Can someone help me out with this question ( pre-calculus)....................

The solution is:  the rate of change is 3.

Here, we have,

Since the graph of f(x) is translated 1 unit down, we need to decrease the value of f(x) by 1 to find g(x):

g(x) = f(x) - 1

f(x) = 3|x| – 4

so, we get,

g(x) = 3|x| – 4 - 1

      = 3|x| – 5

Now, to calculate the rate of change over the interval 2 <= x <= 5, we can use the formula below:

rate = g(5) - g(2)/ 5-2

so, we get,

rate = 9/3 = 3

Therefore the rate of change is 3.

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Answer:

4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

5/1-3/8= 4 5/8

4 5/8- 5/8= 4

Answer:

19, 21, 23

Step-by-step explanation:

Answer:

the coefficient of the squared expression is 5.

Step-by-step explanation:

the equation of a parabola in its vertex form is y=a(x-h)²+k, where (h, k) is the vertex of the parabola.

in this case, h=3, k=-2, so y=a(x-3)-2

plug (4,3) in the equation: 3=a(4-3)²-2, a=5

Answer:

23.1 liters

Step-by-step explanation:

7 x 3.3 = 23.1

Answer:23.

Step-by-step explanation:

For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.

What is function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.

A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).

Four orders of functions live functions with return values and arguments.

This function accepts arguments and gives back a result.

functions that take arguments but have no return values.

functions with return values and no arguments.

functions that have no arguments or return values.

we are given two function f( x) and g( x);

f( x) = 3x- 2 and

g( x) = x2

So, for fg( x), we've to put value of g( x) into f( x);

Hence, the equation will be;

fg( x) = 3x2- 2.

thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.

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The number of trials and the probability of obtaining success will be given as P(X ≤ 2) = 0.9728.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X \sim B(n,p)

The probability that out of n trials, there'd be x successes is given by

\(\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

Assume the random variable X has a binomial distribution with the given probability of obtaining success.

Then the number of trials and the probability of obtaining success will be

P(X ≤ 2), n = 4, p = 0.2

Then we get

\(\rm P(X =2) = \: ^4C_2(0.2)^2(1-0.2)^{4-2}\\\\P (X=2) = 6 \times 0.0256 \\\\P (X=2) = 0.1536\)

Then the cumulative probability will be

\(\rm P(X\leq 2) = 0.9728\)

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Step-by-step explanation:

Step 1- convert 25% into a decimal

Step 2- Multiply 34,400.00 x 0.25

            Which should give you $8600.00

Step 3- Then subtract 34,400.00 from 8600.00

              Which will give you $25800.0

The The thing to remember is Multiply with the discount then subtract your answer from the original price of the item.

Hope This Helps !!

Answer:

Between 6 & 7

Step-by-step explanation:

The square root of 45 is 6.7. So it'll be between 6 & 7.

Answer:

the answer is 8 oz

Step-by-step explanation:

well it says for the first ounce is $0.49 so $0.49 is your first number, then you're trying to figure out how many $.21

2.then to make this easier you subtract $0.49 from $1.96 and that's is $1.47

3.then all you need to do is divide $1.47 By .21 cents anand you should get 7.

4.but don't forget the $0.49 for the first ounce, then 1 ounce add it to the 7 and It will equal 8 oz in total

Step-by-step explanation:

Step-by-step explanation:

hey mate!

you can use gauth math

you can easily find the answer and practice

there are tickets to find tutors who are brilliant at math .

it is so helpful

it is like photo math

first click the photo there is an option and get started!

Answer:

Letter A

Step-by-step explanation:

The domain is the input or the x-value

The range is the output or the y-value

Hope this helps

Answer:

(a) BC = 91 cm

(b) ∠C = 33.4° (nearest tenth)

(c) AD = 79.5 cm (nearest tenth)

Step-by-step explanation:

(a) Pythagoras' Theorem:  a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

⇒ 60² + BC² = 109²

⇒ 3600 + BC² = 11881

⇒ BC² = 11881 - 3600

⇒ BC² = 8281

⇒ BC = √(8281)

⇒ BC = 91 cm

(b) Sine rule to find an angle:

   \(\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}\)

(where A, B and C are the angles, and a, b and c are the sides opposite the angles)

Given:

\(\implies \dfrac{\sin (90)}{109}=\dfrac{\sin C}{60}\)

\(\implies \sin C=60 \cdot\dfrac{\sin (90)}{109}\)

\(\implies \sin C=\dfrac{60}{109}\)

\(\implies C=33.39848847...\textdegree\)

\(\implies C=33.4\textdegree \ \sf(nearest \ tenth)\)

(c) Sine rule to find a side length:

   \(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}\)

(where A, B and C are the angles, and a, b and c are the sides opposite the angles)

Sum of interior angles of a triangle = 180°

Given:

\(\implies \dfrac{AD}{\sin (90)}=\dfrac{60}{\sin (49)}\)

\(\implies AD=\sin (90) \cdot \dfrac{60}{\sin (49)}\)

\(\implies AD=79.5007796...\)

\(\implies AD=79.5 \ \sf cm \ (nearest \ tenth)\)

Answer:

x = 16

Step-by-step explanation:

subtract 12 from both sides to isolate the variable and its coefficient

4x = 64

divide both sides by 4 to get x

x = 16

Answer:

x = 16

Step-by-step explanation:

4x+12=76

Step 1: Subtract 12 from both sides.

4x + 12 - 12 = 76 - 12

4x = 64

Step 2: Divide both sides by 4.

\(\frac{4x}{4} = \frac{64}{4}\)

x = 16

Answer:

⁶⁄₉ = ²⁄₃,     ⁹⁄₆ = ³⁄₂,     ⁹⁄₃ = ⁶⁄₂,     ²⁄₆ = ³⁄₉

Step-by-step explanation:

☀First we will do the extremes of the problem ²/₆

☀Now we will do the means  of the problem ³⁄₉

                 We now have

                       ²/₆ =³⁄₉, now we can solve, here are the possible proportions we can make:

⁶⁄₉ = ²⁄₃,     ⁹⁄₆ = ³⁄₂,     ⁹⁄₃ = ⁶⁄₂,     ²⁄₆ = ³⁄₉

Complete question :

Assume that both populations are normally distributed. ​a) Test whether mu 1 not equals mu 2 at the alpha equals 0.05 level of significance for the given sample data. ​b) Construct a 95​% confidence interval about mu 1 minus mu 2. Sample 1 Sample 2 n 19 19 x overbar 16.2 14.1 s 4.5 3.1

Answer:

(-0.445 ; 4.645)

Null:

H0: mu1 - mu2 = 0

H1 : mu1 - mu2 ≠ 0

Step-by-step explanation:

__________Sample 1 ____ Sample 2

n ___________19 _________19

x overbar ____16.2 ________14.1

s __________ 4.5 _________3.1

The confidence interval : (2 independent means)

(x1 - x2) ± Tcritical * √(s1²/n1) + (s2²/n2)

T(1 - α/2), 36 = 2.03

(16.2 - 14.1) ± 2.03 * √(4.5²/19) + (3.1²/19)

2.1 ± 2.545

Lower boundary = (2.1 - 2.545) = - 0.445

Upper boundary = (2.1 + 2.545) = 4.645

(-0.445 ; 4.645)

Step-by-step explanation

Answer:

E only

Step-by-step explanation:

In conclusion  the value that correctly fills in the blank in the table is 0.69.

Why it is?

To find the relative frequency of boys, we need to use the information given in the frequency table. We know that the total number of boys is 120 - 37 = 83, since the total number of students is 120 and the number of girls is 37.

We can then calculate the relative frequency for boys by dividing the number of boys who prefer math or social studies (40 + 43 = 83) by the total number of students (120):

Relative frequency for boys = (40 + 43) / 120 ≈ 0.69

Rounding to the nearest hundredth, we get:

Relative frequency for boys ≈ 0.69

Therefore, the value that correctly fills in the blank in the table is 0.69.

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Answer:

y = -2x + 21

Step-by-step explanation:

use point intercept form: y = mx + b where m is the slope and b is the y intercept

to find the y intercept, b, plug in values into equation and solve for b

11 = (-2) (5) + b

b = 21

then plug into the equation the slope and intercept!

The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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Answer:

\(\displaystyle y=\frac{1}{2}x-2\)

The point-slope form is represented with the formula:

\(y-y_1=m(x-x_1)\)

We are given a point \((x_1, y_1)\) and a slope: \(\displaystyle \frac{1}{2}\).

We are asked to solve this equation in slope-intercept form, which is:

\(y=mx+b\)

Givens

\(x_1: 10\\\\y_1: 3\\\\\displaystyle m: \frac{1}{2}\)

To solve:

1. Substitute the givens into the point-slope form equation:

\(y-y_1=m(x-x_1)\\\\\displaystyle y-3=\frac{1}{2}(x-10)\)

2. Simplify by using the distributive property, which states:

\(a(b+c)=ab+ac\)

\(\displaystyle y-3=\frac{1}{2}x-5\)

3. Simplify further by combining like terms:

\(\displaystyle y-3+3=\frac{1}{2}x-5+3\\\\\displaystyle y=\frac{1}{2}x-2\)

The final answer in slope-intercept form is:

\(\large \boxed{\displaystyle y=\frac{1}{2}x-2}\)

Answer:

y = 1/2x - 2

Step-by-step explanation:

Step 1:

y = mx + b      Slope Intercept Form

Step 2:

y = 1/2x + b          Equation

Step 3:

3 = 1/2 ( 10 ) + b         Input x and y

Step 4:

3 = 5 + b         Multiply

Step 5:

3 - 5 = b      Subtract 5 on both sides

Step 6:

b = - 2

Answer:

y = 1/2x - 2

Hope This Helps :)

Answer:

100

Step-by-step explanation:

We have the sum of first n terms of an AP,

Sn = n/2 [2a+(n−1)d]

Given,

36= 6/2 [2a+(6−1)d]

12=2a+5d ---------(1)

256= 16/2 [2a+(16−1)d]

32=2a+15d ---------(2)

Subtracting, (1) from (2)

32−12=2a+15d−(2a+5d)

20=10d ⟹d=2

Substituting for d in (1),

12=2a+5(2)=2(a+5)

6=a+5 ⟹a=1

∴ The sum of first 10 terms of an AP,

S10 = 10/2 [2(1)+(10−1)2]

S10 =5[2+18]

S10 =100

This is the sum of the first 10 terms.

Hope it will help.

\(\sf\underline{\underline{Question:}}\)

If sum of first 6 digits of AP is 36 and that of the first 16 terms is 255,then find the sum of first ten terms.

$\sf\underline{\underline{Solution:}}$

$\space$

$\sf\underline\bold\red{||Step-by-Step||}$

$\sf\bold{Given:}$

$\space$

$\sf\bold{To\:find:}$

$\space$

$\sf\bold{Formula\:we\:are\:using:}$

$\implies$ $\sf{ Sn=}$ $\sf\dfrac{N}{2}$ $\sf\small{[2a+(n-1)d]}$

$\space$

$\sf\bold{Substituting\:the\:values:}$

→ $\sf{S6=}$ $\sf\dfrac{6}{2}$ $\sf\small{[2a+(6-1)d]}$

→ $\sf{36 = 3[2a+(6-1)d]}$

→$\sf{12=[2a+5d]}$ $\sf\bold\purple{(First \: equation)}$

$\space$

$\sf\bold{Again,Substituting \: the\:values:}$

→ $\sf{S16}$ $\sf\dfrac{16}{2}$ $\sf\small{[2a+(16-1)d]}$

→ $\sf{255=8[2a + (16-1)d]}$

:: $\sf\dfrac{255}{8}$ $\sf\small{=31.89=32}$

→ $\sf{32=[2a+15d]}$ $\sf\bold\purple{(Second\:equation)}$

$\space$

$\sf\bold{Now,Solve \: equation \: 1 \:and \:2:}$

→ $\sf{10=20}$

→ $\sf{d=}$ $\sf\dfrac{20}{10}$ $\sf{=2}$

$\space$

$\sf\bold{Putting \: d=2\: in \:equation - 1:}$

→ $\sf{12=2a+5\times 2}$

→ $\sf{a = 1}$

$\space$

$\sf\bold{All\:of\:the\:above\:eq\: In \: S10\:formula:}$

$\mapsto$ $\sf{S10=}$ $\sf\dfrac{10}{2}$ $\sf\small{[2\times1+(10-1)d]}$

$\mapsto$ $\sf{5(2\times1+9\times2)}$

$\mapsto$ $\sf\bold\purple{5(2+18)=100}$

$\space$

$\sf\small\red{||Hence , the \: sum\: of \: the \: first\:10\: terms\: is\:100||}$

_____________________________

Answer:

(d) 18 in.

Step-by-step explanation:

When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:

P = s1 + s2 + s3, where

P = 2 + 6 + 10

P = 8 + 10

P = 18

Thus, the perimeter of the triangle is 18 in.

Answer:

I'll consider just 3

Step-by-step explanation:

To check if a number is a prime number it has to undergo series of division.

Let's not forget that a prime number is a number divisible by only itself and one

So for my argument.

2 cannot the number

3 cannot also divide the number

5 and 7 too cannot Divide the number.

I'll consider just 3 as the highest prime number to divide it

Answer:

60 is the measure of C in degrees