A sign on a roadway at the top of a mountain indicates that for the next 4 miles, the grade is 10.5°. Find the change in elevation over that distance for a car descending the mountain. Round to the nearest hundredth.

Answer:

[tex]\fbox {400.41 feet}[/tex]

Step-by-step explanation:

Here we need to take the tan ratio of the angle.

⇒ tan 4° = 28/x = 0.0699268119

⇒ x = 28/0.0699268119

⇒ x = 400.41 feet

Answer:

t+s = 9

4t+9s=51

tulips and succulents combined is 9 plants

the amount of money they have combined is $51

Answer:

134

Step-by-step explanation:

the "nth" term of a sequence means that you can plug in the term number to get the term value

so, if

  11n + 2 is the sequence

  11(12) + 2 is the 12th term

  132 + 2 is the 12th term

  134 is the 12th term

By plugging in the term "place" (1st, 2nd, 3rd, 4th, etc.) for the variable "n", we get a term value.

hope this helps!!

The 12th term of the sequence is 133

The nth term is given as:

Tn = 11n + 1

The 12th term is calculated as:

T(12) = 11(12) + 1

Evaluate

T(12) = 133

Hence, the 12th term of the sequence is 133

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Use the chain rule to differentiate both sides of the given equation with respect to [tex]x[/tex] :

[tex]y = 2 f(g(x))[/tex]

[tex]\dfrac{dy}{dx} = y' = 2 f'(g(x)) g'(x)[/tex]

Differentiate again with the product and chain rules to get the second derivative :

[tex]\dfrac{d^2y}{dx^2} = y'' = \boxed{2 f'(g(x)) g''(x) + 2 f''(g(x)) g'(x)^2}[/tex]

(D)

Answer:

You can make 10 tortillas with one and a half kilograms of ground meat

Step-by-step explanation:

one and a half kilograms to grams

1.5kg x 1000 = 1500g

150 grams prepared to make 1 hamburger

than, 150 x h = 1500

h = 1500 / 150

h = 10

Answer:

10 tortillas

Step-by-step explanation:

First convert kilograms to grams:

   1 kg = 1000 g

⇒ 1.5 kg = 1500 g

Let x = number of tortillas made with 1500 g of meat

Set up a ratio of tortillas and meat and solve for x:

⇒ 1 tortilla : x tortillas = 150 g meat : 1500 g meat

[tex]\sf \implies \dfrac{1}{x}=\dfrac{150}{1500}[/tex]

[tex]\sf \implies 1 \cdot 1500= 150 \cdot x[/tex]

[tex]\sf \implies 1500=150x[/tex]

[tex]\implies \sf x=\dfrac{1500}{150}[/tex]

[tex]\implies \sf x=10[/tex]

Therefore, 10 tortillas can be made with 1.5 kg of ground meat.

Answer:

Slope is 3/4

Step-by-step explanation:

Gradient means slope. So, to find the slope without using the formula, look at two points then count up until you're in line with the other point, then count right until you reach the other point. Remember it must be written as rise/run.

I hope this explanation makes sense!

The points I will use is (0,-2) and (4,1).

Slope is 3/4.

Hope this helps!

If not, I am sorry.

Answer:

opotion has not correct answer

answer is 15.

Answer:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

Step-by-step explanation:

[tex]\left(\sqrt{3}\right)\left(\sqrt[5]{3}\right)=\sqrt[10]{3^7}\quad[/tex]

(√3)([tex]\sqrt[5]{3}[/tex]) = √3 · [tex]\sqrt[5]{3}[/tex]

{√3 = [tex]3^{\frac{1}{2}}[/tex]}                 {radical rule: [tex]\sqrt{x}=x^1^/^2[/tex]}

[tex]\sqrt3[/tex][tex]\sqrt[5]{3}[/tex] =  [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex]

{[tex]\sqrt[5]{3}[/tex] = [tex]3^{\frac{1}{5}}[/tex]}                  {radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex]}

 [tex]3^{\frac{1}{2}}[/tex] · [tex]\sqrt[5]{3}[/tex] =   [tex]3^{\frac{1}{2}}[/tex] · [tex]3^{\frac{1}{5}}[/tex]     {exponent rule:  [tex]a^x*a^y=a^x^+^y[/tex]}

                (1/2 + 1/5 = 5/10 + 2/10 = 7/10)

              [tex]=3^\frac{7}{10}[/tex]        {opposite of radical rule: [tex]\sqrt[n]{x} = x^1^/^n[/tex] ;  [tex]x^\frac{a}{b}=\sqrt[b]{x^a}[/tex]}

             = [tex]\sqrt[10]{3^7}[/tex]

so, the simplified version of this equation can either be written as:

[tex]3^\frac{7}{10}[/tex]    or      [tex]\sqrt[10]{3^7}[/tex]

hope this helps!!

(I can't clearly see the last option, but if it's either of these, then it's correct)

A percentage is a way to describe a part of a whole. The percentage increase of Magikarps is 100%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps. Therefore, The percentage increase of Magikarps is,

Percentage increase = (16-8)/8 × 100% = 100%

Hence, The percentage increase of Magikarps is 100%.

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Answer:

(2,-3) (3,-3)

Step-by-step explanation:

f(x) is y

x² - 5x + 3 = -3

x² - 5x + 6 = 0

ask yourself

which 2 numbers when multiplied give you

+6 and when added give you -5

they are -3 and -2

(x-3)(x-2)

x=3 x=2

when you put x=3 and x=2

in x² - 5x + 3 it's gives -3 which is y

(3,-3) (2,-3)

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Answer:

[tex]\large {\textsf{B and E}}\ \implies x_1=-2\sqrt{5}-3,\ x_2=+2\sqrt{5}-3[/tex]

Step-by-step explanation:

Quadratic Formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Quadratic Equation: ax² + bx + x = 0, where a ≠ 0

Given equation: x² + 6x + 9 = 20

Step 1: Subtract 20 from both sides.

x² + 6x + 9 - 20 = 20 - 20

⇒ x² + 6x - 11 = 0

Step 2: Identify the values of a, b, and c and substitute them in the formula.

⇒ a = 1, b = 6, c = -11

[tex]x=\dfrac{-6\pm\sqrt{\bold{6^2}-4(1)(-11)}}{\bold{2(1)}}\\\\x=\dfrac{-6\pm\sqrt{36\bold{\ - \ 4(-11)}}}{2}\\\\x=\dfrac{-6\pm\sqrt{\bold{36+44}}}{2}\\\\x=\dfrac{-6\pm\sqrt{80}}{2}\\\\x=\dfrac{-6\pm\sqrt{16\times5}}{2}\implies \dfrac{-6\pm\sqrt{\bold{16}}\times\sqrt{5}}{2} \\\\x=\dfrac{-6\pm4\sqrt{5}}{2}[/tex]

Step 3: Separate into possible cases.

[tex]x_1=\dfrac{-6-4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{-4\sqrt{5}}{2}\implies \boxed{-3-2\sqrt{5}\ \ \textsf{or}\ -2\sqrt{5}-3}\\\\x_2=\dfrac{-6+4\sqrt{5}}{2}\implies \dfrac{-6}{2}+\dfrac{4\sqrt{5}}{2}\implies \boxed{-3+2\sqrt{5}\ \ \textsf{or}\ \ 2\sqrt{5}-3}[/tex]

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Answer:

y = -0.5x - 3.5

Explanation:

Take two points: (1, -4), (3, -5)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope \ (m) : \dfrac{-5-(-4)}{3-1} = -\dfrac{1}{2}[/tex]

Equation:

[tex]\sf y- y_1 = m (x - x_1)[/tex]

[tex]\rightarrow \sf y- (-4) = -\dfrac{1}{2} (x -1)[/tex]

[tex]\rightarrow \sf y+ 4 = -\dfrac{1}{2} x + \dfrac{1}{2}[/tex]

[tex]\rightarrow \sf y = -\dfrac{1}{2} x + \dfrac{1}{2} - 4[/tex]

[tex]\rightarrow \sf y = -0.5 x -3.5[/tex]

The formula of a line is:

[tex]f(x) = kx + b[/tex]

k — stands for tg of line angle
b — stands for the y value of a point where the line crosses y axis.

We can see 2 points:
A (1, -4)
B (3, -5)

We can make a system of equations:

[tex]k*1+b=-4\\k*3+b=-5\\[/tex]

From second equation:

[tex]b = -5 - 3k[/tex]

Let's put b in first equation:

[tex]k-5-3k=-4\\-2k=1\\k=- \frac{1}{2}[/tex]

Now we can find b:

[tex]b = -5 -3*- \frac{1}{2}\\b = -5 + 1.5\\b = -3.5[/tex]

The answer is:
-0.5x -3.5

Answer:

[tex]x=\dfrac{11}{4}[/tex]

Step-by-step explanation:

Given:

[tex]9^{-\frac{1}{2}}=\dfrac{27^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

Rewrite 9 as 3² and 27 as 3³:

[tex]\implies (3^2)^{-\frac{1}{2}}=\dfrac{(3^3)^{\frac{1}{4}}}{3^{(x-1)}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 3^{-1}=\dfrac{3^{\frac{3}{4}}}{3^{(x-1)}}[/tex]

Multiply both sides by [tex]3^{(x-1)}[/tex] :

[tex]\implies 3^{-1} \cdot 3^{(x-1)}=3^{\frac{3}{4}}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 3^{(-1+x-1)}=3^{\frac{3}{4}}[/tex]

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

[tex]\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):[/tex]

[tex]\implies x-2=\dfrac{3}{4}[/tex]

[tex]\implies 4(x-2)=3[/tex]

[tex]\implies 4x-8=3[/tex]

[tex]\implies 4x=11[/tex]

[tex]\implies x=\dfrac{11}{4}[/tex]

Answer:

4

Step-by-step explanation:

In triangle JKL, the side opposite the 30 degree angle, JL, is half the length of the hypotenuse, KL. Thus, JL has a length of

[tex]4 \sqrt{2} [/tex]

In triangle JML, the hypotenuse is

[tex] \sqrt{2} [/tex]

times the length of the leg, meaning that x = 4

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

Graphically speaking, linear functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). Linear functions are characterized by slope and intercept:

y = m · x + b     (1)

Slope

m = (7 - 0)/[9 - (- 6)]

m = 7/15

Intercept

b = 4

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

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The equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

The equation is given as:

[tex](\frac18)^{-3a} = 512^{3a}[/tex]

Express the equation as a base of 2

[tex](2^{-3})^{-3a} = 2^{9*3a}[/tex]

Evaluate the products

[tex]2^{9a} = 2^{27a}[/tex]

Cancel out the common base

9a = 27a

The above equation is not true because [tex]9a \ne 27a[/tex]

Hence, the equation [tex](\frac18)^{-3a} = 512^{3a}[/tex] as no solution

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Answer:

m = -3

c = 2

Step-by-step explanation:

This equation is given in slope-intercept form. The general structure of these equations is:

y = mx + c

In this form, "m" represents the slope and "c" represents the y-intercept. As you have been given the entire equation, the only thing you have to do is rearrange the equation to find which values correspond with the variables.

y = 2 - 3x  -----> y = -3x + 2

Therefore,

m = -3

c = 2

Answer:

n = 7

Explanation:

[tex]\rightarrow \sf 3 + 5(2 + 7n) = 258[/tex]

apply distributive method: a(b + c) = ab + ac

[tex]\rightarrow \sf 3 + 10 + 35n = 258[/tex]

simply add the numbers

[tex]\rightarrow \sf 13 + 35n = 258[/tex]

subtract both sides by 13

[tex]\rightarrow \sf 13-13 + 35n = 258-13[/tex]

simplify the following

[tex]\rightarrow \sf 35n = 245[/tex]

divide both sides by 35

[tex]\rightarrow \sf n = 7[/tex]

Answer:

n = 7

Step-by-step explanation:

1) Subtract 3 from both sides.

5(2 + 7n) = 258 - 3

2) Simplify 258 - 3 to 255.

5(2 + 7n) = 255

3) Divide both sides by 5.

2 + 7n = 255/5

4) Simplify 255/5 to 51.

2 + 7n = 51

5) Subtract 2 from both sides.

7n = 51 - 2

6) Simplify 51 - 2 to 49.

7n = 49

7) Divide both sides by 7.

n = 49/7

8) Simplify 49/7 yo 7.

n = 7

The equation of the function is f(x) = x(x + 2)(x -1)(x -3)

From the graph, we have the following highlight:

The above means that:

f(x) approaches positive infinity irrespective of the x value

Hence, the end behavior of the function is:

[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]

Since, the function opens upward.

Then the sign of the leading coefficient is positive

This is the point, where the graph crosses the x-axis.

From the graph, we have the zeros to be:

x = -2, x = 0, x = 1 and x = 3

Since the graph crosses the x-axis at this point, then the multiplicity of the zeros is 1

In (c), we have:

x = -2, x = 0, x = 1 and x = 3

Rewrite as:

x + 2= 0, x = 0, x - 1 = 0 and x - 3 = 0

Multiply these values

f(x) = x(x + 2)(x -1)(x -3)

Hence, the equation of the function is f(x) = x(x + 2)(x -1)(x -3)

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The t-test might be more useful in actual practice when standard deviation or variance is unknown.

The t-test is used to determine how the averages of various data sets differ from one another.

When variance is not provided, the T-test, a particular kind of parametric test, is used to determine how the means of two sets of data differ from one another. When variance is provided, the Z-test indicates a hypothesis test that determines whether the means of two datasets differ from one another.

Example of t-test: If you flip a coin 1,000 times, for instance, you can discover that the outcome is distributed normally over all trials.

Example of z-test: We are conducting research using information gathered from cohorts of students who have taken Elementary Statistics in the past.

T-tests are typically more suitable when addressing issues with small sample sizes, whereas z-tests are suitable for large sample sizes.

Using the t-test for an ordinal variable, their frequency is not even close to a normal distribution, and the arithmetic mean offers an unsuitable measure of location.

Because we frequently don't know the population standard deviation, Z-Tests have this drawback.

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Livia eats a chicken drumstick with 11 grams of protein. She also eats x cheese sticks, each with 7 grams of protein. The table shows y , the total number of grams of protein that Livia will consume if she eats x cheese sticks. Livia may eat only part of a cheese stick, so x may not always be a whole number.

What is the range of the function?

Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.

It is defined as the difference between the maximum value in the data set to the minimum value in the data set.

We have:

The amount of money in tips earned by four restaurant servers waiting on 10 tables is represented by the following data sets:

Alyssa {3, 6, 2, 8, 12, 14, 5, 7, 7, 8}

Bryant {9, 2, 7, 50, 0, 5, 2, 8, 6, 8}

Camila {1, 9, 10, 3, 0, 12, 10, 9, 8, 2}

Devon {4, 2, 8, 15, 20, 7, 5, 0, 6, 2}

The IQR for Alyssa:

IQR = Q3 - Q1

IQR = 8 - 5 = 3

The IQR for Bryant:

IQR = Q3 - Q1

IQR = 8 - 2 = 6

The IQR for Camila:

IQR = Q3 - Q1

IQR = 10 - 2 = 8

The IQR for Devon:

IQR = Q3 - Q1

IQR = 8 - 2 = 6

Thus, Camila's data set has the greatest interquartile range and the value of IQR = 8 option third is correct.

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[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

[tex] \sf \dfrac{2}{15} \div \dfrac{3}{20} = \dfrac{2 \times 20}{15 \times 3} = \dfrac{40}{45} = \dfrac{8}{9} [/tex]

Answer :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \Rrightarrow \dfrac{8}{9} [/tex]

I hope I've helped : )

[tex]\dfrac{1}{50}[/tex]

[tex] \cfrac{2}{15} \times \cfrac{3}{20} [/tex]

[tex] \cfrac{2 \times 3}{15 \times 20} [/tex]

[tex] \cfrac{6}{15 \times 20} [/tex]

[tex] \cfrac{6}{300} [/tex]

[tex] \cfrac{1}{50} [/tex]

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

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Answer = #2 - 1/3^3

Step-by-step explanation:

Answer:

111 cm^2

Step-by-step explanation:

h = 11.4

d = 5  so  r (radius) = 2.5

Surface Area of a Cone Formula: πr^2 + πrs

s represents the slant height of the cone, lets represent this with a drawing.

We have the values of h and r, but we don't have the value of s, meaning we have to find it. We can do this by using pythagorean theorem.

a^2 + b^2 = c^2

These three values can come together to create a right triangle which we can seperate from the rest of the diagram, now we can find s.

s = √(11.4^2 + 2.5^2)   so  s = 11.67

now that we have all of the pieces, we can plug back into the original surface area formula. πr^2 + πrs

π(2.5^2) + π(2.5)(11.67) = 111.29 cm^2 or 111 cm^2

The surface area of the solid cone requiring paint will be 111 square cm.

Let d be the diameter of the base circle, l be the slant height, and h be the height of the cone.

Then the lateral surface area of the cone will be

SA = πrl + πr²

Then the slant height is given as

l² = r² + h²

The exterior of a solid cone is painted. The height of the cone is 11.4 centimeters, and the diameter of its opening is 5 centimeters.

Then the radius of the base circle will be

r = 5 / 2

r = 2.5 cm

The length of the slant height will be

l² = 11.4² + 2.5²

l² = 136.21

 l = 11.67

Then the surface area of the solid cone requiring paint will be

SA = π × 2.5 × 11.67 + π × 2.5²

SA = 29.18π + 6.25π

SA = 35.43π

SA = 111.3

SA ≈ 111 square cm

The surface area of the solid cone requiring paint will be 111 square cm.

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Answer:

  (c)  (-30, 10)

Step-by-step explanation:

Two points will be on the same graph of a proportional relationship if the ratio of values y/x is the same.

__

The given point (x, y) = (60, -20) has a ratio k = y/x = -20/60 = -1/3.

The offered points have y/x ratios ...

(a) 30/-10 = -3

(b) -15/30 = -1/2

(c) 10/-30 = -1/3 . . . . . . the point you are looking for is (-30, 10)

(d) -30/80 = -3/8

Answer:

9

Step-by-step explanation:

√x+5-2=0

√x+3=0

√x= -3

x=9   [(-3)*(-3) = 9]

If the first inequality is written as:

3x ≤ -12

Then the correct option is D.

If it is written as it is in the problem, then neither of the graphs is the correct option.

Here we have the inequalities:

3x ≤ 12

2x + 3 > 11

(notice that in all the options, the first inequality has a negative sign, while in the two given inequalities there are no negative sign. This means that you will never get the correct answer if you use the given information, as the problem is incorrectly written).

First, we need to isolate x on both inequalities, we will get:

3x ≤ 12

x ≤ 12/3

x ≤ 4

(As you can see, because we don't have the negative sign, this inequality is different to all the ones in the options).

And for the other:

2x + 3 > 11

2x > 11 - 3

x > 8/2

x > 4

So neither of the options is actually correct.

If we instead write the first inequality as:

3x ≤ -12

We would solve this as:

x ≤ -4

And in that case, our two inequalities are:

x ≤ -4

x > 4

So the correct graph is graph D.

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Here's your answer down here↓:

Step-by-step explanation:

x^3 - y^3 = (x - y)(x^2 + xy + y^2)

(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2) = (x - y)(x + y)(x^2 + y^2)

Ok. So the factor (x-y) appears once in the top line and once in the second line. So we are going to take it the least amount of times.

So, the factor (x + y) appears in the top line zero times and in the second line one time so we will take it where it appears the least which is zero times so we are still at (x - y)

And it Same goes for the factors of (x^2 + y^2) and (x^2 + xy + y^2)

Answer:

2×3.14×r=75

6.28 r=75

r=75/6.28=11.943=12 inch (nearly)

2) The three ways of naming an angle are by the letter at the vertex, by placing a number or variable inside the angle, or by two letters with the vertex letter placed in the middle.

3) [tex]\angle WXY, \angle YXZ, \angle WXZ[/tex]

4) [tex]X[/tex]