180 miles in 3 hours

Answer: 15.5

Step-by-step explanation: The equation is a. Fill in the letters. 4=a. 15=b. so: Now solve. 4 squared is 16. 15 squared is 225. 225+16= 241.  15.5 is the answer. It's just the Pygotherean Method!

The percentage of $0.95 to $3.80: 25%

What is Percentage?

A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

The terms "out of 100" and "for every 100" can also be used to refer to percentages. For instance, you may say "it snowed 20% of the time" or "it snowed 20 days out of every 100 days."

A decimal can also be used to represent a percentage. For instance, 24 percent, 0.24, 24/100, or 24 hundredths could also be used to represent the percentage. By dividing the percentage by 10, you can obtain the percent in decimal form.

Given,

The material cost for one headband = $0.95

The cost of one headband sold = $3.80

Now to take the percentage of the cost of material of the headband to the selling price of the headband will be:

= (0.95/3.80) x 100

it can be also written as

= (0.95 x 100)/3.80

= 95 / 3.80

= 25%

Hence, The percentage of $0.95 to $3.80 is 25%

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Formula a = 2b + c in subject to b is b = a-c / 2

Changing the subject of formula is a way of rearranging formula to determine missing variable in terms of other variable

Changing the subject of formula is also known as rearranging formula or changing the subject of an equation.

Given ,

Formula : a = 2b + c

Subtracting by c on both sides,

=> a - c = 2b + c - c

=> a - c = 2b

Dividing by 2 on both sides,

=> [tex]\frac{a-c}{2} = b[/tex]

Formula in subject to b is

b = a-c / 2

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The measurement of Angle ∠5=52°

when two parallel lines are cut by a transversal line, then the resultant alternate interior angles are equal.

In the given figure, lines AB║CD.

And ∠3=52, ∠5=?

By using alternate interior angle property ,

Angle ∠3 and ∠5 are cut by a transversal line, so this both angle will be equal

⇒∠3=∠5=52°

Here, the value of ∠5=52°

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Answer:

62feet

Step-by-step explanation:

10x=620

x=62feet

The perimeter usually gives the length of the figure. In a square, which has al its sides equal, the perimeter of the square will be four times its sides. The maximum width of the rectangle is 62 feet.

The perimeter of a rectangle is defined as the total distance covered by its boundaries or the sides. Since the rectangle is comprised of four sides, the perimeter will be the sum of all four sides. The perimeter is a linear measure and its unit is m, cm, feet, etc.

The equation used to calculate the perimeter of a rectangle is given as:

Perimeter = 2 (l + b)

Here l = length

b = breadth

Here the length is four times the width, l = 4x

Width may be b = x

Then perimeter is:

P = 2 (4x + x) = 620

10x = 620

x = 620 / 10 = 62 feet

Thus the width is 62 feet.

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The true statement is that the counterexample must satisfy the conclusion of the conditional statement.

A counterexample is a situation in which the hypothesis and conclusion are both accurate. We employ a counter example to show that a conditional assertion is untrue.

The true statement regarding the counterexample can be written as a conditional assertion.

This is shown to be untrue by a counterexample,

Therefore, only one counter-example is enough to demonstrate the falsity of a proposition. In this case where a counterexample is used to refute a conditional statement.

The counter-example should be supported the conditional statement's hypothesis.

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Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

Answer: $ 875

Step-by-step explanation:

3,500-0.03(4)

3,499.97/4

= $875

The probability that a brand new battery lasts for atleast 2 years is 0.801

From the question, we have the following parameters that can be used in our computation:

Mean, λ = 3 years

The probability of a Poisson distribution is represented as

P(x) = λˣe⁻λ/x!

In this case,

x = At least 2

This means that

x = 2, 3....

So, we have

P(x ≥ 2) = 1 - P(0) - P(1)

This gives

P(x ≥ 2) = 1 - 3⁰ * e⁻³/0! - 3¹ * e⁻³/1!

Evaluate

P(x ≥ 2) = 1 - 0.0497 - 0.1494

Evaluate the difference

P(x ≥ 2) = 0.801

Hence, the probability is 0.801

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Answer:

d = 2 and terms are 6, 8, 10 12 and 14

Step-by-step explanation:

we know

[tex] a_{n} = a_{1} + (n-1)d [/tex]

here a(n) = nth term

a1 = 1st term

n = no. of term

d = common difference

putting the values we get,

178 = 6 + (87-1)d

⇒ 178 = 6 + 86d

⇒86d = 172

⇒ d = 2

So required common difference is 2.

Now the first term is 2

so second term is a2 = 6 + ((2-1)×2) = 8

third term = 6 + ((3-1)×2) = 10

fourth term = 6 + ((4-1)×2) = 12

fifth term = 6 + ((5-1)×2) = 14

The difference between a positive mixed number and negative mixed number is never positive is false.

Depending on how the phrases might be ordered

Hence the given statement, the difference between a positive mixed number and negative mixed number is never positive is false.

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Step-by-step explanation:

A quadratic equation is in the form of

[tex]ax {}^{2} + bx + c[/tex]

C is the y intercept a.k.a the value of c is when x=0,

when x is 0, c is -7 so

c=-7

[tex] {ax}^{2} + bx - 7 [/tex]

Next we know when x is 2, y is 1 so

[tex]a(2) {}^{2} + 2b - 7 = 1[/tex]

[tex]4a + 2b = 8[/tex]

When x is 5, y is -2

[tex]a(5) {}^{2} + b(5) - 7 = - 2[/tex]

[tex]25a + 5b = 5[/tex]

So we have a system of equations, using elimination.

[tex]5a + b = 1[/tex]

[tex] - 6a = 6[/tex]

[tex]a = - 1[/tex]

So

[tex]5( - 1) + b = 1[/tex]

[tex]b = 6[/tex]

Our quadratic is

[tex] - {x}^{2} + 6x - 7[/tex]

The interior angles of triangle add up to give 180 degrees.

The set of all points within a triangle, or all points in the convex hull of the triangle's vertices, is known as the interior of the triangle.

The three angles that make up a triangle's interior are referred to as its interior angles. The total of these three angles is always 180 degrees.

Here given two angles of triangle = 96° and 48°

We know that sum of interior angles = 180°

So x° + 96° + 48° = 180°

x + 144 = 180

x = 180 - 144

x = 36°

To find the value of y,

We know that angle over a straight line is 180°

So ,

96° + y° = 180°

y = 180 - 96

y = 84°

Therefore the value of x = 36° and y = 84° .

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The value of x is 11x+4x=180 and x = 12

The correct option is option c)

What is interior angles?

When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. These are also referred to as supplementary angles.

We are given that the value of two angle is 11x and 4x

Since both lines are parallel and a line intersects both the lines

Hence the sum of these angles is 180 degrees

Hence we get an equation

11x+4x= 180

15x =180

x=12

Hence the correct option is option c)

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Answer:  The correct answers are:

4^4 (same answer for the equation shown) = 256 (option# B) for the first one

((2^2)^4)*2^-5= 8 (option# B) for the first one

Step-by-step explanation: Confirmed correct

Answer:

First one:

[tex]2^{2} (3+1) *[2(7-5)]^{2}[/tex]

= [tex]2^2(4)* [2(2)]^2[/tex]

= [tex]2^2(4)(4)^2[/tex]

= [tex]2^2(4)(16)[/tex]

= [tex]2^2*2^2*2^4[/tex]

= [tex]4*4*4^2[/tex]

= [tex]4^4[/tex]

The answer is four

and for the second one:

[tex]2^8*\frac{1}{2^5}[/tex]

[tex]2^3 = 8[/tex]

the answer is 8

The differentiation or rate of change of the given function y = ln x² will be  2/x.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change with respect to time.

For example the speed 3meter/second.

As per the given,

y = ln x²

By log property

y = 2ln x

Take the first derivative,

dy/dx = 2/x

Hence "The differentiation or rate of change of the given function y = ln x² will be  2/x".

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The equations that are true include the following:

(8 × 7)/2 - 12 = 22 - (2 × 3)

48 ÷ 8 + 2³ = 5 + 3²

In order to determine the equations that have a true and valid solution, we would simplify and evaluate each of the equations as follows:

(8 × 7)/2 - 12 = 22 - (2 × 3)

Opening the bracket on both sides of the equation, we have:

56/2 - 12 = 22 - 6

28 - 12 = 16

16 = 16 (True).

48 ÷ 8 + 2³ = 5 + 3²

Evaluating the exponents, we have:

48 ÷ 8 + 8 = 5 + 9

6 + 8 = 14

14 = 14 (True).

150/5² = 30 - 4² - 12

Evaluating the exponents, we have:

150/25 = 30 - 16 - 12

6 = 2 (False and incorrect).

9² - 7² = 20 ÷ (7 - 2)

Opening the bracket, we have:

9² - 7² = 20 ÷ 5

Evaluating the exponents, we have:

81 - 49 = 4

32 = 4 (False and incorrect).

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Answer:

x = 1

Step-by-step explanation:

- [tex]\frac{5}{2}[/tex] x + [tex]\frac{3}{4}[/tex] x = - [tex]\frac{7}{4}[/tex]

multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

- 10x + 3x = - 7

- 7x = - 7 ( divide both sides by - 7 )

x = 1

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Given equation is:

[tex]-\frac{5}{2}x+\frac{3}{4}x=-\frac{7}{4}[/tex]

Simplifying the left side of the equation.

[tex]\frac{2(-5x)+3x}{4}=-\frac{7}{4}[/tex]

This is equivalent to:

[tex]\frac{-10x+3x}{4}=-\frac{7}{4}[/tex]

This gives:

[tex]\frac{-7x}{4}=-\frac{7}{4}[/tex]

This is equivalent to:

[tex]x=1[/tex]

The answer of the problem by the SAS similarity theorem sides is [tex]\frac{AC}{GI} = \frac{HI}{BC}[/tex].

What is the SAS similarity theorem of triangle?

According to the SAS similarity theorem, two triangles are considered similar if their included angles are congruent and their two sides are proportionate to one other.

It is also known as Side-Angle-Side similarity of two triangles.

There is a common ratio of sides in the given problem figure, which is,

                                   [tex]\frac{AC}{GI} = \frac{HI}{BC}[/tex]

Additionally, these similar sides produce equal relative angles,

                              ∠[tex]ACB =[/tex] ∠[tex]GIH[/tex]

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Using the angle sum property and the definition of congruency, the measure of angle G is determined to be 118°.

Therefore,

ΔCAT ≅ ΔDOG

m∠C = 25°

m∠O = 37°

The following formula is used to determine angle ∠G:

According to the definition of congruency, the arrangement of the letters in the congruency statement shows that angle ∠C is congruent to angle ∠D, angle ∠A is congruent to angle ∠O, and angle T is congruent to angle ∠G, indicating that we have;

m∠C = m∠D = 25°

m∠A = m∠O = 37°

m∠T = m∠G

The measure of angle ∠G and angle ∠T can therefore, be found from the angle sum property of the interior angles of a triangle.

m∠C + m∠A + m∠T= 180° (angle sum property of a triangle)

m∠D + m∠O + m∠G= 180° (angle sum property of a triangle)

m∠G = 180° - (m∠D + m∠O) (subtraction property of equality)

m∠G = 180° - (25° + 37°) = 118°

The measure of angle ∠G, m∠G is 118°

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The correct y-intercept, slope, and equation for the line include the following:

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Note: Each interval on this graph represents 1 unit.

By critically observing the graph, we can reasonably and logically deduce the following points through which the line passes through:

Points (x, y) = (0, 4)

Points (x, y) = (10, 0)

Substituting the given parameters into the formula, we have;

Slope, m = (0 - 4)/(10 - 0)

Slope, m = -4/10

Slope, m = -2/5.

At point (0, 4), a linear equation for the line can be calculated by using the slope-intercept form:

y = mx + c

Where:

Substituting the given parameters into the formula, we have;

y = mx + c

y = -2x/5 + 4

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The Y coordinate of the new point is -1.28 y.

So, the new Y coordinate is:

The rule of dilation for the quadrilateral D is:

The new coordinate plan is:

Then, calculate the Y coordinate as follows:

Therefore, the Y coordinate of the new point is -1.28 y.

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The value of 4x - 16y is -11.

4x - 16y = -11.

Given, two equations

−5x + 10y = 1 and −x − 6y = −10

Now, On subtracting both the equations, we get

−5x + 10y + x + 6y = 1 + 10

- 4x + 16y = 11

On multiplying both the sides by -1, we get

4x - 16y = -11

Hence, the value of 4x - 16y is -11

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In the national park, the probability that a single doe captured (weighed and released) at random in December is undernourished is 25.5%

Data is symmetrically distributed and skew-free in a normal distribution. When the data is shown on a graph, it has the shape of a bell, with the majority of values congregating in the center and diminishing as they move outward.

Due to their structure, normal distributions are sometimes known as bell curves or Gaussian distributions.

Assuming normal distribution we calculate the probability as follows

Definition of variables

mean adult female deer, μ = 67.0 kg

Standard deviation, σ = 7.9 kg

sample, X = 58

Z score, z is given by the formula

= (X - μ) / σ

= (58 - 67) / 7.9

= -1.139 has a p value of 0.2546

P = 25.5%

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Answer:

9i

Step-by-step explanation:

         i² = -1

      [tex]\sqrt{-81}=\sqrt{81i^2}\\[/tex]

                [tex]\sf \bf = \sqrt{9*9*i * i}\\\\ = 9i[/tex]

The probability that a single doe captured (weighed and released) at random in December is undernourished, using the normal distribution, is given by:

0.1271 = 12.71%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for the weights are given as follows:

[tex]\mu = 67, \sigma = 7.9[/tex]

The probability that a doe is undernourished is the p-value of Z when X = 58, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (58 - 67)/7.9

Z = -1.14.

Z = -1.14 has a p-value of 0.1271.

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Answer:

35%

Step-by-step explanation:

35 divided by 100 = 0.35 = 35%