Is there enough information given to prove
the quadrilateral is a parallelogram?
H
H
Yes, both sets of opposite sides are congruent
Yes, both sets of opposite sides are parallel
O No, opposite sides are different lengths
O No, not enough information given

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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Based on the graph given, that will show the same amplitude as function m is; graph D.

The cosine function is :

f(x) = Acos(kx) + M

And the functions are stands for amplitude, k is the angular frequency, M is the midline.

When the function is; m(x) = -2cos(x+π).

The absolute value of the amplitude will be;

2 x |-2| = 4

Therefore, the option that can have the requirement is Graph D.

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As an operations manager for a plant that manufactures batteries, I can use both descriptive statistics and inferential statistics to make better managerial decisions

Descriptive statistics help me to summarize and describe the data collected from the manufacturing process.

For instance, I can use measures such as mean, median, mode, range, and standard deviation to summarize the data on the production output of batteries over a specific period.

Inferential statistics allow me to draw conclusions and make predictions based on the data collected from a sample of batteries produced.

For example, I can use inferential statistics to determine the probability of the battery meeting the required specifications. I can also use inferential statistics to make predictions about future production output, based on the historical data.

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Answer:

0

Step-by-step explanation:

=1/2 × -5,6 × 0

=-8,4×0

=0

Answer:

The minimum value of the function is ƒ(3) = 5.

Step-by-step explanation:

To find the minimum value of ƒ(x), we need to find the vertex of the parabola represented by the function. We can do this by completing the square:

ƒ(x) = x² - 6x + 14

ƒ(x) = (x - 3)² - 9 + 14 (adding and subtracting the square of half the x coefficient, which is -3)

ƒ(x) = (x - 3)² + 5

The vertex of the parabola is at (3, 5), and since the coefficient of the squared term is positive, the parabola opens upward. Therefore, the minimum value of the function is ƒ(3) = 5.

When a force of 21 N acts on a certain object, the acceleration of the object is [tex]3\ m/s^2[/tex]. If the force is changed to 28 N, then the acceleration of the object will be  [tex]4\ m/s^2[/tex].

By Newton's second law,

F = ma ----------(1)

where, F = amount of force needed to accelerate the object

m = object's mass

a = acceleration

When a force of  21 N, acceleration is [tex]3\ m/s^2[/tex]

Now, we put F = 21 N & a = 3 in the equation (1),

Then it becomes,

21 = m(3)

m = [tex]\frac{21}{3}[/tex]

m = 7

Now when F = 28N, we have to find a,

Equation F = ma can be written as,

28 = 7a

a = [tex]4\ m/s^2[/tex]

Therefore the acceleration will be  [tex]4\ m/s^2[/tex], is the force changes to 28 N.

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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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The slope of the line that passes through the points (25,24) and (15,17) is 7/10.

The formula for finding the slope of a line given two points is:

slope = (change in y) / (change in x)

where "change in y" is the difference between the y-coordinates of the two points, and "change in x" is the difference between the x-coordinates of the two points.

So, if we plug in the values from our two points, we get:

slope = (24 - 17) / (25 - 15)

Simplifying the numerator and denominator, we get:

slope = 7 / 10

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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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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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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]

Answer:

G

Step-by-step explanation:

The heights of all the students can vary.

(Everyone isn't the same height.)

Pearson's coefficient of correlation would be -0.144, and the regression coefficients of X on Y are b1 = -0.188 and b₀ = 43.44.

To calculate the Pearson's coefficient of correlation, calculate the mean of x and y :

= (10 + 12 + 13 + 12 + 16 + 15) / 6 = 78 / 6 = 13

Mean of y:

= (40 + 38 + 43 + 45 + 37 + 43) / 6 = 246 / 6

= 41

Then the covariance :

= [(10 - 13) x (40 - 41) + (12 - 13) x (38 - 41) + (13 - 13) x (43 - 41) + (12 - 13) x (45 - 41) + (16 - 13) x (37 - 41) + (15 - 13) x (43 - 41)] / 6

= -1

Pearson's coefficient of correlation (r):

= -1 / ( sqrt (5. 333) x sqrt(9))

= - 0. 144

The regression coefficients of X on Y:

b₀ = 41 - ( - 0.188) x 13

= 43. 44

b₁ =  - 1 / 5.333

=  - 0. 188

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Answer: a and b

Step-by-step explanation:

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

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:

x = 4.04

Step-by-step explanation:

tan = opposite/adjacent

tan30 = x/7

x = tan30(7) = 4.04

The slope to find the cost per guest is 35.

We have,

Cost for 50 guests, g is $2150

Cost for 75 guests is $3025

So, The slope is then calculated as

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (3025 - 2150)/ (75-50)

Slope = 875/25

Slope= 35

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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:

the answer is C

Step-by-step explanation:

sum of angle in a quadrilateral is 360

so

60+128+80+X=360

X=360-60-128-80

X=92°

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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Answer:

1125m2

Step-by-step explanation:

25×45=1125m2

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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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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The expression can be rewritten by given term as;  3^15

We need to simplify the expression below:

(3^2 x 3^3)^3

Remember that we can add these exponents, so we get:

(9 x 9)^3 = 81^3

Then we can rewrite this as:

531441

Takin the product between the exponents we will get:

(3^5)^3

Thus, the solution is 3^15

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The probability of drawing either a diamond or an ace from a deck of cards is [tex]\frac{4}{13}[/tex].

We need to determine the favorable outcomes (cards that satisfy the conditions) and divide that number by the total number of possible outcomes in order to calculate the probability of drawing either a diamond or an ace from a regular 52-card deck of playing cards.

Number of aces in a deck = 4 (one for each suit: hearts, diamonds, clubs, and spades)

Number of diamonds in a deck = 13

One card, the Ace of Diamonds, is both a diamond and an ace, thus we must subtract it once from the total in order to prevent double counting.

Therefore, the favorable outcomes = 4 (number of aces) + 13 (number of diamonds) - 1 (Ace of Diamonds) = 16.

The total number of possible outcomes is 52 (the number of cards in a deck).

[tex]Probability = \frac{ Favorable \ outocomes}{Total\ number\ of\ possible\ outcomes} = \frac{16}{52} = \frac{4}{13}[/tex]

Therefore, the probability of drawing either a diamond or an ace is 4/13 or approximately 0.3077, or 30.77%.

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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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