The square root of 80 is between which two integers?

Answer:

48

Step-by-step explanation:

Answer: x=108

Step-by-step explanation:

First set up an equation by adding the two angles together : x+2/3x

Then you want to set this equal to 180° because a straight line measures 180°: x+2/3x=180

Simplify: 5/3x=180

Multiply but 3/5 on each side: x=108

x=108

Answer:

y=x-2

Step-by-step explanation:

if x: 5, x-2=3

y=x-2

therefore:

y=3

x=5

The graph of the linear equation, 5x - 9y = -7, is in the attachment below.

The linear equation that models a graph can be written in  slope-intercept equation as y = mx + b. The value of the slope, which is the rise over the run of the line is represented as m, while the value of b, which is where the line intercepts the y-axis is b.

Given the linear equation, 5x - 9y = -7, rewrite in slope-intercept form:

5x - 9y = -7

-9y = -5x - 7

-9y/-9 = -5x/-9 - 7/-9

y = 5/9x + 7/9

This means the rise over the run of the line, m is 5/9, while the y-intercept of the graph, b is 7/9.

The graph is shown below.

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\(∫∫∫_R f(x, y, z) dV = ∫∫∫_R f(au, bv, cw) |J| dudvdw\) Where |J| is the absolute value of the Jacobian determinant, which can be calculated using the substitutions made.

To evaluate the given integral with the substitution x = au, y = bv, and z = cw, we need to determine the limits of integration and express the differential element in terms of u, v, and w.

Let's assume the given region R is defined by the bounds\(a ≤ x ≤ b, c ≤ y ≤ d, and e ≤ z ≤ f.\)

First, we substitute the given values into the expression for x, y, and z:

x = au
y = bv
z = cw

Now, we express the differential element dV in terms of u, v, and w:
\(dV = dxdydz\)

Using the substitutions, we have:

\(dV = (dau)(dbv)(dcw)\)

Next, we determine the new limits of integration:

For x:
When x = a, u = 1.
When x = b, u = 1.

For y:
When y = c, v = 1.
When y = d, v = 1.

For z:
When z = e, w = 1.
When z = f, w = 1.

Now, we can rewrite the integral in terms of u, v, and w:

\(∫∫∫_R f(x, y, z) dV = ∫∫∫_R f(au, bv, cw) |J| dudvdw\)

Where |J| is the absolute value of the Jacobian determinant, which can be calculated using the substitutions made.

Please provide the expression for the function f(x, y, z) and the specific region R enclosed by the given bounds, so we can continue evaluating the integral.

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Hence, the number 5.80405471744 when rounded to nearest thousandth is equal to 5.804.

We have the following number - 5.80405471744

We have to round it off to the nearest thousandth.

The rules are as follows -

According to question, we have -

Number = 5.80405471744

We have to round it off to nearest thousand, which means we have to keep three digits after decimal. Therefore -

Rounded Number = 5.804 (Using the rule 2)

Hence, the number 5.80405471744 when rounded to nearest thousandth is equal to 5.804.

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Answer:

x+63°+36°=180°(angle sum property in first triangle)

x+99°=180°

x=180°-99°

x=81°

x + z=180

81°+z=180°

z=180°-81°

z=99°

z+13°+y=180(angle sum property in second triangle)

99°+13°+y=180

112°+y=180°

y=180°-112°

y=68°

therefore, x=81°  z=99°  y=68°

hope it helps you

Answer:

are you stupif? no dumas

Step-by-step explanation:

9514 1404 393

Answer:

  Paul is using 1 grid = 100%; Rebecca is using 2 grids = 100%

Step-by-step explanation:

We assume that a full grid and half of another are shaded.

If 1 grid is taken to be 100%, then the total amount shaded is 100% +50% = 150%, as Paul says.

__

If the two full grids are taken to be 100%, then the full shaded grid is 50% of the total, and the additional half-shaded grid is 25% of the total. That makes a total of 50% +25% = 75% of the total being shaded, as Rebecca says.

Given:

There is a ratio given as 16:9 of width to height and diagonal is 27 iniches

Required:

We need to find the value of height

Explanation:

By ratio

where w is width and h is height

by using pythagorean theorem

to find h

Final answer:

height is 13.24 inches

The total number of common tangents that can be drawn to the circles is 2.

A tangent serves as  line that touches the circle at a single point  whereby the  point where tangent meets the circle is the tangency.

A tangent to a circle can be described as the straight line  that touches the circle at only one point.

Therefore, from the definition, The total number of common tangents that can be drawn to the circles is 2.

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The coefficient of variation for SAT scores at this school is 11.21%. This means that the standard deviation of the SAT scores is about 11.21% of the mean score.

The coefficient of variation (CV) is a measure of relative variability, defined as the ratio of the standard deviation to the mean of a dataset. It is expressed as a percentage and provides a way to compare the variability of datasets with different means.

To calculate the CV for SAT scores at this particular college, we first need to calculate the standard deviation of the dataset. We are given that the average SAT score for incoming freshmen is 535 with a standard deviation of 60. Therefore, the standard deviation (s) is 60.

Next, we need to calculate the mean of the dataset. We are given that the mean (μ) is 535.

The coefficient of variation is then given by:

CV = (s / μ) x 100%

Substituting the values, we get:CV = (60 / 535) x 100%

= 0.1121 x 100%

= 11.21%

Therefore, the coefficient of variation for SAT scores at this school is 11.21%. This means that the standard deviation of the SAT scores is about 11.21% of the mean score. This information can be useful in comparing the variability of SAT scores between different colleges, even if their mean scores are different.

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The coefficient of variation for SAT scores at this school is approximately 11.21%.

The coefficient of variation for SAT scores at this school can be calculated using the following formula:

Coefficient of Variation = (Standard Deviation / Mean) x 100

Given the average math SAT score for incoming freshmen at this particular college is 535 and the standard deviation is

60, we can plug these values into the formula:

Coefficient of Variation = (60 / 535) x 100

Now, let's perform the calculations:

Coefficient of Variation ≈ 11.21 %

So, the coefficient of variation for SAT scores at this school is approximately 11.21%.

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a) a = 2.72 makes the statement P(x ≤ a) = 0.24 true.

b)a = 3.77 makes the statement P(x > a) = 0.41 true.

c) a = 3.37 makes the statement P(2.29 ≤ x ≤ a) = 0.36 true.

Part A:

For a uniform probability distribution with range [2,5], the probability density function is:

f(x) = 1/(5-2) = 1/3 for 2 <= x <= 5

a) To find the value of a such that P(x ≤ a) = 0.24, we need to solve the following equation:

∫[2,a] f(x) dx = 0.24

Simplifying the equation, we get:

(a-2)/(5-2) = 0.24

a-2 = 0.72

a = 2.72

Therefore, a = 2.72 makes the statement P(x ≤ a) = 0.24 true.

b) To find the value of a such that P(x > a) = 0.41, we need to solve the following equation:

∫[a,5] f(x) dx = 0.41

Simplifying the equation, we get:

(5-a)/(5-2) = 0.41

5-a = 1.23

a = 3.77

Therefore, a = 3.77 makes the statement P(x > a) = 0.41 true.

c) To find the value of a such that P(2.29 ≤ x ≤ a) = 0.36, we need to solve the following equation:

∫[2.29,a] f(x) dx = 0.36

Simplifying the equation, we get:

(a-2.29)/(5-2) = 0.36

a-2.29 = 1.08

a = 3.37

Therefore, a = 3.37 makes the statement P(2.29 ≤ x ≤ a) = 0.36 true.

Part B:

Let D be the event that a family owns a dog, and let C be the event that a family owns a cat.

Given information:

P(D) = 0.35

P(C | D) = 0.20

P(C) = 0.32

We need to find:

P(D)

P(D | C)

Using Bayes' theorem, we can write:

P(D | C) = P(C | D) * P(D) / P(C)

Substituting the given values, we get:

P(D | C) = (0.20 * 0.35) / 0.32 = 0.21875

Therefore, the conditional probability that a randomly selected family owns a dog given that it owns a cat is 0.21875.

To find P(D), we can use the following formula:

P(D) = P(D | C) * P(C) + P(D | C') * P(C')

where C' represents the complement of C, i.e., the event that a family does not own a cat.

Since the probability of owning a cat or not owning a cat covers all possibilities, we have:

P(D) = P(D | C) * P(C) + P(D | C') * (1 - P(C))

Substituting the given values, we get:

P(D) = (0.20 * 0.35) + P(D | C') * (1 - 0.32)

We do not have enough information to directly calculate P(D | C'), so we need to use the fact that the probabilities must add up to 1. Thus:

P(D | C') = 1 - P(C' | D)

Using Bayes' theorem, we can write:

P(C' | D) = P(D | C') * P(C') / P

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Answer:

The shortest altitude is 6.72 cm

Step-by-step explanation:

Given that the side lengths are

24 cm, 25 cm, 7 cm

The area of a triangle =

\(A = \sqrt{s \cdot (s-a)\cdot (s-b)\cdot (s-c)}\)

Where;

s = Half the perimeter = (24 + 25 +  7)/2 = 28

A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²

We note that 84/7 = 12

Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7

To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude

Altitude  = A/(1/2 ×base)

Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;

We set the base to 25 cm to get;

Area of the triangle A =  1/2 × base × Altitude

84 = 1/2 × 25 × Altitude

Altitude = 84/(1/2 × 25) = 6.72 cm

The shortest altitude = 6.72 cm.

Answers:

deposition of eroded materials

Step-by-step explanation:

Answer:

(a).   y'(1)=0  and    y'(2) = 3

(b).  \($y'(t)=kb2t\cos(bt^2)$\)

(c).  \($ b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$\)

Step-by-step explanation:

(a). Let the curve is,

\($y(t)=k \sin (bt^2)$\)

So the stationary point or the critical point of the differential function of a single real variable , f(x) is the value \(x_{0}\)  which lies in the domain of f where the derivative is 0.

Therefore,  y'(1)=0

Also given that the derivative of the function y(t) is 3 at t = 2.

Therefore, y'(2) = 3.

(b).

Given function,    \($y(t)=k \sin (bt^2)$\)

Differentiating the above equation with respect to x, we get

\(y'(t)=\frac{d}{dt}[k \sin (bt^2)]\\ y'(t)=k\frac{d}{dt}[\sin (bt^2)]\)

Applying chain rule,

\(y'(t)=k \cos (bt^2)(\frac{d}{dt}[bt^2])\\ y'(t)=k\cos(bt^2)(b2t)\\ y'(t)= kb2t\cos(bt^2)\)  

(c).

Finding the exact values of k and b.

As per the above parts in (a) and (b), the initial conditions are

y'(1) = 0 and y'(2) = 3

And the equations were

\($y(t)=k \sin (bt^2)$\)

\($y'(t)=kb2t\cos (bt^2)$\)

Now putting the initial conditions in the equation y'(1)=0

\($kb2(1)\cos(b(1)^2)=0$\)

2kbcos(b) = 0

cos b = 0   (Since, k and b cannot be zero)

\($b=\frac{\pi}{2}$\)

And

y'(2) = 3

\($\therefore kb2(2)\cos [b(2)^2]=3$\)

\($4kb\cos (4b)=3$\)

\($4k(\frac{\pi}{2})\cos(\frac{4 \pi}{2})=3$\)

\($2k\pi\cos 2 \pi=3$\)

\(2k\pi(1) = 3$\)  

\($k=\frac{3}{2\pi}$\)

\($\therefore b = \frac{\pi}{2} \text{ and}\ k = \frac{3}{2\pi}$\)

The y'(1) =0, y'(2) = 3, and the  \(\rm y'(t) = kb2t \ cos(bt^2)\)  and value of b and k are \(\pi/2\)  and  \(3/2\pi\) respectively.

It is given that the curve  \(\rm y(t) = ksin(bt^2)\)

It is required to find the critical point, first derivative, and smallest value of b.

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a curve:

\(\rm y(t) = ksin(bt^2)\)

Given that the first critical point of y(t) for positive t occurs at t = 1

First, we have to find the first derivative of the function or curve:

\(\rm y'(t) = \frac{d}{dt} (ksin(bt^2))\)

\(\rm y'(t) = k\times2bt\times cos(bt^2)\)   [ using chain rule]

\(\rm y'(t) = kb2t \ cos(bt^2)\)

y(0) = 0

y'(0) = 0

The critical point is the point where the derivative of the function becomes 0 at that point in the domain of a function.

From the critical point y'(1) = 0 ⇒  \(\rm kb2 \ cos(b) =0\)

k and b can not be zero

\(\rm cos(b) = 0\)

b = \(\rm \frac{\pi}{2}\)

and y'(2) =3

\(\rm y'(2) = kb2\times 2 \times cos(b\times2^2) =3\\\\\rm 4kb \ cos(4b) =3\)(b =\(\rm \frac{\pi}{2}\))

\(\rm 4k\frac{\pi}{2} \ cos(4\frac{\pi}{2} ) =3\\\\\rm2 \pi kcos(2\pi) = 3\)

\(\rm2 \pi k\times1) = 3\\\rm k = \frac{3}{2\pi}\)

Thus, y'(1) =0, y'(2) = 3, and the  \(\rm y'(t) = kb2t \ cos(bt^2)\)  and value of b and k are \(\pi/2\)  and  \(3/2\pi\) respectively.

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Answer:

158 degrees

Step-by-step explanation:

We know that Lines A & B are parallel, meaning that the angels would also be parallel.

ex)

angle y = angle x

angle z = angle r

So therefore:

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The force that is applied to move the object is obtained as 25.4 N

Let us recall that in physics work is the product of the force and the distance that is covered.

W = F * d

where W is the amount of work completed, F is the force applied, d is the distance traveled, and theta is the angle formed by the force's and the displacement's directions.

Thus we have;

Work = Force * distance

Force = Work/Distance

= 350J/13.8 m

= 25.4 N

The force that is applied is 25.4 N

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Ka and Kb are both acid-base equilibrium constants, but they apply to different types of reactions. Ka (acid dissociation constant) is used to describe the dissociation of an acid in water, while Kb (base dissociation constant) is used to describe the dissociation of a base in water.

Specifically, Ka is a measure of the strength of an acid in terms of how easily it donates a proton (H+) to a solvent like water. A higher Ka value indicates a stronger acid, while a lower Ka value indicates a weaker acid. Kb, on the other hand, is a measure of the strength of a base in terms of how easily it accepts a proton (H+) from a solvent like water. A higher Kb value indicates a stronger base, while a lower Kb value indicates a weaker base. There is a mathematical relationship between Ka and Kb for conjugate acid-base pairs, which are molecules or ions that differ by the presence or absence of a single proton. The relationship is expressed by the equation: Ka x Kb = Kw, where Kw is the ion product constant for water, which is 1.0 x 10⁻¹⁴ at 25°C. This relationship shows that the stronger the acid, the weaker its conjugate base, and vice versa.

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Answer: Therefore, the GCF of 50 and 75 is 5.

Step-by-step explanation:

To find the greatest common factor (GCF) of 50 and 75, we can compare their factors.

Factors of 50: 1, 2, 5, 10, 25, 50

Factors of 75: 1, 3, 5, 15, 25, 75

By comparing the common factors between 50 and 75, we can see that the GCF is 5, as it is the largest number that divides both 50 and 75 without leaving a remainder.

Answer: 25

Step-by-step explanation:

explanation:

Answer:

10

Step-by-step explanation:

Answer:

0.45

Step-by-step explanation:

You divided 2.25 by 5

Answer:

The new length is 13.5 meters

Step-by-step explanation:

Here, we are interested in calculating the new length of the cloth she wants to use

What we know from the question is that she is making a reduction of 10% from an initial of 15 meters

Thus, the length she is to use can be calculated by first getting what 10% of 15 meters is

Mathematically, that would be ;

10/100 * 15 = 1.5 meters

We now subtract this from the total of 15 meters

= 15 meters - 1.5 meters = 13.5 meters

Answer:

68%

Step-by-step explanation:

hope this helps uwu