Find an equation of the tangent line to the curve at the given point.
y = x³ - 3x + 1, (3, 19)

Answer:

We conclude that the mean age of average viewer has changed

Step-by-step explanation:

H0 : μ = 43

H1 : μ > 43

The test statistic :

(xbar - μ) ÷ σ/sqrt(n)

Sample size, n = 100

xbar = 45 ; σ = 5

Test statistic :

(45 - 43) ÷ 5/sqrt(100)

2 ÷ 0.5 = 4

The Pvalue :

P(Z < 4) = 0.000032

Pvalue < α

0.000032 < 0.05 ; Hence, we reject the Null

We conclude that the mean age of average viewer has changed

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$. Therefore $x=y=12\sqrt{3}$, which is our answer

In a 30-60-90 triangle, the sides have the ratio of $1: \sqrt{3}: 2$. Let's apply this to solve for the variables in the given problem.

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x=y=Let's first find the ratio of the sides in a 30-60-90 triangle.

Since the hypotenuse is always twice as long as the shorter leg, we can let $x$ be the shorter leg and $2x$ be the hypotenuse.

Thus, we have: Shorter leg: $x$Opposite the $60^{\circ}$ angle: $x\sqrt{3}$ Hypotenuse: $2x$

Now, let's apply this ratio to solve for the variables in the given problem. We know that $x = y$ since they are equal in the problem.

Using the ratio of the sides, we have:$x\sqrt{3} = 12\sqrt{3}$ (opposite the $60^{\circ}$ angle is 12$\sqrt{3}$)$x = 2\sqrt{3}\cdot6$ (the hypotenuse is $2x = 12\sqrt{3}$)Simplifying, we have:$x = 12\sqrt{3}$

Therefore, $x=y=12\sqrt{3}$, which is our answer.

For more such questions on ratio of the sides

https://brainly.com/question/31529028

#SPJ8

The first plane is farther from the airstrip after the second leg

The first plane

Initial distance = 150 miles west

Additional distance = 220 miles 30 degrees SW

This means that

Additional distance = 220 * cos(30) miles SW

Additional distance = 190.53 miles

Total distance = 150 + 190.53 = 340.53

The second plane

Initial distance = 220 miles east

Additional distance = 150 miles x degrees SE

This means that

Additional distance = 150 * cos(x) miles SW

Total distance = 220 + 150 cos(x)

Given that

x < 30

We have

Second plane < First plane

220 + 150 cos(x) < 340.53

Evaluate

cos(x) < 0.8035

Take the arc cos of both sides

x < 36

x < 36 is not the same as x < 30

Hence, the first plane is farther

Read more about bearing distance at

https://brainly.com/question/22518031

#SPJ1

Taking the values provided into consideration, the correct answer is option D, the absolute difference being 144,000 and the relative difference being 59,3%.

The absolute difference between the number of people whose first language is English and the number of people whose first language is Spanish is calculated by subtraction:

243,000 - 99,000 = 144,000

To find the relative difference as a percentage, we divide the absolute difference by the compared value (English speakers) and then multiply by 100:

(144,000 / 243,000) x 100 = 59.3%

Therefore, the correct answer is D.

We found the complete question online. It is the following:

Two measurements are given. Find the absolute difference and then find the relative difference as a percentage. Assume that the first quantity is the compared value and the second quantity is the reference value. Round answers to the nearest tenth if necessary.

In Jose's hometown, there are 243,000 people whose first language is English and 99,000 whose first language in Spanish.

A. Absolute difference: 144,000 Relative difference: 14.5%

B. Absolute difference: -144,000 Relative difference: -59,3%

C. Absolute difference: 144,000 Relative difference: 145.5%

D. Absolute difference: 140.000 Relative difference: 59,3%

Learn more about absolute difference here:

https://brainly.com/question/30241593

#SPJ1

Answer: (A)

Step-by-step explanation:

By elimination, none of the other answers choices fit the lines; B, C, and D all have at least one positive slope. Both lines shown in the graph have negative slopes, so both equations have to have a negative x value when simplified, so it's A.

Answer:

\(\frac{1}{8}\)

Step-by-step explanation:

We know that the artist can complete \(\frac{1}{4}\) of a painting in 2 weeks. So, we just have to find half of \(\frac{1}{4}\) to find how much of a painting the artist can do in a week, which is \(\frac{1}{8}\) because half of \(\frac{1}{4}\) is \(\frac{1}{8}\).

Hope this helps! :)

Answer:

"Absolute value" is the non-negative value of a number, disregarding whether or not it has a sign.

Step-by-step explanation:

"Absolute value" is the non-negative value of a number, disregarding whether or not it has a sign. It can be thought of as how far it is away from the number of 0, whether it's to the left or right. Absolute value of a number is written as |x|, where x = any number. Let's say x was -1. |-1| would be 1 because it's 1 away from 0. If x was just 1, then the number would stay the same.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

3000000cm³

Step-by-step explanation:

150cm x 100cm x 200cm = 3000000cm³

Answer:

76.5 hours

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

Part 1 of 2:

(a) The equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the number of hours, y, worked at the second job can be written as:

P = (10x) + (9.25y + 0.7 * 9.25y) - 0.2[(10x) + (9.25y + 0.7 * 9.25y)]

Simplifying the equation:

P = 10x + 9.25y + 0.7 * 9.25y - 0.2(10x + 9.25y + 0.7 * 9.25y)

Part 2 of 2:

(b) If Winona is committed to working 30 hours per week at the first job, let's assume x = 30. We need to find the number of hours per week, y, she would need to work at the second job to reach a biweekly take-home pay of $800.

Using the simplified equation from part (a), we substitute x = 30 and solve for y:

800 = (10 * 30) + (9.25y + 0.7 * 9.25y) - 0.2[(10 * 30) + (9.25y + 0.7 * 9.25y)]

800 = 300 + (9.25y + 0.7 * 9.25y) - 0.2(300 + (9.25y + 0.7 * 9.25y))

Now, we can solve for y:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2(300 + 9.25y + 0.7 * 9.25y)

Simplify the equation:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2 * 300 - 0.2 * 9.25y - 0.2 * 0.7 * 9.25y

Combine like terms:

800 = 300 - 60 + 9.25y - 1.85y - 0.1295y

800 = 240 + 7.32y

Subtract 240 from both sides:

560 = 7.32y

Divide both sides by 7.32:

y ≈ 76.5

Therefore, Winona would need to work approximately 76.5 hours per week at her second job to reach a biweekly take-home pay of $800.

Answer:

It is a triangle.

Step-by-step explanation:

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Plot the given points. The first coordinate is the horizontal distance from the y-axis. The second coordinate is the vertical distance from the x-axis. Positive is right or up. Negative is left or down.

The value of the given expression, -50 + 5/13p, when p = -26 is -60

From the question, we are to evaluate the given expression for the given value of p

The given expression is

-50 + 5/13p

and

The given value of p is p = - 26

Substitute the given value of p into the given expression

That is,

-50 + 5/13p

When p = -26, the expression becomes

-50 + 5/13(-26)

Simplify

-50 + 5(-2)

-50 - 10

= - 60

Hence, the value of the expression is -60

Learn more on Evaluating an expression here: https://brainly.com/question/1811161

#SPJ1

Answer:

7x+10

Step-by-step explanation:

2x(3x)+1x(x+10)

6x+1x+10

7x+10

Answer: -18

Step-by-step explanation:

((-3)2)3

((-3) x 2) x 3

Apply rule (-a) = - a

(-3) = -3

-3 x 2 x 3

-6 x 3

= -18

Answer:

There's 2 red jacks in a deck and 2 black queens in a deck so you have a total of 4 possible cards out of a 52 total in a deck so that would be 4/52 or 1/13 of the time. Statistically 7.6% of the time you will get a red jack or a black queen.

Step-by-step explanation:

.Answer:

-105

Step-by-step explanation:

Given

\(Gas = \$105\) for 6 weeks

Required

Represent this as an integer

If the driver spends $105 on his taxi then it means that the money is debited from the driver's bank account.

Debit implies negative and it is represented by a negative symbon

Hence, the integer that represents this scenario is -105

Answer:

Why is a parent on Brainly??? Kinda weird><>

Step-by-step explanation:

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

Answer:

7i - 2

Step-by-step explanation:

(2 + 5i) - (4 - 2i)

2 + 5i - 4 + 2i

2 - 4 + 7i

7i + 2 - 4

7i - 2

Answer:

3i-2

Step-by-step explanation:

I am not sure it could also be, well I don't know.

Hopefully its correct, sorry if it not.

Answer:

   on the outside of the bracket. The divisor is the number you're dividing by.Set up the division problem with the long division symbol or the the dividend, on the inside of the bracket. The dividend is the number you're dut 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by.Set up the division problem with the long division symbol or the long division brackPut 487, the dividend, on the inside of the bracket. The dividend is the number yoPut 32, the divisor, on the outside of the bracket. The divisor is the number you're dividing by.

Step-by-step explanation:

Answer:

B. encodes; ignores

Step-by-step explanation:

The alternatives for this question are:

A. remembers; forgets

B. encodes; ignores

C. thinks about; remembers

D. processes; attends to

Tim should focus on the relevant fact  that both symbols represent the same value, and disregard the irrelevant differences in their shape. Therefore, the answer choice better fills in the blanks is B. encodes; ignores.

Answers:

5)

a.Highest- 96

Lowest-52

b.74

c. 70-80

d. 13

e. 7

6)

a. 89%

b. 51%

c. In the morning(89%)

Answer:

1%

Step-by-step explanation:

707-700=7 tax

700 x tax percentage=7

tax percentage =7/700

Tax percentage= .01 0r 1%

Answer:

B.  -414,720 x⁷y⁶

Step-by-step explanation:

To find the 4th term of the expansion of (2x - 3y²)¹⁰, we can use the binomial theorem.

The binomial theorem states that for an expression of the form (a + b)ⁿ:

\(\displaystyle (a+b)^n=\binom{n}{0}a^{n-0}b^0+\binom{n}{1}a^{n-1}b^1+...+\binom{n}{r}a^{n-r}b^r+...+\binom{n}{n}a^{n-n}b^n\\\\\\\textsf{where }\displaystyle \rm \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{r!(n-r)!}\)

For the expression (2x - 3y²)¹⁰:

Therefore, each term in the expression can be calculated using:

\(\displaystyle \boxed{\binom{n}{r}(2x)^{10-r}(-3y^2)^r}\quad \textsf{where $r = 0$ is the first term.}\)

The 4th term is when r = 3. Therefore:

\(\begin{aligned}\displaystyle &\;\;\;\;\:\binom{10}{3}(2x)^{10-3}(-3y^2)^3\\\\&=\frac{10!}{3!(10-3)!}(2x)^7(-3y^2)^3\\\\&=\frac{10!}{3!\:7!}\cdot2^7x^7(-3)^3y^6\\\\&=120\cdot 128x^7 \cdot (-27)y^6\\\\&=-414720\:x^7y^6\\\\ \end{aligned}\)

So the 4th term of the given expansion is:

\(\boxed{-414720\:x^7y^6}\)

The value of the inequality equation is x ≤ 7

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

4x ≤ 28   be equation (1)

Now , on simplifying the equation , we get

Divide by 4 on both sides of the inequality equation , we get

x ≤ 7

Therefore , the value of x is less than or equal to 7

All the numbers less than or equal to 7 satisfies the condition for x

The value of the equation x ≤ 7 is shown in the graph below

Hence , The value of the inequality equation is x ≤ 7

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Answer:

59 degrees (just taking a shot)

Step-by-step explanation:

A six sided polygon should have a total degree total of 720 degrees. 105+142+140+124+88+x=720. When you find x, it should equal 121 degrees. Since x and y are both on a straight line, that line has to be 180 degrees. These are supplementary angles. 180-121 should equal 59.

Answer:

Step-by-step explanation:

Hope it helps!!

Triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

Given that, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1).

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

90° counterclockwise rotation: (x, y) becomes (-y, x)

A(2, 7) → A'(-7, 2)

B(6, 5) → B'(-5, 6)

C(4, 1) → C'(-1, 4)

Therefore, triangle ABC with vertices A(2, 7), B(6,5) and C(4, 1): 90° counterclockwise transformation is A'(-7, 2), B'(-5, 6) and C'(-1, 4).

Learn more about the rotation of 90° counterclockwise here:

brainly.com/question/1571997.

#SPJ2

Answer:

Camillo will spend $48.75 dollars

Step-by-step explanation:

Since the better buy cost $1.95 we multiply.

1.95 * 25 = 48.75

So, the answer is 48.75

Hope this helps! :)

Answer:

x ≈ 2.73

Step-by-step explanation:

The two triangles are scaled.

So...

\(\frac{10}{11} = \frac{x}{3}\\\\30 = 11z\\\\x = 30/11\\\\\)

x = 2.727272..... ≈ 2.73

-Chetan K

\(\\ \sf{:}\longrightarrow \dfrac{AB}{BC}=\dfrac{AD}{ED}\)

\(\\ \sf{:}\longrightarrow \dfrac{10}{x}=\dfrac{10+1}{3}\)

\(\\ \sf{:}\longrightarrow \dfrac{10}{x}=\dfrac{11}{3}\)

\(\\ \sf{:}\longrightarrow 11x=30\)

\(\\ \sf{:}\longrightarrow x\approx 3\)