in one year with weekly compounding you need an interest rate of 70% !!

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

4%

Step-by-step explanation: