Definition of equilateral triangle

Answer: The slope is 3/2

Step-by-step explanation:

To find the slope, you need to find the difference between the y coordinates and  divide it by the difference in the x coordinates.

The y coordinates are  -4 and 5

The x coordinates are  -4 and 2

-4 -5 = - 9

-4 - 2 = -6

-9/-6 =  3/2

The required values of the given scale images are as follows:

a. x = 17.5, b. x = 16.67, and x = 5.

a. As we know that scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

As per the given figure a, we can be written as:

35/x = 18/9

35 × 9 = 18x

x = (35 × 9)/18

x = 17.5

b. As per the given figure b, we can be written as:

x/10 = 15/9

x = (15 × 10)/9

x = 150/9

x = 16.67

c. As per the given figure c, we can be written as:

x/2 = 15/6

x = (15 × 2)/6

x = 5

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Answer:

\( - 12 \geqslant - 13 \\ \geqslant - 13 + 12 \\ \geqslant - 1 \)

The required solution to the given inequality q - 12 ≥ -13 would be q ≥ -1. The correct answer would be an option (B).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The inequality is given in the question, as follows:

q - 12 ≥ -13

We have to determine the solution to the given inequality

As per the question, we have

⇒ q - 12 ≥ -13

Add 12 on both sides of the above inequality

⇒ q - 12 + 12 ≥ -13 + 12

⇒ q ≥ -1

Therefore, the required solution to the given inequality would be q ≥ -1.

Hence, the correct answer would be an option (B).

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The reason why it is not appropriate to calculate a two-sample z-interval for a difference in proportions is option (B) The normality of the sampling distribution of the difference in sample proportions cannot be established.

When using a two-sample z-interval for a difference in proportions, it is assumed that the sampling distribution of the difference in sample proportions is approximately normal. However, this assumption relies on two conditions

The samples are independent random samples, and both sample sizes are large enough to ensure that the sampling distribution of the difference in sample proportions is approximately normal.

In this case, the first condition is not met because the microchips were not randomly assigned to a machine. Therefore, the assumption of independence is violated.

As a result, it is not appropriate to calculate a two-sample z-interval for a difference in proportions. Instead, a confidence interval based on the difference in sample proportions using a method like the Wald interval or the Agresti-Coull interval can be used, which does not rely on the normality assumption.

Therefore, the correct option is (B) The normality of the sampling distribution of the difference in sample proportions cannot be established.

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Answer:

t = 16

Step-by-step explanation:

Hope this helped :]

Now,

10/5t - 75 = 12/6

10*6 = 12 (5t - 75)

60 = 60t - 900

60 + 900 = 60t

960 = 60t

t = 960/60

t = 16

I hope it's help you...

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Answer:

j ≤ 25

Step-by-step explanation:

Given that :

Total Planned amount on shopping should not be more Than $100

Items purchased : a pair of Jean and 3 shirts

Cost of t-shirt = $25 each

Cost of pair of Jean = j

Amount spent on pair of jeans=?

Total amount spent on shirt = $25 * 3 = $75

Amount left : $100 - $75 = ≤ 25

Hence amount spent on pair of jeans :

j ≤ 25

Answer:

x = 0.71; y = 2.43

Step-by-step explanation:

y = 2x + 1

y = 9x - 4

9x - 4 = 2x + 1

7x = 5

x = 5/7

y = 2x + 1

y = 2(5/7) + 7/7

y = 10/7 + 7/7

y = 17/7

x = 0.71; y = 2.43

The probability of the three independent events all occurring in three consecutive dice rolls is 1/216.

Assuming a fair six-sided die, the probability of any single roll resulting in a specific number is $1/6$. Since the events are independent, the probability of all three events occurring in three consecutive rolls is the product of the probabilities of each individual event.

Therefore, the probability of getting a specific number on three consecutive rolls is:

$P = (1/6) * (1/6) * (1/6) = 1/216$

So the probability of the three independent events all occurring in three consecutive dice rolls is 1/216.

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Given:

given

Find;

we have to find the values of g(x) at given points of x

The value of expression is,

⇒ x ÷ 12

We have to given that;

The algebraic expression is,

⇒ x divided by 12

Hence, We can formulate;

The value of correct expression is,

⇒ x ÷ 12

⇒ x / 12

Thus, The value of expression is,

⇒ x ÷ 12

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Answer:

A) 49.5

Step-by-step explanation:

11*9=99

99/2= 49.5

Answer:

(c)- 4/13

Step-by-step explanation:

There are 4 types of cards in a ordinary deck clovers, diamands, hearts, and spades

each set has 1 seven each, so 4 sevens total.

Also, each type of card has 13 different cards in it

so, your answer is 4/13

Answer:

The bill before tax and tip was $11.60. Then, a sales tax of 7.5% was added, which is $0.87. So, the total cost of the meal before tip was $11.60 + $0.87 = $12.47. Rajani tipped 12% on the amount after the added sales tax, 12% of $0.87 = $0.10. Therefore, the total cost of the meal, including tax, tip, and the original bill, was $12.47 + $0.10 = $12.57.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Thenks you.

Answer:

8

Step-by-step explanation:

The number of months that having average high temperature above freezing (32 F) is approximately for 3 months.

A function is defined as a relation between a set of inputs having one output each. It is a set of permissible outputs with the property that each input is related to exactly one output.

For the given situation,

The function is \(t=21.55 cos(\frac{\pi }{6}(m-7) )+43.75\)

The temperature for months are calculated using the function t.

Here m = 1 refers January,

m = 2 refers February and so on.

Now substitute m = 1 for January,

⇒ \(t=21.55 cos(\frac{\pi }{6}(1-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(-6) )+43.75\)

⇒ \(t=22.2\)

For February m = 2,

⇒ \(t=21.55 cos(\frac{\pi }{6}(2-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(-5) )+43.75\)

⇒ \(t=25.08\)

For march m = 3,

⇒ \(t=21.55 cos(\frac{\pi }{6}(3-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(-4) )+43.75\)

⇒ \(t=32.9\)

For April m = 4,

⇒ \(t=21.55 cos(\frac{\pi }{6}(4-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(-3) )+43.75\)

⇒ \(t=43.75\)

For May m = 5,

⇒ \(t=21.55 cos(\frac{\pi }{6}(5-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(-2) )+43.75\)

⇒ \(t=54.525\)

For June m = 6,

⇒ \(t=21.55 cos(\frac{\pi }{6}(6-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(-1) )+43.75\)

⇒ \(t=62.41\)

For July m = 7,

⇒ \(t=21.55 cos(\frac{\pi }{6}(7-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(0) )+43.75\)

⇒ \(t=65.3\)

For August m = 8,

⇒ \(t=21.55 cos(\frac{\pi }{6}(8-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(1) )+43.75\)

⇒ \(t=62.41\)

For September m = 9,

⇒ \(t=21.55 cos(\frac{\pi }{6}(9-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(2) )+43.75\)

⇒ \(t=54.525\)

For October m = 10,

⇒ \(t=21.55 cos(\frac{\pi }{6}(10-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(3) )+43.75\)

⇒ \(t=43.75\)

For November m = 11,

⇒ \(t=21.55 cos(\frac{\pi }{6}(11-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(4) )+43.75\)

⇒ \(t=32.975\)

For December m = 12,

⇒ \(t=21.55 cos(\frac{\pi }{6}(12-7) )+43.75\)

⇒ \(t=21.55 cos(\frac{\pi }{6}(5) )+43.75\)

⇒ \(t=25.087\)

Thus from the above temperatures of each month, the temperature for three months are less than 32°F.

Hence we can conclude that the number of months that having average high temperature above freezing (32 F) is approximately for 3 months.

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The correct answer is d  is used to test the effect of the IV on the variability of the DV.

The correct answer is d. The "stand alone F test" is used to test the effect of the independent variable (IV) on the variability of the dependent variable (DV). It is an inferential test commonly used in analysis of variance (ANOVA) to determine if there is a significant difference among the means of three or more groups.

Option a is incorrect because the "stand alone F test" is an inferential test that involves making a conclusion about a population based on sample data.

Option b is incorrect because the "stand alone F test" is used to test the assumption of equal variances, not homogeneity of variance.

Option c is incorrect because the "stand alone F test" can be directional or non-directional, depending on the research question and hypothesis being tested.

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Answer:

1. x=9

2. x=2

3. x=6

Step-by-step explanation:

I only know 1-3 sorry, but hope this helps

Answer:

After 6 minutes, the oven temperature will be: \(125^o\)

Step-by-step explanation:

If the increase in temperature is \(10^o\) per minute, then in 6 minutes, the increase in temperature would be \(6\,*\,10^o=60^o\), therefore, since the initial temperature of the oven was \(65^o\), its temperature after 6 minutes would be:

\(65^o+60^o=125^o\)

Answer:

B. p C. p = 9.

Step-by-step explanation:

Hope this helps!

The standard format for electronic document submission in U.S. federal courts is PDF (Portable Document Format).

PDF, or Portable Document Format, is a widely used file format that allows for the electronic representation of documents. It is designed to be platform-independent, meaning it can be viewed and accessed on different devices and operating systems while retaining its original formatting. In the context of U.S. federal courts, PDF has become the standard format for attorneys to submit documents electronically.

The adoption of PDF as the standard format for electronic document submission in U.S. federal courts brings several advantages. PDF files are generally compact in size, making them easier to transmit and store. They also preserve the interest, fonts, and graphics of the original document, ensuring that the submitted materials are accurately represented.

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(a) The number of ways the books can be arranged in any order is 362880,

(b) The number of ways the mathematics books must be together and the novels must be together is 4320.

Part(a) :

The number of mathematics-book is = 3,

The number of novels is = 5,

The number of biology books is = 1,

So, there are total of (5+3+1) = 9 books

These 9 books can be arranged in 9! = 362880 ways.

Part(b) :

If the mathematics book are together we can consider the mathematics books as 1 book and

if the novels are together then these 5 novels can be considered as one.

So, there are total 3 books which can be arranged in 3! Ways.

And these 5 novels can be arranged in themselves in 5! Ways and

these 3 mathematics books can be arranged in themselves in 3! ways.

So, total number of ways = 3!×3!×5! =6×6×120 = 4320 ways.

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Answer:

  14 square units

Step-by-step explanation:

You want the area of the triangle whose vertices are the points A(-11, 4), B(-7, 8), C(-4, 4).

The area of a triangle is given by the formula ...

  A = 1/2bh

where b is the base of the triangle, and h is the height, the1 perpendicular distance to the opposite vertex.

The diagram shows one side is the horizontal line AC. The length of that is the difference of the x-coordinates of the end points:

  b = -4 -(-11) = 7

The opposite vertex, B, has a y-coordinate of 8, so the height of the triangle is ...

  h = 8 -4 = 4

We now have the information we need to use the area formula:

  A = 1/2(7)(4) = 14 . . . . square units

The area of ∆ABC is 14 square units.

__

Additional comment

You can use the diagram and count grid squares to find the dimensions of the triangle.

The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as a slack. Specifically, it represents the amount by which the left-hand side of the constraint can increase while still satisfying the constraint.

In other words, the slack is the surplus of available resources or capacity beyond what is required to satisfy the constraint.

On the other hand, the difference between the optimal objective function value and the right-hand side of a greater-than-or-equal-to constraint in a linear programming problem is referred to as a shadow price. The shadow price represents the increase in the optimal objective function value for each unit increase in the right-hand side of the constraint, while all other parameters are held constant.

Therefore, the shadow price provides valuable information about the economic value of additional resources or capacity that could be allocated to the corresponding activity or resource constraint.

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Answer:

m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.

Step-by-step explanation:

Given,

Total cost of maths book and novel = $54

Let,

Cost of maths book = m

Cost of novel = n

According to given statement;

m+n=54      Eqn 1

the price of the math textbook, m, is $8 more than 3 times the price of the novel

m = 3n+8     Eqn 2

m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.

Step-by-step explanation:

The polynomial function is h(x)=\(\sqrt[3]{64x^{3}+27x^{6} }\). The degree of the polynomial is 6 and the leading coefficient is 27.

Given that,

The polynomial function is h(x)=\(\sqrt[3]{64x^{3}+27x^{6} }\)

We have to analyze the function to see if it is a polynomial function. State the degree and leading coefficient if the function is a polynomial.

The sum of one or more terms, each of which is either a number or a number multiplied by the independent variable and raised to a positive integer exponent, is known as a polynomial function.

The exponent of the variable, or zero if there is no variable, determines a term's degree.

The biggest term degree is the Degree of the Function.

The Distributive Property is used to join terms having the same Degree.

Usually, terms are presented in order of decreasing Degree.

An nth degree polynomial function of x is often stated as follows:

F(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² +... + a₁x + a₀

So,

h(x)=\(\sqrt[3]{64x^{3}+27x^{6} }\\\)

Therefore, the degree of the polynomial is 6 and the leading coefficient is 27.

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Answer:

I belive the answer is b

Step-by-step explanation:

hope this helps !!!

The value of the ratio a:b is 2:1

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b\(\sqrt{3}\) = \(\frac{1}{2 - \sqrt{3} }\)

Rationalizing the right hand side by the conjugate surd which is 2 + \(\sqrt{3}\)

\(\frac{1}{2 - \sqrt{3} }\)  x \(\frac{2 + \sqrt{3} }{2 +\sqrt{3} }\) = \(\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}\) = \(\frac{2 + \sqrt{3} }{1}\) = 2 + \(\sqrt{3}\)

Equating,

a + b\(\sqrt{3}\) = 2 + \(\sqrt{3}\)

Comparing the variables,

a = 2,   b\(\sqrt{3}\) = \(\sqrt{3}\), b = 1

The ratio, a: b = 2:1

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