Listed below are the overhead widths​ (in cm) of seals measured from photographs and the weights​ (in kg) of the seals. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the critical values of r using α=0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the​ seals?

The following expressions are equivalent to 36x + 24y is 6(6x+4y).

6x(6+4y)

6(6x+4y)

12(3x+2y)

4(9x+6y)

We have,

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols. The expression consists of unknown variables

36x + 24y

=6(6x)+6(4y)

=6(6x+4y)

Therefore, The following expressions are equivalent to 36x + 24y is 6(6x+4y).

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Answer:

|x + 6|  = 2

Step-by-step explanation:

For a general absolute value equation:

| f(x) |  = b

We can rewrite it as:

f(x) = b

f(x) = -b

with b > 0.

Because in the number line we have only two points graphed, this means that our absolute value equation has two solutions.

And we can conclude that one solution comes from the equation:

f(x) = b

And the other solution comes from the equation:

f(x) = -b

And thus, f(x) is a linear equation, that we can simply write as:

x - c

Then our equations can be rewritten as:

x - c = b

x -c = -b

Now let's look at the graph, we can see that the two solutions are:

x = -8

and

x = -4

Let's input each one of these in one of our above equations (the order does not matter).

-4 - c = b

-8 - c = -b

The larger value of x, (x = -4) needs to be in the equation with the positive value of b.

From the first equation we can get:

b = -4 - c

now we can replace the variable "b" in the second equation by "-4 - c" to get:

-8 - c = -(-4 - c)

-8 - c = 4 + c

-8 - 4 = c + c

-12 = 2c

-12/2  =c

-6 = c

Now that we know the value of c, we can input it in the equation:

b = -4 - c

to find the value of b

b = -4 - (-6) = -4 + 6 = 2

b = 2

Then the absolute value equation is:

|x - (-6) | = 2

|x + 6|  = 2

Answer:

x=5 is in the domain

Step-by-step explanation:

sqrt(x-5) ≥ 0

Square each side

(sqrt(x-5))^2 ≥ 0^2

x-5≥0

x≥5

This is the domain of x

Answer:

9/4

Step-by-step explanation:

f(x) is continuous and differentiable on (0,9).

We want to find c using the following equation.

f'(c)=(f(9)-f(0))/(9-0)

This will require us to find f'(x) first.

f(x)=sqrt(x) is the same as   f(x)=(x)^(1/2)

Using power rule to differentiate this gives f'(x)=(1/2)(x)^(1/2-1) or simplified f'(x)=(1/2)x^(-1/2) or f'(x)=1/(2x^(1/2)).

So we want to solve:

(1/2)c^(-1/2)=(f(9)-f(0))/(9-0)

Simplify denominator on right:

(1/2)c^(-1/2)=(f(9)-f(0))/9

This will require us to find f(9) and f(0).

If f(x)=sqrt(x), then f(9)=sqrt(9)=3 and f(0)=sqrt(0)=0.

So we have the following equation so far:

(1/2)c^(-1/2)=(3-0)/9

Simplify numerator on right:

(1/2)c^(-1/2)=3/9

Multiply both sides by 2:

c^(-1/2)=6/9

Raise both sides to the -2 power:

c^(1)=(6/9)^(-2)

Note c^1=c:

c=(6/9)^(-2):

Note negative exponent means to find reciprocal of base to change exponent to opposite

c=(9/6)^2

Apply the second power:

c=81/36

Reduce by dividing top and bottom by 9:

c=9/4

This means the slope of the tangent to the curve f at x=9/4 is the same value as the slope of the secant line going through points (0,0) and (9,3).

Also 9/4 is between 0 and 9... According to the theorem we were suppose to get a value c between x=0 and x=9.

Confirmation:

Slope of the secant line is (3-0)/(9-0)=3/9=1/3.

Slope of the tangent line to curve f at x=9/4.

f'(x)=(1/2)x^(-1/2)

f'(9/4)=(1/2)(9/4)^(-1/2)

f'(9/4)=(1/2)(3/2)^(-1)

f'(9/4)=(1/2)(2/3)

f'(9/4)=1/3

They are indeed equal values (talking about the 1/3 from the secant and the tangent.)

Answer:

0.16777216

Step-by-step explanation:

(. 8)^8=0.16777216

Answer:

Step-by-step explanation:

shaded area = area of outer figure - area of inner figure........

Answer:

2(1)+y =1 for × intercept

2x+(1)=1 for y intercept

Answer:

[tex]14<15[/tex]

[tex]0<2x+10<62[/tex]

[tex]-10<2x<52[/tex]

[tex]-5<x<26[/tex]

~OAmalOHopeO

Answer:

In the picture below.

Step-by-step explanation:

From the commenter and answer above, confirmed on edge 2022.

Step-by-step explanation:

The following configurations are evaluated, as given or stated within the interrogate:

P(Q) = 0.6

P(R) = 0.9

When the variable constant of Q and R transition into independent events within the function notation, the product of the individual values, as equated to those particular independent variables, is required.

For example:

If P(Q) = 0.6 and P(R) = 0.9, and Q and R fuse, then find the product of 0.9 and 0.6 is obligated:

0.9 * 0.6 = 0.54

Thus, given the independent events, P(Q and R) is equivalent to 0.54.

ASK YOUR SIR BRO I DONT KNOW

Answer:

17690

Step-by-step explanation:

The amount Michael owes is given by :

y = - 290x +18,560

x = number of months ; y = amount owed

Amount owed after 3 months :

Put x = 3 in the equation :

y= - 290(3) +18,560

y = - 870 + 18560

y = 17690

According to the general form of a linear equation :

y = mx + c

Where, m = slope ; c = intercept

The slope = - 290 ; Intercept = 18560

Slope is the change in y per unit change in x ; The slope means that amount owed, y decreases by 290 per month

The intercept shows that the original amount borrowed is 18560

Amount Michael owes his father decreases by 290 per month.

Answer:

23.5

Step-by-step explanation:

The median is the middle value when the numbers are put in order from smallest to largest

17,19, 20, 21, 22, 25, 29, 30, 32, 35

There are 10 numbers

17,19, 20, 21, 22,      25, 29, 30, 32, 35

The middle is between 22 and 25

(22+25)/2 = 47/2 =23.5

Answer:

N = 1000

Step-by-step explanation:

The population growth of species per capita of any geographical can be computed by using the formula:

[tex]\dfrac{dN}{dT}=rN (1 - \dfrac{N}{K})[/tex]

here;

N = population chance

T = time taken

K = carrying capacity

r = the constant exponential growth rate

From the given equation, we can posit that the value of r will be the greatest at the time the value of dN is highest:

As such, when the population chance = 1000

[tex]\dfrac{dN}{dT}=0.17 * 1000 (1 - \dfrac{1000}{10000})[/tex]

[tex]\dfrac{dN}{dT}=0.17 * 1000 (0.9)[/tex]

[tex]\dfrac{dN}{dT}= 153[/tex]

At N = 5000;

[tex]\dfrac{dN}{dT}= 85[/tex]

At N= 8000;

[tex]\dfrac{dN}{dT}= 34[/tex]

At N = 10000

[tex]\dfrac{dN}{dT}= 0[/tex]

Answer:

See explanation

Step-by-step explanation:

Given

See attachment for proper presentation of question

Required

Mean and Range

To do this, we simply calculate the mean and the range of each row.

[tex]\bar x = \frac{\sum x}{n}[/tex] ---- mean

Where:

[tex]n = 4[/tex] ---- number of rows

[tex]R = Highest - Lowest[/tex] --- range

So, we have:

Sample 1

[tex]\bar x_1 = \frac{1027+ 994 +977 +994 }{4}[/tex]

[tex]\bar x_1 = 998[/tex]

[tex]R_1 = 1027- 994[/tex]

[tex]R_1 = 33[/tex]

Sample 2

[tex]\bar x_2 = \frac{975 +1013 +999 +1017}{4}[/tex]

[tex]\bar x_2 = 1001[/tex]

[tex]R_2 = 1017 - 975[/tex]

[tex]R_2 = 42[/tex]

Sample 3

[tex]\bar x_3 = \frac{988 +1016 +974 +997}{4}[/tex]

[tex]\bar x_3 = 993.75[/tex]

[tex]R_3 = 1016-974[/tex]

[tex]R_3 = 42[/tex]

Sample 4

[tex]\bar x_4 = \frac{998 +1024 +1006 +1010}{4}[/tex]

[tex]\bar x_4 = 1009.5[/tex]

[tex]R_4 = 1024 -998[/tex]

[tex]R_4 = 26[/tex]

Sample 5

[tex]\bar x_5 = \frac{990 +1012 +990 +1000}{4}[/tex]

[tex]\bar x_5 = 998[/tex]

[tex]R_5 = 1012 -990[/tex]

[tex]R_5 = 22[/tex]

Sample 6

[tex]\bar x_6= \frac{1016 + 998 +1001 +1030}{4}[/tex]

[tex]\bar x_6= 1011.25[/tex]

[tex]R_6= 1030-998[/tex]

[tex]R_6= 32[/tex]

Sample 7

[tex]\bar x_7 = \frac{1000 +983 +979 +971}{4}[/tex]

[tex]\bar x_7 = 983.25[/tex]

[tex]R_7 = 1000-971[/tex]

[tex]R_7 = 29[/tex]

Sample 8

[tex]\bar x_8 = \frac{973 +982 +975 +1030}{4}[/tex]

[tex]\bar x_8 = 990[/tex]

[tex]R_8 = 1030-973[/tex]

[tex]R_8 = 57[/tex]

Sample 9

[tex]\bar x_9 = \frac{992 +1028 +991 +998}{4}[/tex]

[tex]\bar x_9 = 1002.25[/tex]

[tex]R_9 = 1028 -991[/tex]

[tex]R_9 = 37[/tex]

Sample 10

[tex]\bar x_{10} = \frac{997 +1026 +972 +1021}{4}[/tex]

[tex]\bar x_{10} = 1004[/tex]

[tex]R_{10} = 1026 -972[/tex]

[tex]R_{10} = 54[/tex]

Sample 11

[tex]\bar x_{11} = \frac{990 +1021 +1028 +992}{4}[/tex]

[tex]\bar x_{11} = 1007.75[/tex]

[tex]R_{11} = 1028 -990[/tex]

[tex]R_{11} = 38[/tex]

Sample 12

[tex]\bar x_{12} = \frac{1021 +998 +996 +970}{4}[/tex]

[tex]\bar x_{12} = 996.25[/tex]

[tex]R_{12} = 1021 -970[/tex]

[tex]R_{12} = 51[/tex]

Sample 13

[tex]\bar x_{13} = \frac{1027 +993 +996 +996}{4}[/tex]

[tex]\bar x_{13} = 1003[/tex]

[tex]R_{13} =1027 -993[/tex]

[tex]R_{13} =34[/tex]

Sample 14

[tex]\bar x_{14} = \frac{1022 +981 +1014 +983}{4}[/tex]

[tex]\bar x_{14} = 1000[/tex]

[tex]R_{14} = 1022 -981[/tex]

[tex]R_{14} = 41[/tex]

Sample 15

[tex]\bar x_{15} = \frac{977 +993 +986 +983}{4}[/tex]

[tex]\bar x_{15} = 984.75[/tex]

[tex]R_{15} = 993-977[/tex]

[tex]R_{15} = 16[/tex]

The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.

Suppose we're measuring something whose values are numeric. For each value of that thing we observe, we plot a dot above that value in the number line. Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

LEt suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

The dot plot is skewed to the right due to majority of the data occur to the right of the dot plot.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. Outliers usually occur with a frequency of one.

For Class A the dots are spread out more.

For Class B, the dots are more grouped together.

Here, Looking at the dot plot, it can be seen that the numbers that range from 16 to 21 have only one dot.

The statement that best compares the variability of the quiz scores for Class A and Class B is A; The scores on the quiz for Class A have more variability than the scores for Class B.

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Answer:

A. $15

B. $25

C. 84 peaches

Answer:

a)3dozenx$5=$15

b)60=5 dozen 5x$5=$25

c)35/5=7,7 dozen, 7 x 12= 84

Step-by-step explanation:

9514 1404 393

Answer:

  $144

Step-by-step explanation:

Multiplication is used to simplify repeated addition. To find the total cost, add up the costs of each of the tickets.

  6 child tickets will cost $10 +10 +10 +10 +10 +10 = 6×$10 = $60

  6 adult tickets will cost $14 +14 +14 +14 +14 +14 = 6×$14 = $84

Then the total cost of all of these tickets will be ...

  $60 +84 = $144 . . . . cost of zoo tickets in all

Answer:

4 scoops of ice cream

Step-by-step explanation:

Plug in the total cost, number of scoops of nuts, and number of liquid toppings into the formula. Then, solve for s:

C = 0.50s + 0.35n + 0.25t

3.55 = 0.50s + 0.35(3) + 0.25(2)

3.55 = 0.50s + 1.05 + 0.5

3.55 = 0.50s + 1.55

2 = 0.50s

4 = s

So, the sundae had 4 scoops of ice cream.

Step-by-step explanation:

4. the area of semi circle R =

3²/5² × 75π = 9/25 × 75π = 27π cm²

5. the ratio of their areas = 1²:7² = 1:49

Answer:

t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks

S = V * t

V = S / t = 20 mi * 5280 ft/mi / 2800  sec  = 37.7 ft/sec

Since 88 ft/sec = 60 mph

the speed is 60 * 37.7 / 88 = 25.7 mph

Answer:

Step-by-step explanation:

345ftyfthftyft.plk,k,

Answer:

Hello,

Anwser is C

Step-by-step explanation:

[tex]y=log_9(12x)\\\\9^y=12x\\\\9^x=12y\ inverting \ x \ and \ y \\\\y=\dfrac{9^x}{12} \\[/tex]

Answer:

They will hike 16% of the trail in Georgia.

Step-by-step explanation:

We have that:

The hiking trail is of 2600 miles.

416 of those miles are in Georgia?

What percent of the trail will they hike?

Georgia distance multiplied by 100% and divided by the total distance. So

416*100%/2600 = 16%

They will hike 16% of the trail in Georgia.

Answer:

Step-by-step explanation:

Not a clear list of options and/or reference frame

Probably     0.5      if angle t is measured from the positive x axis.

Answer:

[tex] x = 8\sqrt{2} [/tex]

Step-by-step explanation:

Leg = x

Hypotenuse = 16

[tex] x\sqrt{2} = 16 [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16}{\sqrt{2}} \times \dfrac{\sqrt{2}}{\sqrt{2}} [/tex]

[tex] x = \dfrac{16\sqrt{2}}{2} [/tex]

[tex] x = 8\sqrt{2} [/tex]

Solution :

Amounts spent on a trip : $31.11, $25.01, $18.53, $14.37, $24.16, $21.91

Confidence interval = 80%

Average amount spent = 8 to 9 years old

One sample T confidence interval

μ : Mean of variance

80% of confidence interval results :

Using statistical software,

Variable : data

Sample mean : 22.515

Std. Err. = 2.3479945

DF = 5

L. limit : 19.049632

U. Limit : 25.980368

SD = 5.75

Critical value = 1.476

Answer:

n ≥  3

Step-by-step explanation:

Applying the remainder term in evaluating the minimum order of the Taylor polynomial

absolute error ≤ 10^-2

[tex]\sqrt{1.06}[/tex]

∴ n ≥   ?

The remainder term is the leftover term after computation ( dividing one polynomial with another )

attached below is the detailed solution

The minimum order of the Taylor polynomial, n≥3

Taylor polynomial is a series of functions that has an infinite sum of terms that are expressed in terms of the function's derivatives.

[tex]\rm f(a)+\frac{f'(a)}{1!} (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +....,[/tex]

Applying the Taylor series polynomial, the minimum order of the Taylor polynomial, centered at 0

[tex]\rm f(0)+\frac{f'(0)}{1!} (x-0)+\frac{f''(0)}{2!} (x-0)^{2} +....,[/tex]

f(x) = [tex]\sqrt{x+1}[/tex]

[tex]f'(x)=\frac{1}{2}[/tex]

[tex]f''(x)=3/8[/tex]

substituting in the Taylors series

T(x) = [tex]1+\frac{x}{2} -\frac{x^{2} }{8} +\frac{x^{3} }{16}[/tex]......

T(0.06) = [tex]1+\frac{0.06}{2} -\frac{0.06^{2} }{8} +\frac{0.06^{3} }{16}...[/tex]

T(0.06) =1.03

f(0.06) =

[tex]\sqrt{0.06+1}\\= 1.03[/tex]

Therefore, the minimum order of the Taylor polynomial, n≥3

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9514 1404 393

Answer:

  A.  4 feet/(1 second)

Step-by-step explanation:

A "unit" is one of something. A unit rate is a rate that has 1 of something in the denominator. Look down the list at the denominators and find the value that has 1 as a denominator:

  [tex]\dfrac{4\text{ feet}}{1\text{ second}}[/tex]

Answer:

V = 64.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos V = adj side/ hypotenuse

cos V = 3/7

Taking the inverse cos of each side

cos ^-1 ( cos V) = cos ^-1 (3/7)

V=64.62306

Rounding to the nearest tenth

V = 64.6

Answer:

V=64.6

Step-by-step explanation:

the same thing as other guy, lol