How many solutions does the following equation have?
-5(z+1)=-2z+10
Choose 1 answer:
A: No solutions
B: Exactly one solution
C: Infinitely many solutions

Answer:

C

Step-by-step explanation:

An arithmetic sequence has a common difference d between consecutive terms.

Sequence a

30 - 10 = 20

90 - 30 = 60

270 - 90 = 180

This sequence is not arithmetic

Sequence b

200 - 100 = 100

300 - 200 = 100

400 - 300 = 100

This sequence is arithmetic but is finite, that is last term is 400

Sequence c

300 - 150 = 150

450 - 300 = 150

600 - 450 = 150

This sequence is arithmetic and infinite, indicated by ........ within set

Sequence d

2 - 1 = 1

4 - 2 = 2

8 - 4 = 4

This sequence is not arithmetic

Thus the infinite arithmetic sequence is sequence c

Answer:

False

Step-by-step explanation:

Regression model is a set of statistical process which estimates the relationship between two variables. The one variable is dependent variable and the other is independent variable. The statistician should not use printout C to perform a t-test in regression model.

Answer:

5

----------

( n+1)(n+2)

Step-by-step explanation:

5

----------

n ( n+1)

Replace n with n+1

5

----------

(n+1) ( n+1+1)

5

----------

( n+1)(n+2)

We replace every 'n' with n+1 and simplify

[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]

Answer:

B - %9230.77

Step-by-step explanation:

the original price of the fencing before the trade discount was approximately $9,230.77.

To find the original price of the fencing before the trade discount, we need to calculate the amount that corresponds to a 35% decrease from the discounted price.

Let's denote the original price as "P". The discounted price is given as $6,000.

The discounted price is calculated by subtracting the discount amount from the original price:

Discounted price = Original price - Discount amount

The discount amount is determined by multiplying the original price by the discount rate:

Discount amount = Original price × Discount rate

Given that the discount rate is 35% (or 0.35), we have:

Discount amount = P × 0.35

Substituting the discounted price of $6,000, we can write the equation as:

$6,000 = P - (P × 0.35)

Simplifying the equation:

$6,000 = P(1 - 0.35)

$6,000 = P(0.65)

To solve for P, we divide both sides of the equation by 0.65:

P = $6,000 / 0.65

P ≈ $9,230.77

Therefore, the original price of the fencing before the trade discount was approximately $9,230.77.

The correct answer is B. $9,230.77.

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Answer:

(1, -9)  yes

(7,3)  no

(-9,4)  no

(0, -9) yes

Step-by-step explanation:

The y value must be -9

The x value can be any value to satisfy   the equation y = -9

Answer:

The Variable has a coefficient.

Step-by-step explanation:

Answer:

number of nickel = 60

number of dimes  = 20

Step-by-step explanation:

1 nickel = 5 cents

1 dimes = 10 cents

$1 = 100 cents

we will use these value to solve the questions

_______________________________

Total no of coins = 80

let the number of nickels be x

let the number of dimes be y

thus,

x+y = 80

y = 80-x   equation 2

value of x nickels = 5x

value of y dimes = 10y

Total value of x nickels and y dimes = 5x+10y

The total value of the coins is $5.00

total value of the coins in cents = 5*100 = 500

thus

5x+10y = 500

using y = 80-x   from equation 2

5x + 10(80 - x) = 500

5x + 800 - 10x = 500

-5x = 500 - 800 = -300

x = -300/-5 = 60

Thus,

number of nickel = 60

number of dimes = 80-60 = 20

Answer:

c is congruent to e congruent means to be the same

Step-by-step explanation:

From your earlier questions, we found

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

so the wave has amplitude √29. The weight's maximum negative position from equilibrium is then -√29, so you are solving for t in the given interval for which

[tex]\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac{\sqrt{29}}2[/tex]

Divide both sides by √29:

[tex]\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)=-\dfrac12[/tex]

Take the inverse sine of both sides, noting that we get two possible solution sets because we have

[tex]\sin\left(\dfrac{7\pi}6\right)=\sin\left(\dfrac{11\pi}6\right)=-\dfrac12[/tex]

and the sine wave has period 2π, so [tex]\sin x=\sin(x+2\pi)=\sin(x+4\pi)=\cdots[/tex].

[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{7\pi}6+2n\pi[/tex]

OR

[tex]\implies 4\pi t+\tan^{-1}\left(\dfrac52\right)=\dfrac{11\pi}6+2n\pi[/tex]

where n is any integer.

Now solve for t :

[tex]t=\dfrac{\frac{7\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]

OR

[tex]t=\dfrac{\frac{11\pi}6+2n\pi-\tan^{-1}\left(\frac52\right)}{4\pi}[/tex]

We get solutions between 0 and 0.5 when n = 0 of t ≈ 0.196946 and t ≈ 0.363613.

Answer:

f(1/3) = 6

Step-by-step explanation:

f(x) =-3x+7

Let x = 1/3

f(1/3) =-3*1/3+7

        = -1 +7

       = 6

Answer:

f(1/3) = 6

Step-by-step explanation:

The function is:

● f(x) = -3x+7

Replace x by 1/3 to khow the value of f(1/3)

● f(1/3) = -3×(1/3) +7 = -1 +7 = 6

Answer:

x^2 -12x+35

Step-by-step explanation:

(x−5)(x−7)

FOIL

first  x*x = x^2

outer -7x

inner -5x

last -7*-5 = 35

Add them together

x^2 -7x-5x +35

x^2 -12x+35

Answer:

Step-by-step explanation:

x*x=2x

x*-7=-7x

-5*x=-5x

-5*-7=+35

2x-12x+35

A

Answer:

Hope this helps :)

Step-by-step explanation:

A scatter plot is a two-dimensional diagram that displays individual data points based on the intersection of two variables, shown as vertical and horizontal axes. Individual data points or values are plotted at particular coordinates of the two variables being studied. Patterns of data points provide a visual representation of relationship between the two variables. A wide range of jobs and careers use this valuable analytical tool for data analysis and decision making.

My conclusion,

They help organize important data for future occurences.

When we write expression 5√(4x² + 1) + 20x / √(4x² + 1) as singled term factorised completely, we have 5(4x² + 4x + 1) / √(4x² + 1) (Option A)

5√(4x² + 1) / 1 + 20x / √(4x² + 1)

Least common multiple (LCM) is √(4x² + 1)

[(5√(4x² + 1) × √(4x² + 1) + 20x] / √(4x² + 1)

[5(4x² + 1) + 20x] / √(4x² + 1)

[20x² + 5 + 20x] / √(4x² + 1)

[20x² + 20x + 5] / √(4x² + 1)

5(4x² + 4x + 1) / √(4x² + 1)

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Complete question

See attached photo

Answer:

Step-by-step explanation:

This problem can be solved using the compound interest formula

[tex]A= P(1+r)^t[/tex]

Given data

A, final amount =?

P, principal = $586

rate, r= 6.6% = 0.066

Time, t= 13 years

Substituting our values into the expression we have

[tex]A= 586(1+0.066)^1^3\\\ A= 586*(1.066)^13\\\ A= 586*2.295\\\ A= 1344.87[/tex]

To the nearest cent the in 13 years the CD will be worth $1344.9

Answer:

Option C - Reject H0. We have convincing evidence that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722.

Step-by-step explanation:

First of all let's define the hypothesis;

Null hypothesis;H0; μ = $48,722

Alternative hypothesis;Ha; μ > $48,722

Now, let's find the test statistic for the z-score. Formula is;

z = (x' - μ)/(σ/√n)

We are given;

x' = 48,722

μ = 49,870

σ = 3900

n = 50

Thus;

z = (49870- 48722)/(3900/√50)

z = 2.08

So from online p-value calculator as attached, using z = 2.08 and α = 0.05 ,we have p = 0.037526

This p-value of 0.037526 is less than the significance value of 0.05,thus, we reject the claim that that the mean salary offer for accounting graduates of this university is higher than the national average of $48,722

Answer:

82

Step-by-step explanation:

Plug in the variables into the equation and solve for B but remember your order of operations when solving multiplication/division before addition/subtraction.

B = 4*25-9*2

B = 100-18

B = 82

Step-by-step explanation:

83P (E)=17-17P (E),

P (E)=17/100=0.17

Answer:

2.7 in²

Step-by-step explanation:

Given that ∆BAC ~ is similar to ∆EDF, the ratio of the area of ∆BAC to the area of ∆EDF = the square of the ratio of their corresponding sides.

Thus, let x be the area of ∆EDF

[tex] \frac{6}{x} = (\frac{3}{2})^2 [/tex]

[tex] \frac{6}{x} = \frac{9}{4} [/tex]

Cross multiply

[tex] x*9 = 4*6 [/tex]

[tex] 9x = 24 [/tex]

[tex] \frac{9x}{9} = \frac{24}{9} [/tex]

[tex] x = 2.67 [/tex]

Area of ∆EDF = 2.7 in²

Answer:

2·5·5·5·5

Step-by-step explanation:

2(5)^4 is equivalent to 2·5·5·5·5; 2 is used as a multiplicand just once, but 5 is used four times.

Answer:

About $1.75 per tennis balls

Step-by-step explanation:

A tin of 4 tennis balls costs $6.99. We are asked to find the price of one tennis ball.

We need to find the unit price, or price per ball.

Divide the cost by the number of tennis balls.

cost / tennis balls

cost = $6.99

tennis balls = 4 tennis balls

$6.99 / 4 tennis balls

Divide 6.99 by 4.

$1.7475 / 1 tennis ball

Round to the nearest cent or hundredth. The 7 in the thousandth place tells us to round the 4 to a 5 in the hundredth place.

$1.75 / 1 tennis ball

It would cost approximately $1.75 for one tennis ball.

Answer:

a) No sufficient evidence to support the claim that the two machines produce rods with different mean diameters.

b) P-value is 0.80

c)  −0.3939 <μ< 0.4939

Step-by-step explanation:

Given Data:

sample sizes

n1 = 15

n2 = 17

sample means:

x1 = 8.73

x2 = 8.68

sample variances:

s1² = 0.35

s2² = 0.40

Hypothesis:

H₀ : μ₁ = μ₂

H₁ :  μ₁ ≠ μ₂

Compute the pooled standard deviation:

[tex]s_{p} = \sqrt{\frac{(n_{1} - 1)s_{1}^{2} + (n_{2} - 1)s_{2}^{2}}{n_{1} +n_{2} -2} }[/tex]

    [tex]= \sqrt{\frac{(15-1)0.35+(17-1)0.40}{15+7-2}}[/tex]

    [tex]= \sqrt{\frac{(14)0.35+(16)0.40}{30}}[/tex]

 [tex]= \sqrt{\frac{4.9+6.4}{30}}[/tex]

 [tex]= \sqrt{\frac{11.3}{30}}[/tex]

[tex]= \sqrt{0.376667}[/tex]

= 0.613732

= 0.6137

Compute the test statistic:

[tex]t = \frac{x_{1} -x_{2} }{s_{p} \sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } } }[/tex]

[tex]= \frac{8.73-8.68}{0.6137\sqrt{\frac{1}{15}+\frac{1}{17} } }[/tex]

[tex]= \frac{0.05}{0.6137\sqrt{0.06667+0.05882} } }[/tex]

[tex]= \frac{0.05}{0.6137\sqrt{0.12549} } }[/tex]

[tex]= \frac{0.05}{0.6137(0.354246)} } }[/tex]

[tex]= \frac{0.05}{0.6137(0.354246)} } }[/tex]

= 0.05 / 0.217401

= 0.22999

t = 0.230

Compute degree of freedom:

df = n1 + n2 -2 = 15 + 17 - 2 = 30

Compute the P-value from table using df = 30

P > 2 * 0.40 = 0.80

P > 0.05 ⇒ Fail to reject H₀

Null hypothesis is rejected when P-value is less than or equals to level of significance. But here the P-value = 0.80 and level of significance = 0.05. So P-value is greater than significance level. Hence there is not sufficient evidence to support the claim that population means are different.

Construct a 95% confidence interval for the difference in mean rod diameter:

confidence = c = 95% = 0.95

α = 1 - c

  = 1 - 0.95

α = 0.05

Compute degree of freedom:

df = n1 + n2 -2 = 15 + 17 - 2 = 30

Compute [tex]t_{\alpha /2}[/tex] with df = 30 using table:

t₀.₀₂₅ = 2.042

Compute confidence interval:

= [tex](x_{1}-x_{2})-t_{\alpha/2} ( s_{p} )\sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } }[/tex]

= (8.73 - 8.68) -  2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]

= 0.05 - 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]

= 0.05 - 1.253175 [tex]\sqrt{0.06667+0.05882} } }[/tex]

= 0.05 - 1.253175 [tex]\sqrt{0.12549} } }[/tex]

= 0.05 - 1.253175 (0.35424))

= 0.05 - 0.443925

= −0.393925

= −0.3939

[tex](x_{1}-x_{2})+t_{\alpha/2} ( s_{p} )\sqrt{\frac{1}{n_{1} }+\frac{1}{n_{2} } }[/tex]

= (8.73 - 8.68) +  2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]

= 0.05 + 2.042 ( 0.6137 ) [tex]\sqrt{\frac{1}{15} +\frac{1}{17} }[/tex]

= 0.05 + 1.253175 [tex]\sqrt{0.06667+0.05882} } }[/tex]

= 0.05 + 1.253175 [tex]\sqrt{0.12549} } }[/tex]

= 0.05 + 1.253175 (0.35424))

= 0.05 + 0.443925

= 0.493925

= 0.4939

−0.3939 <μ₁ - μ₂< 0.4939

Hello, please consider the following.

[tex]\displaystyle \forall x \in \mathbb{R}\\\\\dfrac{e^{2x}-1}{e^x-1}\\\\=\dfrac{(e^x)^2-1^2}{e^x-1}\\\\=\dfrac{(e^x-1)(e^x+1)}{e^x-1}\\\\=e^x+1\\\\\text{So, we can find the limit.}\\\\\lim_{x\rightarrow 0} \ {\dfrac{e^{2x}-1}{e^x-1}}\\\\=\lim_{x\rightarrow 0} \ {e^x+1}\\\\=e^0+1\\\\\large \boxed{\sf \bf \ =2 \ }[/tex]

Thank you

Answer:

1 box of 20 and 1 box of 14

They will cost $410

Step-by-step explanation:

1. Find how many boxes of 20 DVD movies can be bought

415 - 240 = 175

1 box of 20 DVD movies can be sold

2. Find how many boxes of 14 DVD movies can be bought from $175

175 - 170 = 5

1 box of 14 DVD movies can be bought

3. Find the cost

240 + 170 = 410

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer:

B

Step-by-step explanation:

we take the only point we know

(0,20)

in A when x =0

[tex]f(x)=e^{20x} =e^{20*0}=1[/tex]

in B when x=0

[tex]f(x)=20e^x=20e^0=20*1=20[/tex]

fits

in C

[tex]f(x)=20^x=20^0=1[/tex]

in D

[tex]f(x)=20^{20x}=20^{20*0}=20^0=1[/tex]

so the only choice is B

Negative Integers are :

Answer:

Find a common denominator on the right side of the equation

Step-by-step explanation:

The equation before the problem is

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

The next step in solving the above equation is to fibd tge common denominator on the right side of the equation.

X² + b/a(x) + (b/2a)²= -c/a + b²/4a²

X² + b/a(x) + (b/2a)²= -4ac/4a² + b²/4a²

X² + b/a(x) + (b/2a)²=( b²-4ac)/4a²

The right side of the equation now has a common denominator

The next step is to factorize the left side of the equation.

(X+b/2a)²= ( b²-4ac)/4a²

Squaring both sides

X+b/2a= √(b²-4ac)/√4a²

Final equation

X=( -b+√(b²-4ac))/2a

Or

X=( -b-√(b²-4ac))/2a

Answer:

d. 27 cubic feet

Step-by-step explanation:

volume of cube = s^3 = B * s

volume of pyramid = (1/3) * B * h

The volume of a pyramid is 1/3 of the area of the base multiplied by the height. The volume of a cube is the area of the base multiplied by the height. Since the volume of a pyramid has the fraction 1/3 and the volume of the cube does not, then the volume of a cube is 3 times greater than the volume of a pyramid that fits inside and has the same base area.

volume of pyramid = 9 cu ft

volume of cube = 3 * 9 cu ft = 27 cu ft

Answer: d. 27 cubic feet

Answer:

27 ft^3 (Answer d)

Step-by-step explanation:

Here the volume of the pyramid is (1/3) the volume of the cube:

Letting s represent the length of one side of the base,

(1/3)(s)^2(s) = 9 ft^3, equivalent to  s^3 = 27.

Solving for s, we get s = 3 ft.

Thus, the volume of the cube is V = s^3 = (3 ft)^3 = 27 ft^3 (Answer d)

Answer:

0.05m^2

Step-by-step explanation:

5 divided by 100