Interest is compounded semianually. Find the amount in the account after the given time.

Vector components are expressed in the form (x, y). The measure of tan m given the coordinate Q is -√32/12

Vector components are expressed in the form (x, y). Given the  coordinates of point Q are (−12,√32), the measure of the angle is expressed as;

m = arctan(y/x)

m = arctan (-√32/12)

Take the tan of both sides

tan m = tan arctan(-√32/12)

tan m = -√32/12

Hence the measure of tan m given the coordinate Q is -√32/12

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The expected value of N will be given as:- Money =  N² -  5.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

It is given in the question that:-

So from the given information, the expression will be:-

N be a random variable that corresponds to your net winnings in dollars.

Money =  N² -  5.

From the above equation, we can calculate the amount earned by the spinner number that comes.

Therefore the expected value of N will be given as:- Money =  N² -  5.

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The number of cups of blackberries Jeff has for every 1 cup of strawberries is 8/15 while making a fruit salad.

Mixed numbers are the number which are used to write the whole number and the fraction number combined. As the whole number and fraction number are expressed together, thus these numbers are called mixed numbers.

Jeff is making a fruit salad. He has 1 1/3 cups blackberries. In the fractional number,

[tex]\text{Blackberries}=1\dfrac{1}{3}\\\text{Blackberries}=\dfrac{3+1}{3}\\\text{Blackberries}=\dfrac{4}{3}[/tex]

Jeff has 2 1/2 cups of strawberries. In the fractional number,

[tex]\text{strawberries}=2\dfrac{1}{2}\\\text{strawberries}=\dfrac{4+1}{2}\\\text{strawberries}=\dfrac{5}{2}[/tex]

Thus, the number of cups of blackberries does he have for every 1 cup of strawberries,

[tex]r=\dfrac{\dfrac{4}{3}}{\dfrac{5}{2}}\\r=\dfrac{4\times2}{3\times5}\\r=\dfrac{8}{15}[/tex]

Hence, the number of cups of blackberries Jeff has for every 1 cup of strawberries is 8/15 while making a fruit salad.

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[tex]~~~~~~~\cos 45^{\circ} = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \dfrac 1{\sqrt 2} = \dfrac{\sqrt 3}{x}\\\\\\\implies x = \sqrt 3 \cdot \sqrt 2\\\\\\\implies x = \sqrt {3 \times 2}\\\\\\\implies x = \sqrt 6[/tex]

Answer:

464 units²

Explanation:

Part A

Length × Width = 8 × 16 = 128 units²

Part B

Length × Width = 24 × 8 = 192 units²

Part C

Length × Width = 12 × 4 = 48 units²

Part D

Length × Width = 24 × 4 = 96 units²

Total Area: 128 + 192 + 48 + 96 = 464 units²

Answer:

464 units²

Step-by-step explanation:

The quickest way to determine the area of the figure is to calculate the area of the total rectangle, then subtract the missing parts.

(see attached diagram)

Total area of the rectangle = width × length

                                             = 24 × (16 + 4 + 4)

                                             = 24 × 24     ← the shape is actually a square!

                                             = 576 units²

Missing Area 1

Top left square = 8 × 8

                         = 64 units²

Missing Area 2

Bottom right rectangle = 4 × 12

                                      = 48 units²

Total area = area of rectangle - missing area 1 - missing area 2

                 = 576 - 64 - 48

                 = 512 - 48

                 = 464 units²

[tex]\huge{\color{magenta}{\fbox{\textsf{\textbf{Answer}}}}}[/tex]

x = -1

Step-by-step explanation:

[tex] \sf\frac{x}{x - 2} + \frac{x - 1}{x + 1} = - 1[/tex]

Taking LCM

[tex] \sf \hookrightarrow \frac{x(x + 1) + (x - 1)(x - 2)}{(x - 2)(x + 1)} = - 1 \\ \\ \sf \hookrightarrow \frac{ {x}^{2} + x + {x}^{2} - 3x + 2 }{ {x}^{2} - x - 2} = - 1 \\ \\ \sf \hookrightarrow \frac{2 {x}^{2} - 2x + 2 }{ {x}^{2} - x - 2 } = - 1[/tex]

Cross multiplying

[tex] \sf \hookrightarrow 2 {x}^{2} - 2x + 2 = - 1( {x}^{2} - x -2) \\ \\ \sf \hookrightarrow 2 {x}^{2} - 2x + \cancel2 = - {x}^{2} + x + \cancel2 \\ \\ \sf \hookrightarrow 3 {x}^{2} - 3x = 0[/tex]

Taking 3 common

[tex] \sf \hookrightarrow {x}^{2} - x = 0 \\ \\ \sf \hookrightarrow x(x - 1) = 0 \\ \\ \sf \hookrightarrow x - 1 = 0 \\ \\ \\ \green{\boxed{ \hookrightarrow x = 1}}[/tex]

Taking x as 1

[tex] \sf \implies\frac{x}{x - 2} + \frac{x - 1}{x + 1} = - 1 \\ \\ \sf \implies \frac{1}{1 - 2} + \frac{1 - 1}{1 + 1} = - 1 \\ \\ \sf \implies - 1 + 0 = - 1 \\ \\ \sf \implies - 1 = - 1[/tex]

Answer: 15.9

Step-by-step explanation:

Answer:

1, 2, 3, 6, 13, 26, 39, 78

Step-by-step explanation:

The factors of a number are the numbers that "go into" 78 "evenly" that is, without a remainder. You can make a factor tree or divide to find the prime factors. Any combination "goes into" 78. That's why we'll include 6 and 26 on this list.

1×78

2×39

3×26

6×13

all make 78!

Answer:

≈ [tex]44.4%[/tex][tex]%[/tex]%

Step-by-step explanation:

The person will wait for no more than 20 minutes if they arrive when the bus is going to stop in 20 minutes, which means that they must arrive 25 minutes after the previous bus stops. So the probability that the person will not wait for more than 20 minutes will be [tex]\frac{20}{45}[/tex] which is about 44.4%.

Answer:

135 cubes

Step-by-step explanation:

Volume of cuboid :

Volume of a small cube :

Number of cubes :

Step-by-step explanation:

Hello all beautiful your day

Answer:

i could help but i don't see the graph chart

Step-by-step explanation:

Answer:

3/5+1/3= 9/15+5/15= 14/15

Step-by-step explanation:

Hi there!

To make fractions have a common denominator, multiply both the numerator and the denominator by a number. In this case, 3/5= 9/15, because both the numerator and denominator are multiplied by 3. 1/3= 5/15, using the same rule. 9/15+5/15=14/15

Hope this helped! If it did, pls press the heart :)

Answer:

Step-by-step explanation:

Formula

speed = distance / time

Givens

speed = ?

distance = 162 miles.

Time = 3 hours.

Solution

speed = 162 / 3

speed = 54 miles per hour.

Answer:

7.065 in^2

Step-by-step explanation:

Answer:

7.06858...in²

if we are using 3.14

7.065in²

Step-by-step explanation:

3 / 2 = 1.5

A = πr²

A = π(1.5²)

A = π(2.25)

A = 7.068in²

(if we are using 3.14 for pi)

A = πr²

A = 3.14(1.5²)

A = 3.14(2.25)

A = 7.065in²

Answer:

The store makes $21 per sweater.

This is the same as the constant of proportionality between the profit made and the number of sweaters sold.

Step-by-step explanation:

$286−$55

Total Profit=$231

Profit Per Sweater=11/$231

Profit Per Sweater=$21

If store buys 11 sweaters for $55 and sells them for $286 then the  store makes a profit of $21 per sweater.

To calculate the profit per sweater, you need to subtract the cost per sweater from the selling price per sweater.

Cost per sweater = Total cost / Number of sweaters

= $55 / 11

= $5

Selling price per sweater = Total selling price / Number of sweaters

= $286 / 11

= $26

Profit per sweater = Selling price per sweater - Cost per sweater

= $26 - $5

= $21

So, the store makes a profit of $21 per sweater.

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Answer:

The given equation is expansion of (a-b)² = a²-2ab+b²

[tex]\sqrt{81-18\sqrt{7}+7} \\ \sqrt{ {9}^{2} -2 \times 9 \times \sqrt{7}+ { \sqrt{7} }^{2} } \\ \sqrt{ {(9 - \sqrt{7})}^{2} } \\ {(9 - \sqrt{7})}[/tex]

hope that help.

Answer:

[tex]9-\sqrt{7}[/tex]

Step-by-step explanation:

Given expression:  [tex]\sqrt{81-18\sqrt{7}+7}[/tex]

To simplify the given expression, use the "A minus B Whole Square" identity.

A minus B Whole Square identity

[tex](a-b)^2=a^2-2ab+b^2[/tex]

Comparing  [tex]81-18\sqrt{7}+7[/tex]  to the right side of the identity:

Therefore:

[tex](9-\sqrt{7})^2=81-18\sqrt{7}+7[/tex]

Finally:

[tex]\sqrt{81-18\sqrt{7}+7}=\sqrt{(9-\sqrt{7})^2}=9-\sqrt{7}[/tex]

Answer:

C) (3 , 2)

Step-by-step explanation:

y is greater than 2x - 7.

Note the point values (x , y). y, in this case, must be greater than x after it is simplified.

~

(3 , -2)

Plug in 3 for x, and -2 for y:

(-2) > 2(3) - 7

-2 > 6 - 7

-2 > -1

(False).

~

(4 , 1)

Plug in 4 for x, and 1 for y:

(1) > 2(4) - 7

1 > 8 - 7

1 > 1

(False).

~

(3 , 2)

Plug in 3 for x, and 2 for y:

(2) > 2(3) - 7

(2) > 6 - 7

2 > 1

(True).

~

∴ C) (3 , 2) is your answer.

~

Step-by-step explanation:

the original retail price was 120% of the manufacturer price (100% manufacturer price + 20% markup).

now, the whole retail price is reduced by 12%.

that means we have to subtract 12% from the 120%.

but careful, we cannot just do 120-12=108.

that is simply because these 120% are now for this calculation the new basic amount and therefore 100%.

we actually need to calculate and subtract 12% of 120 to get the new percentage over the manufacturer price.

we do this by multiplying 120 by (100-12)/100 = 88/100 = 0.88 :

120 × 0.88 = 105.6%

so, the new retail price is now only 5.6% over the manufacturer price.

Answer:

0.96%

Step-by-step explanation:

We are looking for the percent that represents "6 out of 625"

Divide to find the decimal answer:

6/625 means

6 ÷ 625

= 0.0096

Then multiply by 100 to change to a percent.

0.0096 × 100

= 0.96%

Answer:

46.77 cm

Step-by-step explanation:

Perimeter of the semicircle = Circumference + 2r

Answer:

a) angle A = angle Z

angle B = angle X

angle C = angle Y

b) AB= ZX

AC=ZY

BC=XY

c) triangle CAB=YZX

hope it helps you

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The correct option is A, the difference between two cylinders with the same height and different radii.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.

Since the shape of a paper towel is like a cylinder, therefore, the composition that produces a solid with the same shape and dimensions as the roll of the paper towel is a difference between two cylinders with the same height and different radii.

Hence, the correct option is A.

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Step-by-step explanation:

180 ° - 146°=34°

Where by isosceles triangle is 180

Step-by-step explanation:

we have a right-angled triangle :

the Hypotenuse (baseline opposite of the 90° angle) is the 850 ft cable from the top of the tower down to the point on the ground 360 ft away from the tower.

then the ground distance (360 ft) and the height of the tower are the 2 legs.

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse.

in our case

850² = 360² + height²

height² = 850² - 360² = 592,900

height = 770 ft

the tower is 770 ft tall.

Answer:

770 feet

Step-by-step explanation:

Given

Solving

Answer:

3,600

Explanation:

There's nine thousand numbers here, 4,500 of which are even, you will need to subtract mutiples of five from this number, making it even smaller.

subtract the non-even five's (exactly half of the 1800 hundred fives that fit in our little original number, (900!) ) 4,500-900= 3,600. Which should be your answer. :D

Step-by-step explanation:

Answer:

[tex]\frac{3}{20}[/tex]

Step-by-step explanation:

slope/gradient=[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]

                        =[tex]\frac{-9.75+9}{-1-4}[/tex]

                        =[tex]\frac{3}{20}[/tex]

__________________________________________________________

Hello! In this question, we are trying to solve the expression with a given value.

__________________________________________________________

Explanation:

In this question, we were given our f(x) equation: f(x) = x² - 3

We were also given the value of our variable "x": -3

To solve the expression, we would plug in our "x" value, -3, into the "x" variables in our expression and solve.

Solve:

f(x) = x² - 3

f(-3) = (-3)² - 3

= 9 - 3

= 6

Therefore, the value of f(-3) is 6.

__________________________________________________________

Answer:

f(-3) = 6

__________________________________________________________

To solve this problem, you will substitute an existing value into a function in order to find the y-coordinate at that x-coordinate.

Given the function f(x) = x² - 3, evaluate the function at f(-3) by substituting in x = -3:

[tex]f(-3) = -3^2-3[/tex]

Use BPEMDAS, which stands for:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

First, evaluate -3².

[tex]-3\times-3=9[/tex]

Then, evaluate the rest of the expression by subtracting 3 from 9:

[tex]9 - 3 = \boxed{6}[/tex]

The final answer is f(-3) = 6.

Answer:

16 boys

Step-by-step explanation:

in ratio form girls are represented by 5 so if 5 equals to 20 what about 4 and that's how I got the answer good day.