Solve the equation. 3t + 8 = 6t - 13

Answer:

D

Step-by-step explanation:

Solution:-

The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:

                                   f ( x ) = sin ( w*x ± k ) ± b

Where,

                 w: The frequency of the cycle

                 k: The phase difference

                 b: The vertical shift of center line from origin

We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).

We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.

The resulting sinusoidal waveform can be expressed as:

                           f ( x ) = sin ( 2x )  ... Answer

Answer:

After reflection, the coordinates would be A(-6,-8)  B(-2,-6)  C(-4,-2) and  D(-8,-4). After translation, the coordinates would be A(0,-8) B(4,-6)  C(2,-2)  and D(-2,-4).  

Step-by-step explanation:

If the figure ABCD consists of 4 points and we want to reflect this across the x-axis, then the y coordinate values of A, B, C and D will be negated. So,

(-6,8) becomes (-6,-8)

(-2,6) becomes (-2,-6)

(-4,2) becomes (-4,-2)

and (-8,4) becomes (-8,-4).

Now that we know what the reflection is, we translate it 6 units to the right. Therefore, the x value of each coordinate is increased by 6.

(-6,-8) becomes (0,-8)

(-2,-6) becomes (4,-6)

(-4,-2) becomes (2,-2)

and (-8,-4) becomes (-2,-4)

Hope this helped!

Answer:

21=2w+2w+3    18=4w     w=4.5

Answer:

14

Step-by-step explanation:

3 1/2 × 4

Convert 3 1/2 to an improper fraction.

7/2 × 4

7/2 × 4/1

Multiply.

(7× 4) / (2 × 1)

28 / 2

= 14

Answer: 14

Step-by-step explanation: To multiply a mixed number times a whole number, first write each of them as an improper fraction.

So we can rewrite 3 and 1/2 as the improper fraction 7/2

and we can write 4 as the improper fraction 4/1.

If you've forgotten how to write a mixed number as an improper fraction, feel free to ask me below and I will review this with you.

So now we have 7/2 × 4/1.

When we're multiplying fractions, we want to

cross-cancel first whenever possible.

So here, notice that we can cross-cancel 2 and 4 to 1 and 2.

So we have 7/1 × 2/1.

Now we just multiply across the numerators and multiply across the denominators and we have our answer, 14/1 or just 14.

Answer:

-2n

Step-by-step explanation:

f(x)=7-2x {1,2}

f(1)=7-2(1)=5

f(2)=7-2(2)=3

Slope (m)=3/5

{7-2(1)}-{7-2(2)}=3-5=-2

In terms of n=-2n

The upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3]

Given the function of the graph bounded by the inteval [1, 2] expressed as

f(x) = 7 - 2x

The upper limit of the function is the point where the domain of the function x is 2. Substitute x = 2 into the function, we will have:

f(2) = 7 - 2(2)

f(2) = 7 - 4

f(2) = 3

For the lower limit, the domain of the function is at x = 2:

f(1) = 7 - 2(1)

f(1) = 7 - 2

f(1) = 5

Hence the upper and lower sums for the region bounded by the graph of the function and the x-axis on the given interval is [5, 3].

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Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Step-by-step explanation:

Critical points:

The critical points of a function f(x) are the values of x for which:

[tex]f'(x) = 0[/tex]

For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.

The critical points help us find these intervals.

In this question:

[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]

So

[tex]P'(x) = -0.008x + 6[/tex]

Critical point:

[tex]P'(x) = 0[/tex]

[tex]-0.008x + 6 = 0[/tex]

[tex]0.008x = 6[/tex]

[tex]x = \frac{6}{0.008}[/tex]

[tex]x = 750[/tex]

We have two intervals:

(0, 750) and [tex](750, \infty)[/tex]

(0, 750)

Will find P'(x) when x = 1

[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]

Positive, so increasing.

Interval [tex](750, \infty)[/tex]

Will find P'(x) when x = 800

[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]

Negative, then decreasing.

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Answer:

20

Step-by-step explanation:

fist you convert 6l to ml=6×1000

then,300/300:6000/300

gives you 1:20

Answer:

[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]

[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]

And the interval would be:

[tex] (29.10 \leq \mu \leq 73.46)[/tex]

Step-by-step explanation:

For this problem we have the following dataset given:

44 32.8 59.2 31.4 12.7 68.5 84.7 72.5 55.7

We can find the mean and sample deviation with the following formulas:

[tex] \bar X= \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex] s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex]\bar X= 51.278[/tex]

[tex] s= 22.979[/tex]

The confidence interval for the mean is given by:

[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]

The degrees of freedom are:

[tex] df=n-1= 9-1=8[/tex]

The confidence would be 0.98 and the significance [tex]\alpha=0.02[/tex] then the critical value would be:

[tex] t_{\alpha/2}= 2.896[/tex]

Ad replacing we got:

[tex] 51.278 -2.896 \frac{22.979}{\sqrt{9}}= 29.096[/tex]

[tex] 51.278 +2.896 \frac{22.979}{\sqrt{9}}= 73.460[/tex]

And the interval would be:

[tex] (29.10 \leq \mu \leq 73.46)[/tex]

Answer:

24

Step-by-step explanation:

Answer:

  D. The distance from the mean to an inflection point

Step-by-step explanation:

We rarely encounter the actual formula for the normal PDF. It is ...

  [tex]p(x)=\dfrac{1}{\sqrt{2\pi}}e^{-\dfrac{x^2}{2}}[/tex]

In fact, the inflection points are at x = ±1, where the curve changes from being concave downward to concave upward.

So, one standard deviation is the distance from the mean to an inflection point.

The profit made in week 1 is 0.69 and week 2 is 0.71.

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

A takeaway sells 10-inch pizzas and 12-inch pizzas.

From the table

For week 1:

Proportion= 509/ 736 = 0.69

and, week 2:

Proportion= 765/ 1076 = 0.71

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Answer:

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

And replacing we got:

[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]  

Step-by-step explanation:

Information given

n=421 represent the random sample taken

[tex]\hat p=0.65[/tex] estimated proportion of adults  that would erase all of their personal information online if they could

[tex]p_o=0.5[/tex] is the value that we want to test

z would represent the statistic  

Hypothesis to test

We want to check if Most adults would erase all of their personal information online if they could, then the system of hypothesis are :  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

The statistic would be given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

And replacing we got:

[tex]z=\frac{0.65 -0.5}{\sqrt{\frac{0.5(1-0.5)}{421}}}=6.16[/tex]  

From the information given, it is found that the value of the test statistic is z = 6.16.

At the null hypothesis, we test if it is not most adults that would erase all of their personal information online if they could, that is, the proportion is of at most 50%, hence:

[tex]H_0: p = 0.5[/tex]

At the alternative hypothesis, we test if most adults would, that is, if the proportion is greater than 50%.

[tex]H_1: p > 0.5[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In this problem, the parameters are: [tex]p = 0.5, n = 421, \overline{p} = 0.65[/tex].

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.65 - 0.5}{\sqrt{\frac{0.5(0.5)}{421}}}[/tex]

[tex]z = 6.16[/tex]

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Answer:

[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]    

The p value would be given by:

[tex]p_v =2*P(z<-2.23)=0.0257[/tex]  

For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG

Step-by-step explanation:

Information given

[tex]\bar X=46.5[/tex] represent the mean

[tex]\sigma=1.1[/tex] represent the population standard deviation

[tex]n=150[/tex] sample size  

[tex]\mu_o =46.7[/tex] represent the value to verify

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean for this case is 46.7, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 46.7[/tex]  

Alternative hypothesis:[tex]\mu \neq 46.7[/tex]  

Since we know the population deviation the statistic is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex]  (1)  

Replacing we got:

[tex]z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23[/tex]    

The p value would be given by:

[tex]p_v =2*P(z<-2.23)=0.0257[/tex]  

For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG

Answer:

  all are "yes"

Step-by-step explanation:

A polynomial is defined for all values of x. None are excluded. Every value listed is in the domain of f(x) = (x +1)².

Answer:

Step-by-step explanation:

Answer:

x= -3, y= -5

or x= 5, y=3

Step-by-step explanation:

① Label the 2 equations

x² +y²= 34 -----(1)

3x -3y= 6 -----(2)

From (2):

x -y= 2 -----(3)

Notice that (x-y)²= x² -2xy +y²

Thus, (equation 3)²= (equation 1) -2xy

Squaring (3):

(x -y)²= 2²

(x -y)²= 4

Expand terms in bracket:

x² -2xy +y²= 4

x² +y² -2xy= 4 -----(4)

subst. (1) into (4):

34 -2xy= 4

2xy= 34 -4 (bring constant to 1 side)

2xy= 30 (simplify)

xy= 30 ÷2 (÷2 throughout)

xy= 15 -----(5)

From (3):

x= y +2 -----(6)

I'll rewrite 2 of the equations.

x= y +2 -----(6)

xy= 15 -----(5)

Subst. (6) into (5):

y(y+2)= 15

y² +2y= 15

y² +2y -15= 0

(y +5)(y -3)=0

y+5= 0 or y-3=0

y= -5 or y= 3

Subst. into (6):

x= -5 +2 or x= 3 +2

x= -3 or x= 5

Answer:

y=-5,                 y=3

x=-3.,                x=5

Step-by-step explanation:

x^2+y^2=34

3x-3y=6

isolate x in te equation

3x-3y=6

x=3/3 y+6/3

x=y+2

plug the y+2 in the equation:

x^2+y^2=34

(y+2)^2+y^2=34

y^2+4y+4+y^2=34

2y^2+4y=34-4

2y^2+4y=30 divide by 2

y^2+2x-15=0 factorize

(y+5)(y-3)=0 eiter y+5=0 ten y=-5 or y-3=0 then y=3

now plug the solution in the equation

3x-3y=6

3x-3(-5)=6

3x=6-15

x=-9/3=-3

for y=3

3x-3y=6

3x-9=6

3x=15

x=5

median=order them and find the middle=6

mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4

range= the difference between the smallest and largest number=9-3=6

mode= the one that appears the most= 7

The median, mean, range and mode will be 6, 5.4, 9 and 7.

The median is the number in the middle when arranged in an ascending order. The numbers will be:

0, 3, 4, 6, 6, 7, 7, 7, 9.

The median is 6.

The range is the difference between the highest and lowest number which is: = 9 - 0 = 9

The mode is the number that appears most which is 7.

The mean will be the average which will be:

= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.

= 49/9

= 5.4

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Explanation:

The graph shows that f(x) has the y intercept at -5. This is where the red line crosses the vertical y axis. More specifically, the y intercept is located at the point (0,-5)

We're told that g(x) has a y intercept at -1. So we must move f(x) 4 units up to go from y = -5 to y = -1. This is because -5+4 = -1.

Do this for every point on f(x) and you'll end up with g(x) = f(x)+4. Recall that y = f(x). So saying f(x)+4 is the same as y+4 to indicate "shift up 4 units".

f(x) and g(x) have the same slope, but different y intercepts. So they are parallel lines that never cross.

Answer:

12

Step-by-step explanation:

Let's call the width x and the length x + 3. Using the Pythagorean Theorem we can write:

(x + 3)² + x² = 15²

x² + 6x + 9 + x² = 225

2x² + 6x - 216 = 0

2(x² + 3x - 108) = 0

2(x + 12)(x - 9) = 0

x + 12 = 0 or x - 9 = 0

x = -12 or x = 9

x cannot be -12 because length/width can't be negative so x = 9 which means that the length is 9 + 3 = 12.

Answer:

y + 1 = 3x

Step-by-step explanation:

In order for there to be an infinite number of solutions, the two lines need to be the same.

y+1 = 3x

y=3x-1 are both the same

Answer:

a)y + 1 = 3x

Step-by-step explanation:

Answer:

1. continuous random variable

2. not a random variable

3. a continuous random variable

Step-by-step explanation:

The classifications are as follow

a)  The height of the player reported in the game day program is treated as a continuous random variable as these values could be determined through measuring them

b)  The color of student car is not a random variable as it does not contain any quantitative data or we can say numerical data

c)  The exact weight of the bag is a continuous variable as it is lie between the range

Answer:

The sample size 'n' = 242

Step-by-step explanation:

Step(i):-

Given mean of the sample = 5.7

Given standard deviation of the sample (σ)  = 1.8

The Margin of error  (M.E) = 0.12

Level of significance = 0.85 or 85%

Step(ii):-

The margin of error is determined by

[tex]M.E = \frac{Z_{\alpha }S.D }{\sqrt{n} }[/tex]

The critical value Z₀.₁₅ = 1.036

[tex]0.12 = \frac{1.036 X 1.8 }{\sqrt{n} }[/tex]

Cross multiplication , we get

[tex]\sqrt{n} = \frac{1.036 X 1.8}{0.12}[/tex]

√n  =  15.54

Squaring on both sides, we get

n = 241.49≅ 241.5≅242

Conclusion:-

The sample size 'n' = 242

Answer:

14000

Step-by-step explanation:

Of means multiply

10% * 140000

Change to decimal form

.10 * 140000

14000

Answer:

[tex]14000[/tex]

Step-by-step explanation:

[tex]10\% \times 140000[/tex]

[tex]\mathrm{Apply} \: a\% = \frac{a}{100}[/tex]

[tex]\frac{10}{100} \times 140000[/tex]

[tex]\mathrm{Apply} \: \frac{a}{100} \times b = \frac{ab}{100}[/tex]

[tex]\frac{1400000}{100}[/tex]

[tex]\mathrm{Simplify.}[/tex]

[tex]\frac{14000}{1} =14000[/tex]

Answer:

100%

Step-by-step explanation:

Start with x.

x = x/1

Increase the numerator by 60% to 1.6x.

Decrease the numerator by 20% to 0.8.

The new fraction is

1.6x/0.8

Do the division.

1.6x/0.8 = 2x

The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.

The increase is 100%.

Answer:

33%

Step-by-step explanation:

let fraction be x/y

numerator increased by 60%

=x+60%ofx

=8x

denominator increased by 20%

=y+20%of y

so the increased fraction is 4x/3y

let the fraction is increased by a%

then

x/y +a%of (x/y)=4x/3y

or, a%of(x/y)=x/3y

[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]

therefore a=33

anda%=33%

Answer:L=30 S=50

Step-by-step explanation:

3.25 x 50 = 162.5

245 - 162.5 = 82.5

82.5 divided by 30 equals 2.75.

Answer:

Area = 53 in²

Step-by-step explanation:

area of a box = 8 * 6 = 48 in²

area of a triangle = 1/2 * b * h

b = 6 - 4 = 2 in

h = 13 - 8 = 5 in

area of a triangle = 1/2 * 2 * 5 = 5 in²

total area = area of a triangle + area of a box

total area = 5 in² + 48 in²

total area = 53 in²

Answer:

Cost: $247

Discount: $133

Step-by-step explanation:

Simply multiply 380 and 35% off together to get your answer:

380(1 - 0.35)

380(0.65)

247

To find the discount amount, simply subtract the 2 numbers to get your answer:

380 - 247 = 133

Answer:

7/3 or 13/15

Step-by-step explanation:

So you told me that it will be

8/(20/9) -2 11/15 I put parenthesis to make it easier to understand for me

so you must know that a/(b/c)=ac/b si

72/20 -2 11/15 so we work with -2 11/15 which is equal to -30/15 + 11/15 and that will be -19/15 so we have

72/20 - 19/15 we simplify

18/5 - 19/15 so we multiply and divide by 3 in 18/5

54/15 - 19/15 and we add up

35/15 which is equal to

7/3

If this is wrong so we work with -2 11/15 which is equal to -30/15 + 11/15 well it should be so we work with -2 11/15 which is equal to -30/15 - 11/15 and  that equals -41/15 and we get

54/15-41/15

13/15

Answer:

true

Step-by-step explanation:

A prism is a solid with parallelogram sides (usually rectangles) and a polygon for the 2 bases. Any polygon can be the base.

Answer:

Hello!

__________________

Your answer would be (A) True.

Step-by-step explanation: Hope this helped you!

Any polygon can be the base of a prism so the answer is true.

Step-by-step explanation:

define define equation we need the value of the radius and

Answer:

7850 feet.sq

Step-by-step explanation:

the area of a cercle is:

A = r²*π     where r is the radius

A= 50²*3.14 = 7850 ft²