What does it mean if a number divides another number?.

The area of the region bounded by the parabola, the tangent line to this parabola at the point, and the axis is 20/3.

The area of the region bounded by the parabola y=x2, the tangent line to this parabola at (1,1) and the x-axis can be calculated by using integration.

First, we note that the equation of the tangent line to the parabola at (1,1) is y=2x-1. Then, the area of the region can be calculated by the equation:
A=∫01 (2x-1) - (x2)dx
A=∫01(x-x2)dx
A=∫01x dx - ∫01x2dx
A= (x2/2) |01 - (x3/3) |01
A=(1/2) - (1/3)
A=1/6
Let the given parabola be\(y^2=4ax\).

So, the equation of tangent at

\((a,a^2/4) is y=a^2/4 + (x-a)\).On solving this with the parabola equation we get,

x=3a/2, y=3a/2

So, the x intercept is 3a/2 and hence the required area is :∫\((3a/2)(a^2/4)\)dx + ∫\((a/2)(3a/2 - a^2/4)\) dx...on solving this, we get,\(20a^2/12 = 5a^2/3\)= 20/3.

For more such parabola related questions

https://brainly.com/question/29635857

#SPJ11

Answer:

6,912....

Step-by-step explanation:

6 times 12 times 6 time 4 times 4 = 6,912

Answer:

= 360 ft³

Step-by-step explanation:

Rectangular prism

Volume = length x width x height

V = l x w x h

V = 12 x 6 x 4

V = 288 ft³

Triangular prism

Volume = 1/2 x base x height x length

V = 1/2 x 6 x 4 x 6 ( the width of the rectangular prism is the base of the triangular prism)

V = 1/2 x 144

V = 72 ft³

ADD BOTH VOLUMES

= 288 + 72

= 360 ft³

From the steps shown in the table given, we can conclude that: D. in solving the equation, the subtraction property of equality was not applied.

If a + b = c, to apply the subtraction property of equality so that b is moved to the other side of the equation, we would have:

a + b - b = c - b

a = c - b

Thus, from the table given, the none of the steps showed that the subtraction property of equality was applied in solving the equation, so, the answer is: D.

Learn more about the subtraction property of equality on:

https://brainly.com/question/1601404

#SPJ1

Answer:

1) -
2) +

3) -
4) +

Step-by-step explanation:

сумма внутренних углов треугольника не должна превышать 180 градусов

Find the sum:

1.1.1 2+6+(-7) + 10 = 11

​

11=11

The significance level is 0.05.

There is evidence to suggest that the proportion of students at the school who fear public speaking is less than 0.5000.

Test statistic is -6.94 accurate to two decimal places.

We can use a one-tailed hypothesis test with the following null and alternative hypotheses:

Null hypothesis: The proportion of students at the school who fear public speaking is equal to or greater than 0.5000.

Alternative hypothesis: The proportion of students at the school who fear public speaking is less than 0.5000.

The significance level is 0.05.

To conduct the test, we need to find the test statistic and compare it to the critical value.

First, we calculate the sample proportion of students who fear public speaking:

p⁻ = 125/400 = 0.3125

Next, we calculate the standard error of the sample proportion:

SE = sqrt[p⁻(1 - p⁻) / n] = sqrt[0.3125(1 - 0.3125) / 400] = 0.027

Then, we calculate the test statistic:

z = (p⁻ - p) / SE = (0.3125 - 0.5000) / 0.027 = -6.944

Since the alternative hypothesis is that the proportion of students who fear public speaking is less than 0.5000, we use a one-tailed test and look up the critical value for a 5% level of significance in the standard normal distribution table. The critical value is -1.645.

Since the calculated test statistic (-6.944) is less than the critical value (-1.645), we reject the null hypothesis.

Therefore, we can conclude that there is evidence to suggest that the proportion of students at the school who fear public speaking is less than 0.5000.

The test statistic is -6.94 accurate to two decimal places.

Learn more about significance level.

brainly.com/question/13947717

#SPJ11

Answer:

140 cm^2

Step-by-step explanation:

(5 apothems cut the pentagon into 5 rectangles 8 x 3.5)

3.5 x 8 x 5 = 140 cm^2

The points that represent this data are shown in the scatter plot attached below.

In this scenario, the age (in years) would be plotted on the x-axis (x-coordinate) of the scatter plot while the hair length (in inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the age (in years) and the hair length (in inches), a linear equation for the line of best fit is given by:

y = 0.0502x + 7.73

Read more on scatter plot here: brainly.com/question/28605735

#SPJ1

Answer:

value of x = 8

Step-by-step explanation:

well here,

line x is parallel to the line measuring 18

so the two triangles are similar to each other

hence ratio of their sides are equal

so 6/ 12 = x/ 16

=》1/2 = x/16

=》 x = 16 / 2

=》 x = 8

i hope u got it

have a nice day

Answer:

x = \(\frac{16}{3}\)

Step-by-step explanation:

The outer and inner triangles are similar, thus the ratios of corresponding sides are equal, that is

\(\frac{6}{6+12}\) = \(\frac{x}{16}\) , that is

\(\frac{6}{18}\) = \(\frac{x}{16}\) ( cross- multiply )

18x = 96 ( divide both sides by 18 )

x = \(\frac{96}{18}\) = \(\frac{16}{3}\)

Answer:

The inequality to describe the problem is 15 +c >25.

We must sell more than 5 cones to make a profit

Step-by-step explanation:

From this problem,  we can see that we need to sell a number of cones (c), that when added to the 15 cones that we have already sold, the result will be greater than 25.

To set up the inequality sign, we need to, first of all, know the inequality sign that we will be using. From the preceding statement, we can see that we need to sell greater than a certain number of cones.  

This should tell us that we will be needing the greater-than sign (>).

The next step is to know the format the equation should take:

We have sold 15 cones; We need to sell c more to make it greater than 25.

This will be 15 +c >25.

The inequality to describe the problem is 15 +c >25.

from this, we can see that c > 5 cones.

We must sell more than 5 cones to make a profit

Answer: The answer I got is 15.6

Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Answer:

m∠ABD = 88°, m∠CBD = 23°

Step-by-step explanation:

m∠ABD + m∠CBD = m∠ABC = 111°

(-10x + 58) + (6x + 41) = 111

-4x + 99 = 111

-4x = 12

x = -3

m∠ ABD = -10(-3) + 58 = 88°

m∠CBD = 6(-3) + 41 = 23°

Answer:

Step-by-step explanation:

X= -3

Abd = 88 degrees

Cbd = 23 degrees

Set the equation this way and solve:

-10x + 58 + 6x + 41 = 111

-4x + 99 = 111

-4x = 12

X = -3

Answer:

7. B

8. D

Step-by-step explanation:

We can start by creating a table to organize the information:

                  Likes Chocolate (c) Does Not Like Chocolate (~c) Total

Likes Sprinkles (s) 0.25                                                           0.40

Does Not Like Sprinkles (~s)            0.60

Total 0.70                                               0.30                       1.00        

We are given that 40% of friends like sprinkles, so we can fill in that cell of the table. We are also given that 25% of friends who like chocolate also like sprinkles, so we can fill in the cell for likes chocolate and likes sprinkles as 0.25.

To find the proportion of friends who like sprinkles and chocolate, we need to divide the number of friends who like both by the total number of friends who like sprinkles:

proportion = likes chocolate and sprinkles / likes sprinkles

proportion = 0.25 / 0.40

proportion = 0.625

So, approximately 62.5% of friends who like sprinkles also like chocolate.

Therefore, Caleb paid approximately $14,067.90 for the shares.

Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.

Selling price = 130% of the amount paid

$18,189.27 = 1.3 * x

To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:

x = $18,189.27 / 1.3

Calculating this, we find:

x ≈ $14,067.90

To know more about paid,

https://brainly.com/question/14549389

#SPJ11

Answer:

-3x^2 - 21x

Step-by-step explanation:

This question is representing multiplying two functions :

We are finding f(x) * g(x)

We know that f(x) is -3x and g(x) is x + 7, therefore :

(-3x)(x + 7)

Follow FOIL :

First :

(-3x)(x)

-3x^2

Outer :

(-3x)(7)

-21x

Therefore the answer is :

-3x^2 - 21x

Answer:

142 degrees

Step-by-step explanation:

There are 1,381,544 solutions for the given equation with the given restrictions.

To find the number of solutions for the equation x1 + x2 + x3 + x4 = 19, where all xi are non-negative integers such that x1 ≤ 3, x2 ≤ 5, x3 ≤ 7, and x4 ≤ 9, we can use the concept of stars and bars.

First, let's consider the equation x1 + x2 + x3 + x4 = 19 without any restrictions. We can represent this equation using stars and bars as follows:

**************|*************|**************|************
  x1           x2             x3               x4

In this case, we have a total of (19+4-1)C(4-1) = 22C3 = 22! / (3! * 19!) = 1540 possible solutions.

However, we need to consider the restrictions. To do this, we can subtract the number of solutions that violate the restrictions.

Let's consider the restriction x1 ≤ 3. If we set x1 = 4, we will have x2 + x3 + x4 = 15. Using the same stars and bars concept, we have (15+3-1)C(3-1) = 17C2 = 136 possible solutions that violate this restriction.

Similarly, for x2 ≤ 5, x3 ≤ 7, and x4 ≤ 9, we can find the number of solutions that violate each restriction.

By subtracting the number of solutions that violate all the restrictions (136 * 136 * 128), from the total possible solutions (1540), we can find the number of solutions that satisfy all the given conditions.

So, the number of solutions for the equation x1 + x2 + x3 + x4 = 19, where x1 ≤ 3, x2 ≤ 5, x3 ≤ 7, and x4 ≤ 9 is 1540 - (136 * 136 * 128) = 1,381,544.

In conclusion, there are 1,381,544 solutions for the given equation with the given restrictions.

To know more about solutions visit;

brainly.com/question/30665317

#SPJ11

Answer:

  (x -3)/4

Step-by-step explanation:

You multiply rational expressions the same way you multiply fractions. The numerator is the product of the numerators; the denominator is the product of the denominators. Same factors in numerator and denominator cancel to reduce the product to lowest terms.

  \(\dfrac{3(x-3)}{3}\cdot\dfrac{x-7}{4(x-7}=\dfrac{x-3}{1}\cdot\dfrac{1}{4}=\boxed{\dfrac{x-3}{4}}\)

We cancelled the factors of 3 from the first expression, and the factors of (x-7) from the second expression. The final product is the product of the reduced rational expressions.

Answer:

√6 + √5= 4.69

Step-by-step explanation:

First,  simplify the radicals-

in this situation, we have nothing to simplify.

√6 = aprx 2.45

√5 = aprx 2.23

√6 + √5= 4.685

= aprx 4.69

The bike costs $200 and is reduced by 30%

The cost price = $200, percentage loss is 30% or 0.3

We calculate how much the bike's cost is reduced by multiplying its original price with the factor 0.3 = 200 * 0.3 = 60

1. That means it was reduced by $60

Since $60 was removed from the original price, the sale price becomes $200 - $60 = $140

2. Therefore it costs $140 in the sale.

Answer:

\( \boxed{\boxed{ \red{\: x = \begin{cases} \frac{\pi}{8} + 7 + \frac{k\pi}{2} \\ - 6 + \frac{\pi}{12} + \frac{k\pi}{3} \end{cases}}}}\)

Step-by-step explanation:

therefore

\( \therefore \: x = \begin{cases} \frac{\pi}{8} + 7 + \frac{k\pi}{2} \\ - 6 + \frac{\pi}{12} + \frac{k\pi}{3} \end{cases}\)

Answer:

f(3)= -1

Step-by-step explanation:

1. f(3)= 3x - 10

f(3) means that where x is in the equation you put a 3

2. f(3)= 3(3) - 10

3. f(3)= 9 - 10

4. f(3)= -1

The margin of error for the given formula is 2.247.

The formula for a confidence interval is mean ± (z-score)*(standard deviation/square root of sample size). In this case, the mean is not given, but the formula can still be used to find the margin of error.

The z-score for a 95% confidence interval is 1.96, but since the interval is two-tailed, the absolute value of this z-score is used, which is 2.048.

The standard deviation is also not given, but it can be calculated using the given value of 1.1 and assuming a normal distribution. Thus, the margin of error can be calculated by multiplying 2.048 by 1.1 and rounding to three decimal places.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. The formula for a confidence interval includes the sample mean, a z-score or t-score, the standard deviation, and the sample size.

If any of these values are not given, they must be estimated or calculated. In this case, the mean is not given, but the margin of error can still be calculated using the formula. The margin of error represents the maximum amount that the sample mean could differ from the true population mean while still being within the confidence interval.

To know more about confidence interval click on below link:

https://brainly.com/question/29680703#

#SPJ11

Answer: A

Step-by-step explanation: The starting equation is 24 + 0.44x = 19 + 1.69x,

First, combine the x's on the RHS, and the integers on the LHS.

1.69x - 0.44x = 1.25x

24 - 19 = 5

So the equation will be 1.25x = 5

Divide both sides by 1.25 to isolate the x.

x = 4