what is log 8/3 base 5 ​

Answer: 4 exercises

Step-by-step explanation:

If we completed 87.5% of the math exercises before dinner, then we have completed 0.875 × total number of exercises.

Let "\(x\)" be the total number of exercises.

\(0.875x = 28\)

Solving for \(x\), we get:

\(\boxed{\begin{minipage}{4 cm}\text{\LARGE 0.875x = 28 } \\\\\\ \large $\Rightarrow$ $\frac{0.875x}{0.875}$ = $\frac{28}{0.875}$\\\\$\Rightarrow$x = 32\end{minipage}}\)

Therefore, the total number of exercises is 32.

We completed 28 exercises before dinner, so we have:  32 - 28 = 4 exercises left to do after dinner.

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The test statistic for this scenario is 1.14. To calculate the test statistic, we can use the formula:

(test statistic) = (sample proportion - hypothesized proportion) / standard error

Here, the hypothesized proportion is the national proportion of red cars on the road, which is 0.12. The sample proportion is the proportion of red cars in the sample, which is 35/210 = 0.167.

To calculate the standard error, we use the formula:

\(standard error=\sqrt{\frac{(hypothesized proportion * (1 - hypothesized proportion)) }{ sample size} }\)

Plugging in the values, we get:

standard error = √[(0.12 * (1 - 0.12)) / 210] = 0.032

Now, we can calculate the test statistic:

test statistic = (0.167 - 0.12) / 0.032 = 1.14

The test statistic tells us how many standard errors the sample proportion is away from the hypothesized proportion. In this case, the test statistic is 1.14, which means that the sample proportion of Phillies fans driving red cars is 1.14 standard errors away from the national proportion of red cars on the road. We would need to compare this test statistic to a critical value from a t-distribution to determine if the difference is statistically significant at a given level of significance.

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Answer:

\(3 + {8}^{2} + 4 + 5 + 2 \\ = 3 + 64 + 4 + 5 + 2 \\ = 67 + 11 \\ = 78\)

Hope it helps!!

Answer:

3+8²+ 4+5-2= 74

Step-by-step explanation:

8²=64

3+5+4= 12

64+ 12= 76

76-2= 74

Hope that helped :)

b. The displacement over the interval  is  -8 meters.

c. Total distance traveled over the interval 0 is  40/3 meters.

To find the displacement over the given interval, we need to find the change in position of the particle. We can do this by integrating the velocity function over the intervals where the motion is in the positive and negative directions, and then adding these integrals together.

a) The velocity function is v(t) = t³ - 10t² + 24t, 0 < t < 8.

When 0 < t < 4, the particle is moving in the positive direction, so we integrate v(t) from 0 to 4:

∫₀⁴ (t³ - 10t² + 24t) dt = [t⁴/4 - 10t³/3 + 12t²]₀⁴= 16/3

When 6 < t < 8, the particle is also moving in the positive direction, so we integrate v(t) from 6 to 8:

∫₆⁸ (t³ - 10t² + 24t) dt = [t⁴/4 - 10t³/3 + 12t²]₆⁸ = -32/3

When 4 < t < 6, the particle is moving in the negative direction, so we integrate v(t) from 4 to 6:

∫₄⁶ (t³ - 10t² + 24t) dt = [t⁴/4 - 10t³/3 + 12t²]₄⁶ = -8

Therefore, the displacement over the interval 0 < t < 8 is:

Δx = 16/3 - 32/3 - 8 = -24/3 = -8 meters.

b) To find the distance traveled over the given interval, we need to add up the total distance traveled in the positive direction and the total distance traveled in the negative direction.

The total distance traveled in the positive direction is:

∫₀⁴ |t³ - 10t² + 24t| dt = ∫₀⁴ (t³ - 10t² + 24t) dt = 16/3

The total distance traveled in the negative direction is:

∫₄⁶ |t³ - 10t² + 24t| dt = ∫₄⁶ (10t² - t³ - 24t) dt = 8

The total distance traveled over the interval 0 < t < 8 is therefore:

d = 16/3 + 8 = 40/3 meters.

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Answer:

7 , 5 , 9

Step-by-step explanation:

Answer:

Step-by-step explanation:

We may not be able to fit 16 cases in the box because their combined volume will be greater than the box which will make it impossible.

The dimensions of the big box is given as:

Length= 26 cm

Breadth= 15 cm

Height= 20 cm

So its volume can be calculated by:

Volume= Length x Breadth x Height

Volume= 26 cm x 15 cm x 20 cm

Volume1= 7800 cm³

Now, the dimension of one disc case is given as:

Length= 1.6 cm

Breadth= 14.2 cm

Height= 19.3 cm

The volume of one disc case will be:

Volume= 1.6 cm x 14.2 cm x 19.3 cm

Volume= 438.496 cm³

So, volume of 16 disc cases= 16 X volume of one disc case

Volume2= 16 x 438.496 cm³

Volume2= 7015.936 cm³

Since Volume1 < Volume2

So, 16 disc cases cannot be fit into a box.

Answer:

answer = cone

Step-by-step explanation:

just took the test and got it right! :)

The resulting three-dimensional object is a cone.

We have given that,

A triangular cross-section with coordinates at (1, 1), (1, 4), and (3, 1) is rotated about the line x = 1.

We have to determine what will be the resulting three-dimensional object.

A cone is a three-dimensional solid geometric shape having a circular base and a pointed edge at the top called the top.

A cone has one face and a vertex.

Therefore the first option is correct.

The resulting three-dimensional object is a cone.

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Answer: 14

Step-by-step explanation:

Answer: 8,400

Step-by-step explanation:

Answer:

Radius is \(r\approx4.622\,\text{ft}\)

Step-by-step explanation:

\(V=\pi r^2h\\34=\pi r^2(5)\\\frac{34}{5\pi}=r^2\\r=\sqrt{\frac{34}{5\pi}}\\r\approx4.622\,\text{ft}\)

The probability density function is defined as the derivative of the cumulative distribution function. It represents the relative likelihood of a continuous random variable taking on a specific value. The total area under the probability density curve is always equal to 1.

For a continuous random variable X, the probability density function f(x) satisfies the following properties:

1. Non-negativity: f(x) ≥ 0 for all x.

2. Integrates to 1: The integral of the probability density function over the entire range of X is equal to 1:

  ∫[−∞, ∞] f(x) dx = 1

This integral represents the total area under the probability density curve, which must be equal to 1.

To calculate the probability of X falling within a certain interval [a, b], we can use the probability density function as follows:

P(a ≤ X ≤ b) = ∫[a, b] f(x) dx

This integral gives the probability that X takes on a value between a and b.

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Answer: y= 0.0025

Step-by-step explanation:

Answer:

y= 0.0025

Step-by-step explanation:

every number in the y place is mutipled by four so to find y you need to divide 0.01 by 4

Answer:

The answer to your problem is,

Arc de Triomphe:

Step-by-step explanation:

Depends which arc you are talking about I will do the:

Arc de Triomphe

Measurements

164 feet (50 metres)

high and 148 feet (45 metres) wide

It all depends on which arc

Thus the answer to your problem is,

Arc de Triomphe:

Inscribed angles are formed when two chords have 1 common endpoint. The measure of \(\angle ACB\) and \(\overset{\huge\frown}{AC}\)  are:

\(\angle ACB = 32^o\)

\(\overset{\huge\frown}{AC} = 146^o\)

Given that:

\(\overset{\huge\frown}{AB} = 64^o\)

\(\angle ABC = 73^o\)

See attachment

First, we calculate \(\angle ACB\) using:

\(\angle ACB = \frac{1}{2} \times \overset{\huge\frown}{AB}\) ----- An inscribed angle is half the arc it intercepts

So, we have:

\(\angle ACB = \frac{1}{2} \times 64^o\)

\(\angle ACB = 32^o\)

Using the same theorem, we calculate \(\overset{\huge\frown}{AC}\) as follows:

\(\angle ABC = \frac{1}{2} \times \overset{\huge\frown}{AC}\)

So, we have:

\(73^o = \frac{1}{2} \times \overset{\huge\frown}{AC}\)

Multiply both sides by 2

\(2 \times 73^o = 2 \times \frac{1}{2} \times \overset{\huge\frown}{AC}\)

\(2 \times 73^o =\overset{\huge\frown}{AC}\)

\(146^o =\overset{\huge\frown}{AC}\)

Hence:

\(\overset{\huge\frown}{AC} = 146^o\)

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Answer:

your correct answers are 32 and 146

Step-by-step explanation:

to get 32, divide 64 by 1/2

To get 146, multiply 73 by 2

Hope I helped, got it right on test:)

Answer:

x = 7

Step-by-step explanation:

27 = 7x + 6 - 4x      (Given)

27 = 3x + 6             (Simplify)

27 - 6 = 3x + 6 - 6  (Subtract 6 on both sides)

21 = 3x                    (Simplify)

21/3 = 3x/3             (Divide 3 on both sides)

7 = x                        (Simplify)

There are 525 students in the entire school.

According to our question-

84/4 is 21.

The ratio is 1 teacher to every 21 students.

There are 25 teachers in the entire school. If you multiply that by 21, there are 525 students in the entire school.

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Answer:

sinθ = \(\frac{8}{10}\)

Step-by-step explanation:

sinθ = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AC}\) = \(\frac{8}{10}\)

Answer:

sin theta=p/h

=BC/AC

=8cm/10cm

=4cm/5cm

Hope it helps you.

The solution to the system of equation is (14, 6)

1 / 2 x = 10 - 1 / 2 y

8 = x -y

Therefore, let's combine the equation.

1 / 2 x + 1 / 2 y = 10

x - y = 8

x + y = 20

x - y = 8

2y = 12

y = 12 / 2

y = 6

x = 20 - 6

x = 14

Therefore, the solution of the system of equation is (14, 6)

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The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The dramatization club is offering passes to their play to fund-raise for the show's costs. Every understudy ticket sells for $6.50 and every grown-up ticket sells for $11.50. The dramatization club should make at least $1300 from ticket deals to take care of the show's expenses.

Let 's' and 'a' be the number of tickets sold to students and adults, respectively. Then the inequality is given as,

6.5s + 11.5a ≥ 1300

The inequality that could represent the possible values for the number of tickets sold will be 6.5s + 11.5a ≥ 1300.

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The probability that you are correct by making a random guess is 1/5.

According to the given question.

On a multiple choice test, each question has 5 possible answers.

As we know that probability, is a measure of the likelihood of an event to occur. It is calculated by taking the ratios of favorable outcomes to the total number of outcomes.

Here, it is given that there are 5 possible answers of one question.

⇒ Total number of outcomes = 5

Also, only one answer will correct out of 5 possible answers.

Which means, total number of favorable outcomes = 1

Therefore, the probability that you are correct by making a random guess

= favorable outcomes/total number of outcomes

= 1/5

Hence, the probability that you are correct by making a random guess is 1/5.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Step-by-step explanation:

3x + 1

=3x + 1

this is because a variable X is attached to the 3 so it makes the 3x and the 1 unlike

therefore you can not add them.

Answer:

-1/3

Step-by-step explanation:

3x+1=

3x=-1

3x/3=-1/3

x=-1/3

The Scale factor was used to enlarge the picture is 7/ 31.5.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A picture is 7 inches wide and 9 inches long.

A photographer enlarges it so it is 31.5 inches wide and 40.5 inches long.

So, scale factor is

= Original dimension / Enlarged dimension

= 9/ 40.5

= 90/ 405

= 10/45

= 2/9

Now, simplifying the scale factor 7/31.5 because it has Nr < Dr.

= 7/ 3.15

= 70/31.5

= 2/9

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Answer:

-√13/13 or -2.774

Step-by-step explanation:

(3+2-6/√3²+2²)

The point-slope form of the equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

From the graph, we can see that the line passes through the points (-4, 4) and (1, -1). To find the slope of the line, we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points, we get:

m = (-1 - 4) / (1 - (-4)) = -5 / 5 = -1

Therefore, the slope of the line is -1.

The point (-2, -2) is already given in the form (x1, y1). Therefore, we can use this point to write the equation in point-slope form.

Using the point-slope form of the equation and the information we found above, we get:

y - (-2) = -1(x - (-2))

Simplifying, we get:

y + 2 = -x - 2

Subtracting 2 from both sides, we get:

y = -x - 4

Therefore, the equation of the line in point-slope form is y - (-2) = -1(x - (-2)), and in slope-intercept form is y = -x - 4.

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Answer: x = 6x/5

Step-by-step explanation:

Answer:

x = 10/3

Step-by-step explanation:

\(\frac{x}{2} + \frac{2}{2} = \frac{4x}{5}\)

\(\frac{x + 2}{2} = \frac{4x}{5}\)

\(x + 2 = \frac{8x}{5}\)

5x + 10 = 8x

10 = 3x

x = 10/3

The equation F = 3cos(xπ/4) represents the electromotive force acting on the object as it travels through the tube, with the value of x representing its distance from one end of the tube.

To understand the experiment at the University of Georgia, we need to analyze the electromotive force equation and the setup involving an object and a tube.

Given information:

Length of the tube: 0.1 meters.

Electromotive force equation: F = 3cos(xπ/4) Newtons.

Distance of the object from one end of the tube: x.

The equation F = 3cos(xπ/4) represents the electromotive force (F) acting on the object as a function of its distance (x) from one end of the tube.

The electromotive force is given by the cosine function, where the amplitude is 3 and the frequency is determined by the coefficient of xπ/4.

The value of x ranges from 0 (one end of the tube) to 0.1 (the other end of the tube).

As the object moves along the tube, its distance from one end (x) changes, and the electromotive force (F) acting on it varies accordingly, following the cosine pattern.

By plugging different values of x into the equation F = 3cos(xπ/4), the electromotive force at different positions along the tube can be determined.

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