Julie needs to cut 4 pieces of yarn, each with the same length, and a piece of yarn 7.75 inches long. let x represent the length of each of the equal pieces of yarn that julie decides to cut. what is the equation that can be used to determine the total length of all the yarn that she ends up cutting, y? is the graph of the equation continuous or discrete?

Answer:

A B C D

A×B×C×D

3×3×3×6

162

Answer:

B the range, the x- and y-intercept

Step-by-step explanation:

the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).

but the range changes, as for the original function y could only have positive values - even for negative x.

the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.

the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.

the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.

the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.

the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)

[tex] 3 {b}^{x + 1} = 2[/tex]

[tex] {b}^{x + 1} = 2 \div 3[/tex]

[tex] log_{b}(2 \div 3) = x + 1[/tex]

[tex]x = log_{b}(2 \div 3) - 1[/tex]

9514 1404 393

Answer:

  k = 3

Step-by-step explanation:

It is convenient to look at the line y=1 to see that f(0) = 1 and g(3) = 1. Then for x=3, g(3) = f(3 -k) = f(0) = 1

  k = 3

__

k is the amount by which the function has been shifted to the right. By comparing grid-intersection points on f(x) and g(x), we see that g(x) is 3 units to the right of f(x), so k = 3.

9514 1404 393

Answer:

  A

Step-by-step explanation:

The function f(x) is required in the numerator, eliminating choices C and D.

The restriction is that function g cannot be zero, so we cannot have ...

  3x +2 = 0

  3x = -2

  x = -2/3 . . . . . eliminates choice B; confirms choice A

Answer:

five kids .each 6 sweaters and 9 trousers

Step-by-step explanation:

Step-by-step explanation:

198×202=39,996

200×200=40,000

hence,

39,9996 < 40,000

hope it helps

Answer:

b)  [tex]c=1[/tex]

Step-by-step explanation:

From the question, we are told that:

Function

[tex]F(x)=2x^2-4x+9[/tex]

Given

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

Generally, the Function above is a polynomial that can be Differentiated and it is continuous

Where

-F(x) is continuous at (-1,3)

-F(x) Can be differentiated at (-1.3)

-And F(-1)=F(3)

Therefore

F(x) has Satisfied all the Requirements for Rolle's Theorem

Differentiating F(x) we have

[tex]F'(x)=4x-4[/tex]

Equating F(c) we have

[tex]F'(c)=0[/tex]

[tex]4(c)-4=0[/tex]

Therefore

[tex]c=1[/tex]

Answer:

[tex]C(n) = 435n + 150[/tex]

Step-by-step explanation:

Given

[tex]Base = 400[/tex] -- Base charge per month

[tex]Utilities = 150[/tex]

[tex]Adverts = 35[/tex] per month

Required

The cost function

To do this, we multiply the rates by the number of months.

So, we have:

[tex]C(n) = Base * n + Adverts * n + Utilities[/tex]

So, we have:

[tex]C(n) = 400 * n + 35 * n + 150[/tex]

[tex]C(n) = 400n + 35n + 150[/tex]

[tex]C(n) = 435n + 150[/tex]

Answer:

22hrs

Step-by-step explanation:

hope it is well understood?

Answer: x = 24

Step-by-step explanation:

Use the Pythagorean Theorem:

[tex]x^{2}+18^{2}=30^{2} \\x^{2} = 30^{2}-18^{2}\\x=\sqrt{30^{2}-18^{2}}=\sqrt{900-324}=\sqrt{576} =24[/tex]

Answer:

Mark Brainliest please

The answer is 1

Step-by-step explanation:

(1 — x^ m-n) ^-1 + (1- x ^n-m)^ -1

1/[1-x^(m-n)] + 1/[1-x^(n-m)]

1/[1-x^m × x^(-n)] + 1/[1-x^n × x^(-m)]

x^n/(x^n - x^m) + x^m/(x^m - x^n)

x^n/(x^n - x^m) - x^m/(x^n - x^m)

Now taking the LCM here, we get

(x^n - x^m)/(x^n - x^m)

Answer:

(3, 6)

Step-by-step explanation:

The vertex form of a quadratic is y = a(x-h)^2 + k

where (h, k) is the point of the vertex. So the answer is (3,6)

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

Car 1 Car 2

214 220

245 221

239 244

224 225

220 258

295 259

Ordered data:

Car 1 : 214, 220, 224, 239, 245, 295

Sample mean = ΣX/ n ; n = sample size = 6

Sample mean = 1437 / 6 = 239.5

Median = 1/2(n+1)th term = 1/2(7) = 3.5th term

Median = (3rd + 4th) /2 = (224 + 239) /2 = 231.5

Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 29.60 (using calculator)

Car 2 : 220, 221, 225, 244, 258, 259

Sample mean = ΣX/ n ; n = sample size = 6

Sample mean = 1427 / 6 = 237.833

Median = 1/2(n+1)th term = 1/2(7) = 3.5th term

Median = (3rd + 4th) /2 = (225 + 244) /2 = 234.5

Sample standard deviation; √(Σ(x - xbar)²/n-1 ) = 18.21 (using calculator)

A sample of size n taken from a normally distributed population with mean µ and standard deviation σ has a sample mean of µ and standard deviation of σ/√n.

So the sample mean would still be 180.1, while the sample standard deviation would be 100/√94 ≈ 10.31.

Answer:

8x^4+9x^3+4x-1

Step-by-step explanation:

(6x^3 – 5x^2 + 3x – 5) + (8x^4 + 3x^3 + 5x^2 + x + 4)

Group like terms

8x^4+6x^3+3x^3-5x^2+5x^2+3x+x-5+4

8x^4+9x^3+4x-1

Answer:

[tex]\left(6x^3-5x^2+3x-5\right)+\left(8x^4+3x^3+5x^2+x+4\right)[/tex]

Combine like terms

[tex]=8x^4+6x^3+3x^3-5x^2+5x^2+3x+x-5+4[/tex]

Add: -5x²+5x²=0

[tex]=8x^4+6x^3+3x^3+3x+x-5+4[/tex]

Now add 6x³+3x³=9x³

[tex]=8x^4+9x^3+3x+x-5+4[/tex]

Add like terms 3x +x=4x

[tex]=8x^4+9x^3+4x-5+4[/tex]

Now add -5+4=-1

[tex]=8x^4+9x^3+4x-1[/tex]

OAmalOHopeO

Answer:

Step-by-step explanation:

                  4km

[tex]\frac{3 }{27} \frac{miles}{minutes}[/tex] * [tex]\frac{60}{1} \frac{min}{hour}[/tex] * [tex]\frac{1}{.6213} \frac{km}{mile}[/tex]

4km ÷ 10.73 km/hr = .37 hr = 22.3 minutes

Answer:

8m

Step-by-step explanation:

We know that vertically opposite angles are equal.

So, k = 131° [Vertically opposite angles]

and g = 43° [Vertically opposite angles]

We know that linear pair of angles are supplementary (180°).

So, h + 43° = 180° [Linear pair of angles]

=> h = 180° - 43°

=> h = 137°

and m + 131° = 180° [Linear pair of angles]

=> m = 180° - 131°

=> m = 49°

Answer:

B

Step-by-step explanation:

hope it is well understood

Answer:

15 cm

Step-by-step explanation:

Since the traingles are similar, we can find the ratio between the side lengths, and it will be the same for each side.

We can use the side length 9 and 15 to find this ratio. 15/9=5/3. So, the ratio of a side length of the larger triangle to the smaller one is 5/3, so our equation becomes 5/3 = 25/x. Use any method you like to find that x=15.

Hope this helped,

~cloud

Answer:

7000 and 8000 respectively

Step-by-step explanation:

Let x be invested in first account and x+1000 be invested in second account.

ATQ, 830=(5)*x/100+6*(x+1000)/100. Solving it will give us x=7000

The amount Seth invested at 5% is 7000 dollars and the amount Seth invested at 6% is 8000 dollars.

A percentage is a value per hundredth. We can also convert percentages into decimals and fractions.

We know, SI = P×r×t/100, where SI = Simple interest, P = principle,

r = rate in % and t = time in years.

Assuming the total amount to be x dollars.

∴ x×5×1/100 + ( x + 1000)×6×1/100 = 830.

5x/(100) + (6x + 6000)/100 = 830.

5x + 6x + 6000 = 83000.

11x = 77000.

x = 7000.

Therefore the amounts are 7000 and (7000 + 1000) = 8000.

learn more about percentage here :

https://brainly.com/question/24159063

#SPJ2

y + z + r + x = 360

2x + 3x + 4x + x = 360

10x = 360

x = 360/10

x = 36

Now

x = 36

y = 72

z = 108

r = 144

Answered by Gauthmath must click thanks and mark brainliest

Answer:

α = 0.01 ; 2 - tailed

χ² = 16.998

Pvalue = 0.1497

Fail to reject H0

Step-by-step explanation:

Given the data above :

Number of People Making Contribution

Ethnic Group $1-50 $51-100 $101-150 $151-200 Over $200 Row Total

A 77 63 54 39 18 251

B 90 48 76 26 24 264

C 73 67 59 37 30 266

D 108 82 70 50 30 340

Column Total 348 260 259 152 102 1121

1.) The level of significance, α/2 = 0.01/2

2.)

The hypothesis :

H0 : Contribution and Ethnic group are independent

H1 : Contribution and Ethnic group are not independent

The Chisquare statistic :

χ² = (Observed - Expected)²/ Expected

The expected value for each cell is calculated thus :

(Row total * column total) / sum total

The expected values :

77.9197 58.2159 57.992 34.0339 22.8385

81.9554 61.231 60.9955 35.7966 24.0214

82.5763 61.6949 61.4576 36.0678 24.2034

105.549 78.8582 78.5549 46.1017 30.9367

Using the χ² formula above ;

χ² values for each cell are :

0.010855 0.393154 0.274794 0.724635 1.02509

0.789645 2.85902 3.69099 2.68108 0.0000191

1.11055 0.456179 0.098278 0.0240936 1.38826

0.056933 0.125176 0.93165 0.32963 0.028359

Taking the sum :

0.010855+0.393154+0.274794+0.724635+1.02509+0.789645+2.85902+3.69099+2.68108+0.0000191+1.11055+0.456179+0.098278+0.0240936+1.38826+0.056933+0.125176+0.93165+0.3293+0.028359

χ² = 16.998

To obtain the Pvalue :

df = (Row - 1)(column - 1) = (5-1)*(4-1) = 4 * 3 = 12

Pvalue(16.998 ; 12) = 0.1497

If Pvalue < α ; Reject H0 ;

Since Pvalue > α ; WE fail to reject H0

Answer:

last one

Step-by-step explanation:

they both whole

Answer:

(42% ; 48%)

We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%

Step-by-step explanation:

The confidence interval is used to estimate the range of values for which the population value may lie at a certain level of confidence.

Given that :

Phat = 45%

Margin of error = ±3%

The confidence interval is defined as :

C. I = Phat ± margin of error

C. I = 45% ± 3%

Lower boundary :

45% - 3% = 42%

Upper boundary :

45% + 3% = 48%

C.I = (42% ; 48%)

We are 99% confident that the percentage of all adults in the country who favor a plan to break up the megabanks is between 42% and 48%

9514 1404 393

Answer:

  $11,715.65

Step-by-step explanation:

The applicable formula is ...

  FV = P(1 +r/n)^(nt)

where principal P earns interest at rate r compounded n times per year for t years.

  FV = $9500(1 +0.042/12)^(12·5) = $9500(1.0035^60) ≈ $11,715.65

The account will hold $11,715.65 after 5 years.

Step-by-step explanation:

[tex] \frac{{(3 + u)}^{2} }{8} [/tex]

[When u = 5]

[tex] = \frac{{(3 + 5)}^{2} }{8} [/tex]

[tex] = \frac{ {(8)}^{2} }{8} [/tex]

[tex] = \frac{8 \times 8}{8} [/tex]

= 8 (Ans)

-2(a - 7)

(Using Distributive property)

= - 2 × a -2 × (-7)

= -2a + 14 (Ans)

Answer:

7. 8

8. -2a+14

Step-by-step explanation:

(Excuse this form of the expression)

7.

u = 5

(3 + u)²

---------

   8

Plug in

(3 + 5)²

---------

   8

  (8)²

---------

   8

64

---- = 8

8

8.

-2(a - 7)

Multiply -2 with each number in the parenthesis

-2a + 14

Answer:

13

Step-by-step explanation:

f(x) = 4x + 1

Let x= 3

f(3) = 4*3+1

    = 12+1

   = 13

Answer:

-290

Step-by-step explanation:

(-260) +(-30)

=-260-30

=-290

Answer:

the answer is -290

Step-by-step explanation:

it is telling us to add so we can see that both the numbers have the same sign which is negative

when the signs are all the same, we can add and we got -290

Answer:

The probability is 0.857

Step-by-step explanation:

We know that:

There is a total of 440 cars

There are 63 cars with defective turn signals

There are 39 with defective tires.

Now we want to find the probability that a randomly selected car does not have defective turn signals.

If all the cars have the same probability of being selected, this probability will be equal to the quotient between the number of cars that do not have defective turn signals and the total number of cars.

We know that the total number of cars is 440

And 63 of these have defective turn signals, then the rest don't.

440 - 63 = 377 cars do not have defective turn signals.

Then the probability is:

P = 377/440 = 0.857