Julian made an apple pie in a pie tin with a diameter of 6 inches. What is the pie tin's radius?

The ∆GHI is an isosceles triangle and have the base angles m∠H and m∠G equal to 74° and the angle I is equal to 32°.

An isosceles triangle have the measure of its base angles to be equal, and the sum of the interior angles sum up to 180°.

Given that sides IG ≅ HI, then the triangle ∆GHI has two sides with similar length and base angles so;

angles m∠H and m∠G are the base angles and m∠G = 74°

m∠I = 180° - (74 + 74)° {sum of interior angles of a triangle}

m∠I = 32°

Therefore, the ∆GHI is an isosceles triangle and have the base angles m∠H and m∠G equal to 74° and the angle I is equal to 32°.

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Answer:

Below

Step-by-step explanation:

y= 1/4 x + 1

The graph has a y-axis intercept of +1     (y = mx + b form)

 last one looks correct....at x = 4   the value is 2 which is correct

The equation of the plane passing through the three points (1,3,1), (2,8,8), and (11,8,2) is 7x - 17y + 10z = -34

An equation is a mathematical statement that shows the equality or balance of two expressions. It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.

We can find the equation of a plane passing through three points using the cross product of the vectors connecting two of the points.

Let's first find two vectors that lie on the plane:

v1 = (2,8,8) - (1,3,1) = (1,5,7)

v2 = (11,8,2) - (1,3,1) = (10,5,1)

Next, we can find the normal vector to the plane using the cross product of v1 and v2:

n = v1 x v2 = <7, -17, 10>

The equation of a plane is given by Ax + By + Cz = D, where A, B, and C are the coefficients of the normal vector n = <A, B, C> and D is the constant determined by the coordinates of any point on the plane.

Let's use the point (1,3,1) to find D:

D = A * 1 + B * 3 + C * 1 = 7 - 51 + 10 = -34

Therefore, the equation of the plane passing through the three points (1,3,1), (2,8,8), and (11,8,2) is:

7x - 17y + 10z = -34

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Answer:

The formula for the area of a circle is given by Pi * r^2, where r is the radius of the circle. If the area of the circle is 100 Pi, we can solve for the radius:

100 Pi = Pi * r^2

r^2 = 100

r = 10

The formula for the circumference of a circle is given by 2 * Pi * r. Substituting the value of r = 10, we get:

C = 2 * Pi * r = 2 * Pi * 10 = 20 * Pi

So, the circumference of the circle is 20 Pi.

The most likely scientific explanation for improvement after wearing this jewelry was D. Some people may feel improvement after a week because their body is healing naturally, without help from the ions.

The placebo effect is the best scientific explanation for why so many people experience better after donning a particular piece of jewelry.

The placebo effect happens when users of a product claim to be experiencing physical or mental changes as a result of using it, despite the fact that the product itself lacks the ingredients necessary to produce these effects. The jewelry is acting as a placebo in this scenario.

After a week, some people may experience improvement as their bodies begin to recover on their own, without the aid of the ions.

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The Correct statement about Standardized units is (c) Standardized units are units that have the same meaning for everyone who uses them. When using standardized​ units, people can communicate measurements and know  they mean same thing to both people.

The Standardized Units are a set of units of measurement that have been universally recognized and adopted for specific quantities.

The International System of Units (SI) is the most widely used system of standardized units, and includes units for measuring length, mass, time, electric current, temperature, and other physical quantities.

The Standardized Units play a crucial role in scientific experiments, as well as in manufacturing processes, and in providing precise information on medication dosages, food labeling, and other important areas.

Therefore , standardized units ensure uniformity and comparability of measurements across different fields and geographic locations.

What is meant by standardized units and why are they​ useful?

Choose the correct answer below.

(a) Standardized units are the units that were once standard but have since been phased out for more precise definitions of measurements. They are useful for historical​ reason, as knowledge of these older units allows people to translate the measurements of the past into the units of today.

(b) Standardized units are the units that have been determined by a monarchy. They allow educated peoples who use them to distinguish themselves from the common folk who do not.

(c) Standardized units are units that have the same meaning for everyone who uses them. When using standardized​ units, people can communicate measurements and know that they mean the same thing to both people.

(d) Standardized units are units that are about the same for each person. For example the length of a​ person's foot is a foot. These units are useful​ because, for​ example, anyone with a foot can use their own to get a measurement.

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The expected value for the card that Dan selects is 2.5, as it is the average of the probabilities of selecting each card.

The expected value for the card that Dan selects is calculated by taking the sum of the product of each card and its respective probability. The probability distribution for the deck of four cards is as follows: Card 1 has a probability of 0.25, card 2 has a probability of 0.4, card 3 has a probability of 0.2, and card 4 has a probability of 0.15. To calculate the expected value, we first multiply each card number by its respective probability and then add each product together. This gives us 0.25 x 1 = 0.25, 0.4 x 2 = 0.8, 0.2 x 3 = 0.6, and 0.15 x 4 = 0.6. Adding all of these together gives us a total of 2.5, which is the expected value for the card that Dan selects.

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Answer:

(z + 6)(z + 4)

Step-by-step explanation:

z² + 10z + 24

consider the factors of the constant term (+ 24) which sum to give the coefficient of the z- term (+ 10)

the factors are + 6 and + 4 , since

6 × 4 = + 24 and 6 + 4 = + 10 , then

z² + 10z + 24 = (z + 6)(z + 4) ← in factored form

The lattice point of the inverse is (3, 0).

To find the lattice points of the inverse of the function f(x), we need to find the points where both x and y are integers.

To find the inverse of the function, we switch the x and y values, then solve for y:

y = log2(-x + 3) - 4

x = log2(-y + 3) - 4

y = 3 - 2^(x + 4)

For x and y to be integers, both 2^x and - 2^(x + 4) must be integers.

This occurs when y is a positive integer and y <= 2, since 2^y becomes larger than 3 for y > 2.

Thus, the only lattice point of the inverse is (3, 0).

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Answer:

[tex]\huge\boxed{\sf Time = 18.5\ minutes}[/tex]

Step-by-step explanation:

Time = Distance / Speed

Using the normal speed and time, we will first find the distance to her friends house.

Here,

Speed = 50 km/h

Time = 24 minutes / 60 = 0.4 hours

So,

Distance = 50 × 0.4

Now, finding time when the speed is 65 km/h.

So,

Time = Distance / Speed

Time = 20 km / 65 km/hr

To convert it into minutes, we multiply it by 60.

So,

Time = 0.31 × 60

[tex]\rule[225]{225}{2}[/tex]

The point a shows -2.9, b shows -2 5/8 and c shows -7/3.

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction.

Given:

We have first -7/3 which can be written as -2.33

and, -2 5/8 can be written as -21/8 or -2.625

and, the third is -2.9

So, the point a shows - 2.9.

and point b shows -2.625 or -2 5/8.

an point c shows -2.33 or -7/3.

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A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex.

A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.

In three-dimensional space, a sphere is a collection of points that are all located at the same r-distance from a single point. The radius of the sphere is equal to r, and the provided point is its center.

The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface.

The right cylinder is created when the centers of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centers.

A three-sided polyhedron consisting of a triangle base, a translated copy, and three faces connecting equivalent sides is known as a triangular prism in geometry. If the sides of a right triangle are not rectangular, the prism is oblique.

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Define the following solids:

(a) cone, (b) sphere, (c) cylinder, (d) prism.

The equation to find the number of overtime hours worked on the second day is 19.5x = 87.75.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Earning of Lynette for one hour when she works overtime = $19.50

She worked overtime twice this week.

One day she worked 3 hours of overtime.

Earning on first day = 3 × $19.50 = $58.50

Total earnings for overtime = $146.25

Earnings on second day = $146.25 - $58.50 = $87.75

Let x be the number of hours worked overtime.

19.5x = 87.75

x = 4.5

Hence the required equation is 19.5x = 87.75.

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The shaded region in the graph represents the possible solution sets to the inequality.

Given is the inequality -

x² + 15 ≥ 23

The given inequality is -

x² + 15 ≥ 23

Refer to the graph attached.

The shaded region represents the possible solution sets to the inequality above.

Therefore, the shaded region in the graph represents the possible solution sets to the inequality.

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The expression 2x² + 8x - 8 represents a polynomial.

An expression represents a polynomial when these following conditions are satisfied:

The exponents for this problem are given as follows:

2, 1 and 0.

(as the constant term has an exponent of zero).

Which are both integer and non-negative, hence the expression 2x² + 8x - 8 in fact represents a polynomial.

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Answer:

Step-by-step explanation:

To find the time it takes for the car to travel 950 m, we need to find the time it takes for each segment and add them up. Let's call the travel time for the first quarter t1, and the travel time for the remaining 3 quarters t2.

a) Travel time:

For the first quarter (0 m to 237.5 m), the equation for the velocity can be found using the kinematic equation:

v = v0 + at

where v0 is the initial velocity (0 m/s), a is the acceleration (+5.40 m/s^2), and t is t1.

So,

t1 = (v - v0) / a = (0 - 0) / 5.40 = 0

For the next 3 quarters (237.5 m to 950 m), the equation for the velocity can be found using the kinematic equation:

v^2 = v0^2 + 2ad

where d is the displacement (950 m - 237.5 m = 712.5 m), and a is the acceleration (-1.80 m/s^2).

So,

t2 = sqrt((2ad + v0^2) / a) = sqrt((2 * -1.80 * 712.5 + 0^2) / -1.80) = sqrt(1286.25 / -1.80) = sqrt(709.03) = 26.6 s

Adding t1 and t2 gives the total travel time:

t = t1 + t2 = 0 + 26.6 = 26.6 s

b) Maximum speed:

To find the maximum speed, we need to find the velocity at the halfway point (475 m) by using the kinematic equation:

v = v0 + at

where v0 is the initial velocity (0 m/s), a is the acceleration (+5.40 m/s^2), and t is t1.

So,

v = 0 + 5.40 * (475 / 237.5) = 4.96 m/s

The maximum speed is 4.96 m/s.

sorry for making it so long.

In the experiment, the subject whose behavior is being assessed are observational units. The observational unit in this instance is Harley (Dog).

We will first investigate if canines can comprehend both non-human and human gestures in this investigation. The dogs were placed around 2.5 meters apart from the experimenter so that the researchers could test this. Two glasses were placed one on either side of the experimenter.

A gesture would be made at one of the cups by either the experimenter (pointing, bowing, or staring) or by a non-human object (a mechanical arm pointing, a doll pointing, or a stuffed animal looking). After then, the scientists would observe whether the dog would approach the cup that was pointed out. Six dogs were put to the test. We'll focus on one of the dogs who participated in both of his trial sets.

The four-year-old mixed breed dog was given the name Harley. Each of the ten trials in a set consisted of one gesture and one pair of cups. In order to see if Harley would approach a particular cup, the experimenter bowed toward it during one round of experiments.

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In pounds and ounces, 96 kg equals 216 lb, 1 oz.

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The value of the differential dy when y = x^4 - x^2 + 1 , x = 1 , x = 1, and dx = 0.1 is (D) dy = 0.5.

To find the value of dy, we need to first find the derivative of the function y = x^4 - x^2 + 1. The derivative is given by y' = 4x^3 - 2x. At x = 1, the value of y' is 4(1)^3 - 2(1) = 2. The differential dy is given by dy = y' * dx, where dx = 0.1. So, dy = 2 * 0.1 = 0.2.

Correct Question :

Find the value of the differential dy when y = x^4 - x^2 + 1 , x = 1, and dx = 0.1. ?A. dy = 0.2 B. dy = 0.6 C. dy = 0.12 D. dy = 0.5 E. dy = 6

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Answer:

I don't know. I hope this helps!

Step-by-step explanation:

Answer:

C , B , A

Explanation:

In any triangle, there is a direct relation between the measure of the angle and the length of the opposite side.

This means that:

- The longest side will be the one opposite to the largest angle

- The shortest side will be the one opposite to the smallest angle

In the given triangle:

- The longest side is BC, this means that the largest angle is angle A

- The shortest side is AB, this means that the smallest angle is C

- CA has an intermediate length (AB < CA < BC), this means that measure angle B will be greater than C and less than A

Based on the above, the order from the smallest angle to the largest angle will be as follows:

C < B < A

Step-by-step explanation:

Hope its Helps :]

Answer:

(f - h) (-4) = 26.

Step-by-step explanation:

First, find the value of f(-4):

f(x) = x² + 4

f(-4) = (-4)² + 4 = 16 + 4 = 20

Next, find the value of h(-4):

h(x) = x-2

h(-4) = -4 - 2 = -6

Finally, subtract h(-4) from f(-4) to find (f - h) (-4):

(f - h) (-4) = f(-4) - h(-4) = 20 - (-6) = 20 + 6 = 26

So (f - h) (-4) = 26.

The value of tanθ is either 3/2 or -3/2.

We can solve for the value of tanθ by squaring both sides of the equation 2 - cos(2θ) = 3sinθcosθ, then using the identity tan^2(θ) = sin^2(θ)/cos^2(θ).

Starting with the left-hand side:

(2 - cos(2θ))^2 = 9sin^2(θ)cos^2(θ)

Using the identity cos(2θ) = 2cos^2(θ) - 1, we can simplify:

(2 - 2cos^2(θ) + 1)^2 = 9sin^2(θ)cos^2(θ)

Expanding the square and simplifying:

9 = 8sin^2(θ)cos^2(θ)

Finally, dividing both sides by 8cos^2(θ)sin^2(θ) (which is non-zero since sinθ ≠ cosθ) and using the identity tan^2(θ) = sin^2(θ)/cos^2(θ), we get:

tan^2(θ) = 9/8

Taking the square root of both sides, we have:

tan(θ) = ±3/2

So, the value of tanθ is either 3/2 or -3/2.

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4min/hr jon can paddle in the water.

consider the velocity formula:

velocity = distance/time

The given information is:

Distance downstream = 5 miles

Distance upstream = 6 miles

Trip time = 3 hours

Time downstream = (5 / 5+6)(3) = 15/11 hours

Time upstream = (6 / 5+6)(3) = 18/11 hours

velocity downstream = 5 / 15/11 = 11/3mi/hr + 1mi/hr

velocity upstream = 6 / 18/11 = 11/3mi/hr - 1mi/hr

average velocity = 11/3 or 3.6667 or 4 mi/hr

This question can also be calculated in another way:

velocity = distance/time

time = distance/velocity

x + 1 for downstream because it is on current and x - 1 for upstream because it is against the current.

3hours = (5 / x + 1) + (6 / x - 1)

3(x + 1)(x - 1) = 5(x - 1) + 6(x + 1)

3x^2 - 3x + 3x - 3 = 5x - 5 + 6x + 6

3x^2 - 3 = 11x + 1

3x^2 - 11x - 4 = 0

using a quadratic equation, we can find the roots of the equation:

The roots are = 4, -1/3

since there is no negative velocity, x = 4 mi/h

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For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

Given that,

x              y

-5            0

-1            -8

1             -12

4            -18

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

Then,

Points are,  ( - 5,0 ) , ( -1,-8), (1,-12) , (4,-18)

Points are,  ( - 5,0 ) , ( -1,-8)

Slope m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

m = [tex]\frac{-8-0}{-1-(-5)}[/tex]

m = [tex]\frac{-8}{-1+5}[/tex]

m = [tex]\frac{-8}{4}[/tex]

m = -2

Points are,  ( -1,-8 ) , ( 1,-12),

m = [tex]\frac{-12-(-8)}{1-(-1)}[/tex]

m = [tex]\frac{-12+8}{1+1}[/tex]

m = [tex]\frac{-4}{2}[/tex]

m = -2

Points are,  ( 1,-12 ) , ( 4,-18),

m = [tex]\frac{-18-(-12)}{4-1}[/tex]

m = [tex]\frac{-18+12}{3}[/tex]

m = -6/3

m = -2

Then, m = -2

Therefore,

For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

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For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

Given that,

x              y

-5            0

-1            -8

1             -12

4            -18

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

Then,

Points are,  ( - 5,0 ) , ( -1,-8), (1,-12) , (4,-18)

Points are,  ( - 5,0 ) , ( -1,-8)

Slope

m = -2

Points are,  ( -1,-8 ) , ( 1,-12),

m = -2

Points are,  ( 1,-12 ) , ( 4,-18),

m = -6/3

m = -2

Therefore,

For all the points slope is constant. Hence they all lie on a certain line, then the m = -2.

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Answer:

[tex]5\cdot \sqrt{5}\cdot \sqrt[3]{x^4}\cdot y\cdot z^2[/tex] = [tex]5\cdot \sqrt{5}\cdot x\sqrt[3]{x}\cdot y\cdot z^2[/tex]

Step-by-step explanation:

Let's take the individual terms and convert them to radical form

[tex]5^{\frac{3}{2}} = (5^3)}^{\frac{1}{2}} = 125^{\frac{1}{2}[/tex]

A term raised to the power 1/2 is nothing but the square root of that term

[tex]125^{\frac{1}{2}} = \sqrt{125} = \sqrt{25\cdot 5} = \sqrt{25} \sqrt{5} = 5 \sqrt{5}[/tex]

[tex]x^{\frac{4}{3}} = (x^4)^{\frac{1}{3}} = \sqrt[3]{x^4}[/tex]  since any term raised to 1/3 is the cube root of that term

We can simplify this further by noting [tex]x^4 = x^3 \cdot x[/tex]'

So [tex]\sqrt[3]{x^4} = \sqrt[3]{x^3} x = x\sqrt[3]{x}[/tex]

The other exponents are integers

Putting them all together we get

[tex]5^{\frac{3}{2} }x^{\frac{4}{3}}yz^2 = 5\cdot \sqrt{5}\cdot x\sqrt[3]{x}\cdot y\cdot z^2[/tex]

The truth values of a compound statement are displayed in a truth table for all feasible combinations of the truth values of its component propositions.

A truth table is a graph that shows the truth value of one or more compound propositions for any two compound propositions that can have the same truth value. It is used to judge whether a logical argument is sound. A truth table is made up of rows and columns, each row having the truth value of the compound proposition for the specified set of truth values, and each column containing the truth value of the individual proposition. The propositions that make up the compound proposition must first be identified, and all potential combinations of truth values for each of those propositions must then be listed in order to produce a truth table. The truth value of the compound proposition can then be calculated for each combination. Applying reasoning to the provided combination will do this. The truth value of the compound proposition will then be shown in the truth table for each combination of truth values. This can assist in determining the viability of a given logical argument.

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The graph does not represent a function, as it has vertically aligned points.

A relation represents a function when each input value is mapped to a single output value.

On the function graph, a vertical line through the graph of the function would cross the graph twice for x > -4, meaning that there are inputs is mapped to two outputs, hence the relation is not a function.

This means that the correct option is given by option B.

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The sum of a quadratic trinomial with the same variable is twice the individual and the difference will be zero.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know a quadratic equation is of the form ax² + bx + c.

The sum will be,

(ax² + bx + c) + (ax² + bx + c).

= 2ax² + 2bx + 2c.

= 2(ax² + bx + c).

The difference will be,

ax² + bx + c - (ax² + bx + c).

= 0.

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The correct system of inequalities to represents this scenario are,

⇒ x² - 2y ≤ 5,000

⇒ 2x + 5y < 1000

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

The value of a company’s stock is represented by the expression x²- 2y and the company’s purchases are modeled by 2x + 5y.

Here, The company’s goal is to maintain a stock value of at least $5,000.

Hence, We get;

⇒ x² - 2y ≤ 5000

And, keeping the purchases below $1,000.

Hence, We get;

⇒ 2x + 5y < 1,000

Thus, The correct system of inequalities to represents this scenario are,

⇒ x² - 2y ≤ 5,000

⇒ 2x + 5y < 1000

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Answer:

x2 – 2y ≥ 5000

2x + 5y < 1000

Step-by-step explanation:

I got it right on the test.