A decimal number is represented by (3 x 110) + (5 x 1100) + (8 x 11000).
Question 1
Which decimal is represented by the given expansion?
Responses
A 35.835.8
B 0.03850.0385
C 0.3580.358
D 3.58

Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1

Answer: The given equation is

f(x) = x^{4} - 1

x- and y-intercept of the graph of the function f(x) = x^4 - 1 is

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

A graph of the above point is attached

Step-by-step explanation:

Given equation, f(x) = x^{4} - 1

let's assume the above equation with respect to y to find intercept i.e

y = x^{4} - 1 .........................(i)

Now, for the x-intercept put y = 0 in eq.(i)

So, we get,

0 = x^4 - 1

x^4 = 1

x = -1, +1

from above we get the x-intercept (1,0), (−1,0)

Now, for the y-intercept put x = 0 in eq.(i)

So, we get

y = 0^4 - 1

y = -1

from above we get the y-intercept (0, -1)

Therefore, from all above

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

Graph of the given equation f(x) = x^4 - 1 with intercept is

Answer:

1st option

Step-by-step explanation:

given the graph of f(x) then the graph of f(x) ± c is a vertical translation of f(x)

• if - c then a shift down of c units

• if + c then a shift up of c units

then for f(x) + 4 is a shift up of 4 units

The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.

We are given that;

Line a is parallel to line b

Line m is parallel to line n.

A) We want to prove that line a is perpendicular to n.

From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.

Now, we know that by definition of a right angle that ∠1 will also be a right angle.

Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.

B) We want to prove that line b is perpendicular to n.

The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

Thus, b will be perpendicular to n.

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Answer:

74

Step-by-step explanation:

(73 + 85 + 70 + 63 + x)/5 = 73.

You find the average by adding all of the test scores and dividing that number by the number of tests.  We had four test, so will will take that total, plus some mystery number (let's call it x), we divide that total by 5 because now there are 5 tests and not 4.  We already know what we want the average to be, we want the average to be 73.  We now have:

(291 + x)/5 = 73  Multiply both sides by 5

291 + x =365  Subtract 291 from both sides to get

x = 74

Answer: 74

Step-by-step explanation:

The mean is the average of all the values, which we find by finding the sum of each value and dividing by the total number of data points.

With 5 data points, we can use this equation to find, x, or the data point needed to obtain a mean of 73:

[tex]\frac{73+85+70+63+x}{5}=73\\ 291+x=365\\x=74[/tex]

Answer:

90 kilo per hour

Step-by-step explanation:

hope that helps!!

The expression for the total area of the wall is 10x.

What is area of rectangle?

Let l be length and b be breadth of the rectangle.

Then the area is the product of length and breadth of the rectangle.

That is area = l* b

We can find the expression for the total area of the wall as shown below:

Let the total length of the wall be x.

Height=10 ft

Total area = Height*Length

Putting the value of length and breadth in the above formula.

Total area = 10*x

Total area = 10x

Hence, the expression for the total area of the wall is 10x.

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Answer: 13 inches by 2 inches

Step-by-step explanation:

26 can be made by:

1 x 26

2 x 13

There are only 2 possibilities for the dimensions.

2 x 3 + 7 is 13, which fits the requirements.

Which means, the length is 13 and the width is 2.

Answer:

See below

Step-by-step explanation:

Using PEDMAS:

O Subtract 12 from the product of 5 and 3, then multiply by 87​

Answer:

10.6 ft

Step-by-step explanation:

to find the diagonal length of the stairway we can use the pythagorean theorem or a^2 + b^2 = c^2

6'4" is also 6 1/3' or 19/3'

8'6" is also 8 1/2' or 17/2'

now square them both

361/9 + 289/4

make them have the same denominator

1444/36 + 2601/36

add them

4045/36

take the square root

10.6000524 is your answer

10.6 ft

Answer:

300

Step-by-step explanation:

30+30+w+x+y+z = 360 (all angles round a point add up to 360)

Simplifying :

60 + w+x+y+z = 360

Subtracting 60 from both sides :

w+x+y+z = 300

Hope this helped and brainliest ?

Sum of entire angle=360°

so

The probability is P = 0.135

First, we need to find the individual probabilities, that are given by the quotient between the number of outcomes that meet the condition and the total number of outcomes.

The joint probability is given by the product between the individual probabilities, so we get:

P = (1/2)*(3/6)*(28/52) = 0.135

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Using the hint that the ratio of surface areas is the scale factor squared, the surface area of prism 1 is 36 square cm

From the figure, we have the following parameters

Prism 1 = 3 cm

Prism 2 = 8 cm

Calculate the scale ratio of dilation from prism 2 to prism 1 using the following equation

Scale ratio = Prism 1/Prism 2

Substitute the known values in the above equation

Scale ratio = 3m/8m

This gives

Scale ratio = 0.375

The surface area of prism 1 is then calculated using the following equation

Area of prism 2 = Scale ratio^2 * Area of prism 1

Substitute the known values in the above equation

Area of prism 2 = 0.375^2 * 256 square cm

Evaluate the product

Area of prism 2 = 36 square cm

Hence, the surface area of prism 1 is 36 square cm

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The equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]

The equation is defined by 2y = 3x + 2

Rewrite the equation in the form y = mx + c

[tex]y=\frac{3}{2}x + 1[/tex]

The slope, m = 3/2

The y-intercept, c = 1

The equation perpendicular to the given line will be of the form:

[tex]y-y_1=\frac{-1}{m}(x-x_1 )[/tex]

Substitute [tex]x_1=3, y_1=2, and m=\frac{3}{2}[/tex] into the equation above

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

Therefore, the equation of the perpendicular line is [tex]y=-\frac{2}{3}x+4[/tex]

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As you've pointed out, R is a different region that I originally thought. The area of R can be computed using either

[tex]\displaystyle \int_0^2 x^2 \, dx + \int_2^{10} -\frac x2 + 5 \, dx[/tex]

or

[tex]\displaystyle \int_0^4 (10-2y)-\sqrt y \, dy[/tex]

Either way, you've gotten the correct area for part (a).

For part (b), we can use part of the integral with respect to [tex]y[/tex] above. The horizontal distance between the curves [tex]y=x^2[/tex] and [tex]y=-\frac x2+5[/tex] is obtained by first solving for [tex]x[/tex],

[tex]y=x^2 \implies x=\sqrt y[/tex]

[tex]y=-\dfrac x2+5 \implies x = 10-2y[/tex]

so the length of each cross section is [tex]10-2y-\sqrt y[/tex].

The height of each cross section is [tex]3y[/tex].

Then the volume of the solid is

[tex]\displaystyle \int_0^4 3y \left(10-2y-\sqrt y\right) \, dy = \boxed{\int_0^4 -6y^2 + 30y - 3y^{3/2} \, dy}[/tex]

The instructions don't say to evaluate, but if you're looking for practice the volume ends up being 368/5, or 73  3/5.

Answer: 46.48 m²

Step-by-step explanation:

this question was answered already, go search it up

The solution set of the given inequality has a domain of (-∞, ∞) and the vertex(h,k) = (1, -9)

The solution set for inequality is the set of all solutions for which the inequality is defined. It can also be represented in an interval notation.

Given that:

By rewriting the equation in the parabola standard form 4p(y-k) = (x - h)², we have:

[tex]\mathbf{4\times \dfrac{1}{4}(y-(-9)) = (x-1)^2}[/tex]

Therefore, the parabola properties are:

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The true statement is mean > median

The mean is the average value.

So, we have

Mean = Sum/Count

This gives

Mean = (8 * 1 + 10 * 3 + 14 * 2)/(1 + 3 + 2)

Evaluate

Mean = 11

The mode is the measure with the highest frequency.

So, we have

Mode = 10

The median is the middle element

So, we have

Median = 10

The mean (11) is greater than the mode and the median

Hence, the true statement is mean > median

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Using the Factor Theorem, the function factored into linear factors is given as follows:

[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

-9 is a zero of f(x), hence [tex]x_1 = -9[/tex] and:

3x³ + 23x² - 35x + 9 = (x + 9)(ax² + bx + c)

ax³ + (b + 9a)x² + (9b + c)x + 9c = 3x³ + 23x² - 35x + 9

The coefficients are given as follows:

Hence:

3x³ + 23x² - 35x + 9 = (x + 9)(3x² - 4x + 1)

[tex]3x^2 + 23x^2 - 35x + 9 = 3(x + 9)(x - 1)\left(x - \frac{1}{3}\right)[/tex]

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The attached graph represents the piecewise function.

The piecewise function is given as:

f(x) = 3x - 5, x ≤ -1

      = -2x + 3, -1 < x < 4

      = 2, x ≥ 4

To plot the graph, we simply plot the equations together with their domains

i.e.

3x - 5 with the domain of x ≤ -1,  -2x + 3 with the domain of -1 < x < 4 and 2 with the domain of x ≥ 4

See attachment for the graph of the function

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Considering the given regression equation, the number of weeks that will pass before the value of the stock reaches $600 is of:

B. 8.3.

The value of the stock y after x weeks is given as follows:

log(y) = 0.3x + 0.296.

We have to solve for x when y = 600, hence:

log(600) = 0.3x + 0.296

0.3x = 2.7782 - 0.296

x = (2.7782 - 0.296)/0.3

x = 8.3 weeks.

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Answer:

x = 24

Step-by-step explanation:

x + 11 = 35

x = 35 - 11

x = 24

x+11=35

Subtract 11 on both sides.

Subtract 11 from 35 to get 24.

The linear functions are: y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

As a general rule, linear functions take any of the following forms:

y = mx + b

Ax + By = C

y - y1 = m(x - x1)

Any equation that take a different form is not a linear function

Using the above as a guide, the linear functions are:

y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

Other functions are nonlinear

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The mathematical reasoning for Step 3 is a distributive property.

It should be noted that the distributive property is the multiplication of the sum of two to more addends by a number that will give same result.

In this case, the mathematical reasoning for Step 3 is a distributive property.

Therefore, the correct option is C.

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Answer: C. Distributive Property

Answer

[tex]2 \times 2 + 6 \times 2 + \frac{8}{2 } [/tex]

[tex]4 + 12 + 4[/tex]

[tex]16 + 4[/tex]

[tex]20[/tex]

The probability that a student attended the game, given that the student is from North Beach is 0.65.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a student attended the game, given that the student is from North Beach = number of North beach students that attended the game / total number of students who attended the game

110 / 170 = 0.65

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The number of ways when the choice is not relevant is 4

The number of colors are:

Colors, n = 4

The color to choose are:

r = 3

Relevant choice

When the choice is relevant, we have:

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^4P_3[/tex]

Evaluate

Ways = 24

Hence, the number of ways when the choice is relevant is 24

Not relevant choice

When the choice is not relevant, we have:

[tex]Ways = ^nC_r[/tex]

This gives

[tex]Ways = ^4C_3[/tex]

Evaluate

Ways = 4

Hence, the number of ways when the choice is not relevant is 4

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The solution to the Questions are

(a)

The alternate hypothesis demonstrates that there are two possible outcomes for the test.

(b)

Here we have

[tex]n_{1}=40,\\\\ \bar{x}_{1}=102,\sigma_{1}=5,n_{2}=50,\bar{x}_{2}=99,\sigma_{2}=6[/tex]

(b)

Here the test is two-tailed. So for [tex]\alpha =0.04[/tex], the critical values of the z-test are -2.05 and 2.05.

Decision rule: If z > 2.05 or z<-2.05, reject H0

(c)

Test statistics will be

[tex]z=\frac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu_{2})}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}} \\\\\\z=\frac{(102-99)-(0)}{\sqrt{\frac{5^{2}}{40}+\frac{6^{2}}{50}}}[/tex]

z=2.59

(d)

The two-tailed nature of the test is shown by the alternative hypothesis.

(e)

The result of the test yields the following P-value: 0.0096

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The total amount of Chandra's investments after 8 years exists at $110.03 Compound interest.

The formula for calculating the compound interest exists described as;

[tex]A = P(1+r/n)^{nt[/tex]

where, P is the amount invested = $75

r be the rate. = 0.048

t be the time = 8 years

n = 12 (monthly)

Substitute, the values in the above equation, then we get

[tex]$A = 75(1+0.048/12)^{96[/tex]

A = 75(1.467)

A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03 Compound interest.

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The number of boxes with 20kg = 15

The number of boxes with 25 kg = 35.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Total weight of all boxes = 1175kg

Total number of boxes = 50

X + Y = 50........................(1)

20X + 25Y = 1175 .............(2)

(1) [tex]\times[/tex] 20

20 (X + Y = 50)

20X + 20Y = 1000 .............(3)

Subtracting (3) from (2), we get

20X + 25Y = 1175 -

20X + 20Y = 1000

--------------------

5Y = 175

Y = 175/5

Y = 35

Substitute the value of y in (1), then we get

X + Y = 50

X + 35 = 50

X = 50 - 35

X = 15

The value of X = 15 and Y = 35

Number of boxes with 20kg = 15

Number of boxes with 25 kg = 35.

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