kim places £500 in a bank account the pays 3% simple interest each year
how much interest will she earn each year?
how much will she have in her account after 1 year

Answer:

Step-by-step explanation:

[tex] \mathsf{3(2 \frac{1}{2} - 1) + \frac{3}{10} }[/tex]

Convert mixed number to improper fraction

[tex] \mathrm{3( \frac{5}{2} - 1) + \frac{3}{10} }[/tex]

Calculate the difference

⇒[tex] \mathrm{3( \frac{5 \times 1}{2 \times 1} - \frac{1 \times 2}{1 \times 2} }) + \frac{3}{10} [/tex]

⇒[tex] \mathrm{ 3 \times( \frac{5}{2} - \frac{2}{2}) } + \frac{3}{10} [/tex]

⇒[tex] \mathrm{3 \times ( \frac{5 - 2}{2} ) + \frac{3}{10} }[/tex]

⇒[tex] \mathrm{3 \times \frac{3}{2} + \frac{3}{10} }[/tex]

Calculate the product

⇒[tex] \mathrm{ \frac{3 \times 3}{1 \times 2} + \frac{3}{10} }[/tex]

⇒[tex] \mathrm{ \frac{9}{2} + \frac{3}{10}} [/tex]

Add the fractions

⇒[tex] \mathsf{ \frac{9 \times 5}{2 \times 5} + \frac{3 \times 1}{10 \times 1} }[/tex]

⇒[tex] \mathrm{ \frac{45}{10} + \frac{3}{10} }[/tex]

⇒[tex] \mathrm{ \frac{45 + 3}{10 } }[/tex]

⇒[tex] \mathrm{ \frac{48}{10} }[/tex]

Reduce the numerator and denominator by 2

⇒[tex] \mathrm{ \frac{24}{5} }[/tex]

Further more explanation:

Addition and Subtraction of like fractions

While performing the addition and subtraction of like fractions, you just have to add or subtract the numerator respectively in which the denominator is retained same.

For example :

Add : [tex] \mathsf{ \frac{1}{5} + \frac{3}{5} = \frac{1 + 3}{5} } = \frac{4}{5} [/tex]

Subtract : [tex] \mathsf{ \frac{5}{7} - \frac{4}{7} = \frac{5 - 4}{7} = \frac{3}{7} }[/tex]

So, sum of like fractions : [tex] \mathsf{ = \frac{sum \: of \: their \: number}{common \: denominator} }[/tex]

Difference of like fractions : [tex] \mathsf{ \frac{difference \: of \: their \: numerator}{common \: denominator} }[/tex]

Addition and subtraction of unlike fractions

While performing the addition and subtraction of unlike fractions, you have to express the given fractions into equivalent fractions of common denominator and add or subtract as we do with like fractions. Thus, obtained fractions should be reduced into lowest terms if there are any common on numerator and denominator.

For example:

[tex] \mathsf{add \: \frac{1}{2} \: and \: \frac{1}{3} }[/tex]

L.C.M of 2 and 3 = 6

So, ⇒[tex] \mathsf{ \frac{1 \times 3}{2 \times 3} + \frac{1 \times 2}{3 \times 2} }[/tex]

⇒[tex] \mathsf{ \frac{3}{6} + \frac{2}{6} }[/tex]

⇒[tex] \frac{5}{6} [/tex]

Multiplication of fractions

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term.

When any number or fraction is divided by a fraction, we multiply the dividend by reciprocal of the divisor. Let's consider a multiplication of a whole number by a fraction:

[tex] \mathsf{4 \times \frac{3}{2} = \frac{4 \times 3}{2} = \frac{12}{2} = 6}[/tex]

Multiplication for [tex] \mathsf{ \frac{6}{5} \: and \: \frac{25}{3} }[/tex] is done by the similar process

[tex] \mathsf{ = \frac{6}{5} \times \frac{25}{3} = 2 \times 5 \times 10}[/tex]

Hope I helped!

Best regards!

Answer:

[tex]\large \boxed{\sf \bf \ \ C. \ \$ 695 \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

At the beginning, we have $290.

After 1 year, we get 290 + 6% * 290 = 290 (1+0.06)= 290 * 1.06

After n years, we get [tex]290\cdot 1.06^n[/tex]

So after 15 years, we get.

[tex]290\cdot 1.06^{15}=695.0018...[/tex]

Thank you

Answer:

the third option

Step-by-step explanation:

as any number is greater than -2

Answer:

5 feet

Step-by-step explanation:

Since Jackson's bedroom is a rectangle, it has dimensions of length times width. Suppose the length is l and the width is w.

The area of a rectangle is given by A = lw, where l is the length and w is the width. Here, we know the area is 90, so:

lw = 90

We also know that this area of 90 square feet is 9 times that of the closet, so suppose the area of the closet is c. Then:

9c = 90

Divide by 9:

c = 90/9 = 10 square feet

So, the area of the closet is 10 square feet. Since the width is 2, we know the length will be:

A = lw

10 = lw

10 = 2 * l

l = 10/2 = 5

The length is thus 5 feet.

~ an aesthetics lover

Answer:

5 ft

Step-by-step explanation:

If his bedroom is 9 times of his closet, then that means you divide the area of his bedroom by 9.  So, 90 divided by 9=10.  That means the closet has an area of 10 sq. ft.  As we all know, the area is the length times width.  So if the width is 2 ft, then we need to multiply it by a number so it will equal 10.  You can do 10 divided by 2 to find it, which equals 5.  That means the length of the closet is 5 sq. ft.

Answer:

18a - 12

Step-by-step explanation:

6(3a-2)

6*3a - 6*2

18a - 12

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]18a - 12[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\6(3a-2)\\-----------------\\\rightarrow \text{Distribute the '6' into '3a' and '-2'.}\\\\\rightarrow 6 * 3a = 18a\\\\\rightarrow 6 * -2 = -12\\\\\\\text{Therefore:}\\\\6(3a-2)\rightarrow \boxed{18a - 12}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

y=-2x-15

Step-by-step explanation:

first find the slope. the formula for finding slope is (y_1 - y_2)/(x_1 - x_2) (rise over run) so we plug in the values and get (-6+4)/(-5+6)= -2/1=-2 so m=-2 and we have y=-2x+b. then plug in either point for x and y and solve for b. -5= -2*-5 +b, -5= 10+b, b=-15, y=-2x-15

Answer:

y=-0.5x-8

Step-by-step explanation:

i got it right

Answer:

yes

The statement 'C' explains the difference between a plane and a ray.

i.e. A plane does not have a formal definition, and a ray is described through undefined terms.

Step-by-step explanation:

A plane does not have a formal definition, and a ray is described through undefined terms. The statement is true because

A plane is basically an undefined term as it could be named using three non-straight points - also called noncollinear points. A plane is basically a flat two-dimensional object having no thickness.

In Geometry, we have a variety of undefined terms, including point, line and plane. All other terms in Mathematics (Geometry) could be defined from the mentioned three undefined terms.

Therefore, the statement 'C' explains the difference between a plane and a ray.

i.e. A plane does not have a formal definition, and a ray is described through undefined terms.

Keywords: plane, point, line, ray

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Answer:

21.7 m

Step-by-step explanation:

The question above is a right angle triangle and we would be using the trigonometric function of tangent to solve for it.

tan θ = Opposite/ Adjacent

Opposite side = Height = unknown

Adjacent = 20sqrt(3) m

θ = Angle of Elevation = 30°

Hence, we have:

tan 30° = Opposite/ 20√3

Opposite = tan 30° × 20√3m

Opposite = 20m

Height of the tower = Height of the observer + Height (Opposite side)

Height = 20m

Height of the the observer as given in the question is = 1.7m

Height of the tower = 20m + 1.7m

= 21.7m

Therefore, the height of the tower = 21.7m

Answer:

The weights are 50 lb, 35 lb, and 35 lb.

Step-by-step explanation:

The three boys weight x, y, and z pounds.

One boy weighs 50 lb, so x = 50. The other 2 boys have the same weight, so y = z.

The average weight is the sum of the three weights divided by 3.

(x + y + z)/3 = 40

(50 + y + y)/3 = 40

2y + 50 = 120

2y = 70

y = 35

z = y = 35

Answer: The weights are 50 lb, 35 lb, and 35 lb.

Answer: 35 lb, 35 lb, and 40 lb

Step-by-step explanation:

(50+X+X)/3 = 40

50 + 2X = (40)(3)

2X = 120 - 50

X = 70/2

X = 35

Answer:

linda will get 35 candies

Answer:

Linda gets 33 candies

Step-by-step explanation:

Let's call Linda's number of sweets x and make an equation for the total number of candies:

70 = 4+ x + x

Then simplify it:

70 = 4 + 2x

We then solve for x ( which is the number of candies Linda gets ):

70 - 4 = 4 + 2x  - 4

66 = 2x

66 ÷ 2 = 2x ÷ 2

33 candies = x ( amount Linda gets )

HOPE THIS HELPED

Answer:

Step-by-step explanation:

This study investigated three mathematics teachers' construction process of geometric structures using compass and straightedge. The teacher-student-tool interaction was analysed. The study consists of the use of a compass and straightedge by the teachers, the ideas of the teachers about their use, and the observations regarding the learning process during the construction of the geometric structures. A semi-structured interview was conducted with the teachers about the importance of the use of a compass and straightedge to construct geometric structures. It was found that teachers taught compass and straightedge constructions in a rote manner where learning is little more than steps in a process. The study concludes with some suggestions for the use of a compass and straightedge in mathematics classes based on the research results. SUMMARY Purpose and significance: For more than 2,000 years, the way in which geometric structures could be constructed with the help of compasses and straightedges has caught the attention of mathematicians. Nowadays, mathematics curriculums place an emphasis on the use of the compass and straightedge. The compass and straightedge is more important in constructing geometric structures than other drawing tools such as rulers and protractors. Because steps taken with a compass and straightedge cannot be seen at first glance and this situation become a problem for students. However, 'doing compass and straightedge construction early in the course helps students to understand properties of figures'

Answer:

Option D

Step-by-step explanation:

Option D's equation is in slope-intercept form. Slope-intercept form equations are used for linear functions.

Nonlinear functions would have an exponent (that is higher than 1), 'x' as an denominator in a function, or a square/cube root symbol in it's equation.

Option D should be the correct answer.

Hope this helps.

Answer and Step-by-step explanation:

A) Probability of taken two odd numbered token without replacement:

P(3) = 2/5 = 0.4

P(7) = 1/4 = 0.25

Construct a probability distribution:

 X          3          7

p(X)      0.4      0.25

B) Mean of the probability distribution:

E(X) = ∑xp

E(X) = 3*0.4 + 7*0.25

E(X) = 2.95

Variance of the probability distribution:

V(X) = [tex]\Sigma X^{2}p - [E(X)]^{2}[/tex]

V(X) = [tex]3^{2}*0.4+7^{2}*0.25 - (2.95)^{2}[/tex]

V(X) = 7.1475

Mean and variance of the probability distribution are 2.95 and 7.145, respectively.

Answer:

210 ways

Step-by-step explanation:

The number is ₁₀C₄=10!/4!*6! = 210 ways

Hope this helps. Please mark as brainliest

The correct answer is 210

They can do this in ¹⁰C₄ ways. Because there is no order to be followed while selecting, we use the combinations formula

ⁿCₓ = n!/x!(n-x)! , where n is the number of people, and x is the sample

Substituting n = 10, x = 4, we get

​¹⁰C₄ = 10!/4!(10-4)!

¹⁰C₄ = 10!/4!6!

¹⁰C₄ = 10*9*8*7*6/4!6!

¹⁰C₄ = 10*9*8*7/4*3*2*1

¹⁰C₄ = 210

So, the group of 4 members can be sent in 210 ways.

There are 210 different groups of 4 members they could send.

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A

Step-by-step explanation:

Answer:

60 miles per hour

Step-by-step explanation:

Total distance= 180 miles

Total time =3 hours

Average rate of change= ?

Distance= Rate × time

Make Time the subject of the formula

Time= Distance / Rate

Make average rate of change the subject of the formula

Average rate of change = Distance / time

= 180 miles / 3 hours

= 60 miles per hour

Answer:

Equation is y = 5x - 6

Step-by-step explanation:

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

m is slope, and c is y-intercept:

[tex]slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]

(x1, y1) = (1, -1)

(x2, y2) = (0, -4)

[tex]m = \frac{ - 4 - 1}{0 - 1} \\ \\ m = 5[/tex]

for y-intercept, consider (1, -1):

[tex]y = mx + c \\ - 1 = (5 \times 1) + c \\ - 1 = 5 + c \\ c = - 6[/tex]

substitute in general equation:

[tex]y = 5x - 6[/tex]

It's an example of rotation symmetry, if the image appears unchanged. If the rotation symmetry exists there is a one centre point around which an image appears unchanged.

Answer:

It's an example of rotation symmetry, if the image appears unchanged. If the rotation symmetry exists there is a one centre point around which an image appears unchanged.

Answer:

1

Step-by-step explanation:

I believe it is 1. Just picture or draw a diagram of the constraints. Don't quote me on this though...

Answer:

Step-by-step explanation:

apply sine formula

[tex]\frac{a}{sin ~A} =\frac{b}{sin~B} \\\frac{25}{sin~58} =\frac{28}{sin ~B} \\sin~B=\frac{28}{25} \times sin~58\\B=sin^{-1} (\frac{28}{25} \times sin ~58)=71.77 \approx 72 ^\circ[/tex]

so third angle=180-(58+72)=180-130=50°

∠C=50°

[tex]cos ~C=\frac{a^2+b^2-c^2}{2ab} \\or ~2abcos~C=a^2+b^2-c^2\\2*25*28*cos ~50=25^2+28^2-c^2\\c^2=625+784-1400 *cos~50\\c^2=1409-899.90\\c^2=509.1\\c=\sqrt{509.1} \approx 22.56 \approx 22.6[/tex]

so one triangle is formed.

Answer:

130

Step-by-step explanation:

Probability of green:

Number of attempts:  

Expected number of landing on green:

Answer: 130 times

Answer:

the slope of the line represented by the table is y = 2/11x

Step-by-step explanation:

y = mx + b

slope: (y² - y¹) / (x² - x¹)

(4 - 2) / (22 - 11) = 2/11

plug in an x and y value to find b

y = 2/11x + b

2 = (2/11)(11) + b

2 = 2 + b

b = 0

the y-intercept is 0

your equation is y = 2/11x

Answer:

always b is equal to 9 is rhdx forum post in is ek of

Answer:

6.7 cm

Step-by-step explanation:

A+B+C=180°

55°+B+82°=180°

B=43°

Using the formulae

(Sin A)/a = (Sin B)/b

(Sin 55)/8 = (Sin 43)/b

b = [8(Sin 43)]/(Sin 55)

b= 6.7 cm

Answer:

-8.

Step-by-step explanation:

x + 16 - 20 = 2x + 20 - 16

x - 4 = 2x + 4

x - 2x = 4 + 4

-x = 8

x = -8.

The mystery number 'm' that satisfies the stated conditions is - 8.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Let, The mystery number be 'm'.

So, When you add 16 to my mystery number then subtract 20,

m + 16 - 20,

you get the same result as when you add my mystery number to itself, then add 20 and subtract 16,

m + m + 20 - 16.

Therefore,

m + 16 - 20 = m + m + 20 - 16

m - 4 = 2m + 4.

- m = 8.

m = - 8.

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Answer:

(x+3)(x-2)

Step-by-step explanation:

We can immediately see that there are roots at x = -3, and x = 2.

Because the website gives us that this in the form of (x + _) (x - _), our anwser is (x+3)(x-2)

oops I just saw your comment. Too late i guess...

Answer:

f(x)=1(x+3)(x-2)

Step-by-step explanation:

Answer:

x = -0.4

x = -(2/5)

Answer:

x = ± √5

Step-by-step explanation:

Please indicate exponentiation by using the symbol " ^ ":

5x^2 + 25x = 0

Divide all three terms by 5.  We get:

x^2 + 5 = 0, or x^2 = -5

Then x = ± √5

Answer:

C

Step-by-step explanation:

let hypotenuse of triangle with 60°=y

[tex]\frac{8\sqrt{2}}{y} =sin ~60\\8 \sqrt{2}=y \times \frac{\sqrt{3}}{2} \\y=\frac{16 \sqrt{2}}{\sqrt{3}} =\frac{16 \sqrt{6}}{3}[/tex]

Answer:

A

Step-by-step explanation:

Let us start with B = 90

That would mean that each of the other 2 angles must add to 90 which makes each of them 45.

But the question doesn't allow that. B has to be greater than 90 which means that the other two angles must be less that 45 each.

the only answer that does that is A

Answer:

9 and 15

Step-by-step explanation:

9 10 11 12 13 14 15