Please help and show work

Answer: (√2)(2) = 2√2

Step-by-step explanation:

To simplify the expression 3√2 - √2, you can factor out the common term √2:

3√2 - √2 = (√2)(3 - 1)

Now, subtract the numbers in parentheses:

(3 - 1) = 2

(√2)(2) = 2√2

The following are the values and correct description for the expressions:

(5/6) × (3/2) = 5/4 and is greater than 5/6

(5/6) × (7/8) = 35/48 and is less than 5/6

(5/6) × (9/9) = 5/6 and is equal to 5/6

(5/6) × (1¾) = 35/24 and is greater than 5/6

The given expressions can be simplified to get a value that can be used to describe them in comparison to the fraction 5/6 as follows:

(5/6) × (3/2) = (5 × 1)/(2 × 2)

(5/6) × (3/2) = 5/4 which is greater than 5/6

(5/6) × (7/8) = (5 × 7)/(6 × 8)

(5/6) × (7/8) = 35/48 which is less than 5/6

(5/6) × (9/9) = (5 × 1)/(6 × 1)

(5/6) × (9/9) = 5/6 and is equal to 5/6

(5/6) × (1¾) = (5/6) × (7/4)

(5/6) × (1¾) = (5 × 7)/(6 × 4)

(5/6) × (1¾) = 35/24 and is greater than 5/6

Therefore, the expressions (5/6) × (3/2) is greater than 5/6, (5/6) × (7/8) is less than 5/6, (5/6) × (9/9) is equal to 5/6, and (5/6) × (1¾) is greater than 5/6

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Answer:

The answer is 24.1 unit²

Step-by-step explanation:

Volume of prisms=cross sectional area×h

cross sectional area=Volume of prisms/height

A=216.9/9

A=24.1 unit²

The scatterplot suggests the following types of data relationship: B. strong negative correlation.

In Mathematics and Statistics, a positive correlation is used to described a scenario in which two variables move in the same direction and are in tandem.

This ultimately implies that, a positive correlation exist when two variables have a linear relationship or are in direct proportion. Hence, when one variable increases, the other variable generally increases, as well.

By critically observing the scatterplot shown in the image attached above, we can reasonably infer and logically deduce that it represents a strong negative correlation because the data points increased from left to right and down to up respectively.

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Answer:

Let's start by calculating how much it costs to rent one kart for one hour:

$60 (rental fee per kart) + $15 (hourly fee per kart) = $75 per kart per hour

Since Diddy and Dixie have a total budget of $210 banana coins, they can rent:

$210 ÷ $75 per kart per hour = 2.8 karts per hour

Since they cannot rent a fractional part of a kart, they must round down to 2 karts per hour.

Therefore, with their budget, Diddy and Dixie can rent 2 karts for 1 hour, or 1 kart for 2 hours.

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The tangent identity is: tan x = sin x / cos x. It relates the tangent, sine, and cosine of an angle in a right triangle.

The Pythagorean identity is: sin² x + cos² x = 1. .

The length of the hypotenuse of a right triangle with legs of equal length is √2 times the length of either leg.

The 30-60-90 triangle theorem states that the length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the legs (a and b): c² = a² + b².

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The solution of the system of equations is (8, 2).

Given is a system of equations x-2y = 4 and x+3y = 14, we need to find the solution of the system of equations,

So, the equations are =

x-2y = 4

x = 2y + 4......(i)

x+3y = 14

x = -3y + 14..........(ii)

Equating the equations since their LHS is same,

2y + 4 = -3y + 14

5y = 10

y = 2

Put y = 2 in any equation to find the value of x,

So,

x = 2(2)+4

x = 8

Hence the solution of the system of equations is (8, 2).

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Answer:

[tex]\displaystyle{(f+g)(x)=3x^2+8x+7}[/tex]

Step-by-step explanation:

Given both functions f(x) and g(x):

[tex]\displaystyle{f(x)=5x^2+8x}\\\\\displaystyle{g(x)=-2x^2+7}[/tex]

Finding (f+g)(x), is the same as finding the sum of both functions, f(x) + g(x). Therefore:

[tex]\displaystyle{(f+g)(x) = f(x)+g(x)}\\\\\displaystyle{(f+g)(x)=(5x^2+8x)+(-2x^2+7)}\\\\\displaystyle{(f+g)(x)=5x^2+8x-2x^2+7}\\\\\displaystyle{(f+g)(x)=3x^2+8x+7}[/tex]

Answer: $400

Step-by-step explanation:

Discount = 15%

The original price/value of an item is always 100%

So selling price (%) = original price - discount = 100%-15% = 85%

We got selling price as 85%

This implies that 85% = 340

Let's find 1% first, then 100%

1% = 340÷85 = 4

100% = 4 × 100 = $400

The usual (normal/original) price is $400

Juan sold a bicycle at a discount of 15% if the selling price was $340 then the usual price of the bicycle was $400.

percentage, a relative value indicating hundredth parts of any quantity.

Let's represent the usual price of the bicycle by P.

Since Juan sold the bicycle at a discount of 15%, the selling price (S) would be 85% of the usual price (P).

We can express this relationship as an equation:

S = 0.85P

We also know that the selling price of the bicycle was $340.

Substituting S = $340 into the equation above, we get:

$340 = 0.85P

To find P, we can solve for it:

P = $340 / 0.85

P = $400

Therefore, the usual price of the bicycle was $400.

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Answer:

G

Step-by-step explanation:

The heights of all the students can vary.

(Everyone isn't the same height.)

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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Answer:

L = 9

Step-by-step explanation:

6x8=48

432÷48=9

The only valid value for t is approximately 1.53 seconds when the ball's height is 4 meters.

We are given the equation for the height of the ball h as a function of time t:

h(t) = 3 + 7t - 5t²

We want to find all values of t for which the height h is 4 meters. So, we set h(t) equal to 4 and solve for t:

4 = 3 + 7t - 5t²

Rearrange the equation to form a quadratic equation:

0 = 5t² - 7t - 1

Now, we can use the quadratic formula to solve for t:

t = (-b ± √(b² - 4ac)) / 2a

In our equation, a = 5, b = -7, and c = -1. Plugging these values into the quadratic formula, we get:

t = (7 ± √((-7)² - 4 * 5 * (-1))) / (2 * 5)

t = (7 ± √(49 + 20)) / 10

t = (7 ± √69) / 10

We have two possible solutions for t:

t = (7 + √69) / 10 ≈ 1.53 (rounded to the nearest hundredth)

t = (7 - √69) / 10 ≈ -0.13(rounded to the nearest hundredth)

Since time cannot be negative, we discard the second solution.

So, the only valid value for t is approximately 1.39 seconds when the ball's height is 4 meters.

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Answer:

quadratic

Step-by-step explanation:

linear is a straight line

exponential is a simple curved graph

Answer:

c is -3

Step-by-step explanation:

We are shifting the parabola 3 units to the right.

f(x+c) is a shift c units to the left so we need to shift -3 units

f(x-3) is a shift 3 units to the right 3 units

The number of ways to choose four cards from standard deck and arranging them in row is 270725.

Number of four card hands from a standard 52 card deck can be dealt is 13.

We know that from combination formula,

C(n, k) = n!/k!(n - k)!

The total cards in a standard deck of cards = 52

We have to choose four cards from the deck and have to arrange them in row so we cannot reuse another card.

So, the number of ways to choose four cards from standard deck and arranging them in row = C(52, 4) = 52!/4!(52 - 4)! = 52!/4!48! = (52*51*50*49)/(4*3*2*1) = 270725.

Number of four card hands from a standard 52 card deck can be dealt = 52/4 = 13.

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After considering the given options we come to the conclusion that the answer is 112 in² which is Option B.

The lateral surface area of a square pyramid is the summation of the areas of the side faces only, on the other hand

surface area = lateral area + area of the base.

The lateral area of a square pyramid = 2al (or) 2a√ [ (a 2 /4) + h² ].

Now, to get the surface area, we have to add the area of the base (which is a 2) to each of these formulas.

For the given case, we are given a square pyramid. Hence, all four sides are equivalent in length. We can apply Pythagoras theorem to evaluate the slant height (h) of the pyramid.

The slant height is given by h = √(a² + l²),

Here

a = length of one side

l = height of the pyramid.

Applying this information, we can evaluate the lateral surface area of the square pyramid

Lateral surface area = 2a * √((a²)/4 + l²)

                    = 2 * 8 * √((8²)/4 + 10²)

                    = 112 in²

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The complete question is

The net below shows a square pyramid. What is the lateral surface area?

A. 176 in^2

B. 112 in^2

C. 64 in^2

D. 210 in^2

The value of probability that a point chosen randomly inside the rectangle is in each given shape are,

a) P = 16.67%

b) P = 10.42%

We have to given that;

A rectangle is shown in image in which triangle and square are shown.

Now, The area of triangle is,

A = 1/2 x 5 x 4

A = 10 unit²

And, Area of Square is,

A = 4 x 4

A = 16 unit²

Area of rectangle is,

A = 12 x 8

A = 96 units²

Hence, The value of probability that a point chosen randomly inside the rectangle is in square is,

⇒ P = area of square / area of rectangle

⇒ P = 16 / 96

⇒ P = 1/6 × 100%

⇒ P = 16.67%

And, The value of probability that a point chosen randomly inside the rectangle is in square is,

⇒ P = area of triangle / area of rectangle

⇒ P = 10 / 96

⇒ P = 10/96 × 100%

⇒ P = 10.42%

Thus, The value of probability that a point chosen randomly inside the rectangle is in each given shape are,

a) P = 16.67%

b) P = 10.42%

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Answer:

24

Step-by-step explanation:

Compare the known similar sides - - -

10 is to 30, and 14 is to 42. Triangle B is 3x Triangle A.

So the unknown side in Triangle B is 3x 8cm, so 24cm.

The bond's APR is 4.25%.

The formula for face value of the bond is given as following

F=P(1+rt) where F=face value, P= Purchase value, r=Annual rate & t=time of bond.

The given values are P=$5700, t=4 years & F=$6669

Substituting the above values we get

6669=5700(1+r*4)

0.17=4r

r=4.25%.

Hence, the APR for the given bond is 4.25%.

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The  total surface area of this triangular prism is 976 square cm.

Here, we have,

Total surface area of a figure

The total surface area is the sum of the area of the faces of a figure.

The given shape is made up of three rectangles and 2 triangles.

Surface area = 2[25*10] + (14 * 10) + (24 * 14)

Surface area = 2(250) + 140 + 336

Surface area = 976 square cm

Hence the total surface area of this triangular prism is 976 square cm

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Answer:

Assuming you only have an investment income of $127.5 and a credit card interest payment of $305, your total gain/loss for the year would be -$177.5 ($127.5 - $305 = -$177.5). This means you have a net loss of $177.5 for the year.

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Answer:

[tex]\huge\boxed{\sf Opposite = 125.86 \ ft}[/tex]

Step-by-step explanation:

This question will be solved using trigonometric ratios.

Angle = θ = 40°

Adjacent = 150 ft

Opposite = ?

Using trigonometric ratio, tan θ.

[tex]\displaystyle tan \theta = \frac{opposite}{adjacent} \\\\Put \ the \ given.\\\\tan \ 40 = \frac{opposite}{150} \\\\0.839 = \frac{opposite}{150} \\\\Multiply \ both \ sides\ by \ 150\\\\0.839 \times 150 = opposite\\\\125.86 \ ft = Opposite\\\\Opposite = 125.86 \ ft\\\\\rule[225]{225}{2}[/tex]

Since 0.033 < 0.05, the owner should reject the null hypothesis. There is strong proof that the actual percentage of consumers who order an espresso and bring their own cups is far lower than the actual percentage of customers who order coffee and bring their own cups.

Scientists begin their investigation with the presumption that there is some form of relationship between the factors.

The alternative, often known as the null hypothesis, contends that such a connection doesn't exist.

The null hypothesis, although appearing dull, is an essential part of the research.

The following are the proper assumptions to test the owner's assertion:

H0: pExpress  - pCoffee = 0

Ha: pExpress - pCoffee < 0

Since p-value = 0.0330 < 0.05, we reject the null hypothesis.

Thus, the correct option for this hypothesis test is:

Since 0.033 < 0.05, the owner should reject the null hypothesis. There is strong proof that the actual percentage of consumers who order an espresso and bring their own cups is far lower than the actual percentage of customers who order coffee and bring their own cups.

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Answer:

1125m2

Step-by-step explanation:

25×45=1125m2

Answer:

0

Step-by-step explanation:

=1/2 × -5,6 × 0

=-8,4×0

=0

Answer:

X = 20.25°

Step-by-step explanation:

Interior angle of the same side are suplementery which means their sum is equal to 180° .

So 38° +( 8x - 26°) = 180°

12° + 8x = 180° .... Simplify 38 and 26

8x = 180°- 12° .... taking 12 to the left side it

change the sighn to -ve

8x = 162° .... simplify

8x/8 = 162°/8 .... dividing both side 8

x = 20.25°

Answer: a and b

Step-by-step explanation:

Shift 4 units right, reflect over the y-axis, shift 2 units down is the transformation applied.

The parent function f(x) = 2x is transformed to g(x) = (2x-2)⁻²

To determine the transformations applied to f(x), we can work from the inside out, starting with the expression 2x-2:

Shift 2 units to the right: This can be achieved by replacing x with (x-2).

This gives us the expression 2(x-2) = 2x-4.

Reflect over the y-axis: This can be achieved by replacing x with (-x).

This gives us the expression 2(-x)-4 = -2x-4.

Square and take the reciprocal: This can be achieved by applying the transformation f(x) -> 1/f(x)².

This gives us the expression (-1/2x-4)².

Therefore, the transformations applied to f(x) are shift 2 units to the right, reflect over the y-axis, and square and take the reciprocal.

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