Consider the following. x = e4t, y = t + 7
Eliminate the parameter to find a Cartesian equation of the curve.

Answer:

y+6 = 3/5(x-4)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y --6 = 3/5( x-4)

y+6 = 3/5(x-4)

Answer:

1280 sq inches

Step-by-step explanation:

A = LW

A = 40 in. * 32 in.

A = 1280 sq inches

Answer:

Step-by-step explanation:

Since the TV screen is a rectangle

Area of a rectangle = l × w

where

l is the length / height

w is the width

From the question

height = 32 inches

width = 40 inches

Substitute the values into the above formula

That's

Area of TV screen = 32 × 40

We have the answer as

Hope this helps you

Answer:

1.6101529

Step-by-step explanation:

Given the following :

Number of samples (n) = 210

Sample mean (x) = 5

Population standard deviation = 0.9

Population mean (m) = 4.9

Since the standard deviation of the population is known, we can use the z statistic

Z = (x - m) / standard error

Standard error = sd / √n

Standard error = 0.9 / √210

Standard error = 0.9 / 14.491376

Standard error= 0.0621059

Z statistic = (5 - 4.9) / 0.0621059

Z statistic = 0.1 / 0.0621059

Z statistic = 1.6101529

Answer:

(a) At 21.46 psi, the TPMS trigger a warning for this car.

(b) The probability that the TPMS will trigger a warning is 0.0001.

(c) The probability that the tire’s inflation is within the recommended range is 0.6826.

Step-by-step explanation:

We are given that tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure. Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).

(a) It is stated that TPMS warns the driver when the tire pressure of the vehicle is 26% below the target pressure.

So, the TPMS trigger a warning for this car when;

Pressure = 29 psi - 26% of 29 psi

               = [tex]29-(0.26 \times 29)[/tex]  = 21.46 psi

At 21.46 psi, the TPMS trigger a warning for this car.

(b) Suppose tire pressure is a normally distributed random variable with a standard deviation equal to 2 psi.

Let X = The pressure at which TPMS will trigger a warning

So, X ~ Normal([tex]\mu=29, \sigma^{2} =2^{2}[/tex])

Now, the probability that the TPMS will trigger a warning is given by = P(X [tex]\leq[/tex] 21.46)

        P(X [tex]\leq[/tex] 21.46) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{21.46-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -3.77) = 1 - P(Z < 3.77)

                                                              = 1 - 0.9999 = 0.0001

The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.

(c) The manufacturer’s recommended correct inflation range is 27 psi to 31 psi.

So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)

     P(27 psi < X < 31 psi) = P(X < 31 psi) - P(X [tex]\leq[/tex]27 psi)

     P(X < 31 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{31-29}{2}[/tex] ) = P(Z < 1) = 0.8413

     P(X [tex]\leq[/tex] 27 psi) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{27-29}{2}[/tex] ) = P(Z [tex]\leq[/tex] -1) = 1 - P(Z < 1)

                                                        = 1 - 0.8413 = 0.1587

Therefore, P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.

At 21.46 psi, the TPMS trigger a warning for this car.

The probability that the TPMS will trigger a warning is 0.0001.

The probability that the tire’s inflation is within the recommended range is 0.6826.

Given that,

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 26% below the target pressure.

Suppose the target tire pressure of a certain car is 29 psi (pounds per square inch).

We have to determine,

At what psi will the TPMS trigger a warning for this car.

What is the probability that the TPMS will trigger a warning.

What is the probability that the tire’s inflation is within the recommended range.

According to the question,

So, the TPMS trigger a warning for this car when;

Pressure = 29 psi - 26% of 29 psi

[tex]Pressure = 29- (0.26 \times 29) = 21.46psi[/tex]

At 21.46 psi, the TPMS trigger a warning for this car.

Let X = The pressure at which TPMS will trigger a warning

So, X ~ Normal [tex]\mu = 29, \sigma^2 = 2^2\\[/tex]

Now, the probability that the TPMS will trigger a warning is given by = P(X≤  21.46).

[tex]P(X\leq 21.46) = P (\dfrac{X-\mu}{\sigma}\leq \dfrac{21.46-29}{2}) = P(Z\leq -3.77) = 1-P(Z<3.77) \\\\= 1-0.9999 = 0.0001[/tex]

The above probability is calculated by looking at the value of x = 3.77 in the z table which has an area of 0.9999.

So, the probability that the tire’s inflation is within the recommended range is given by = P(27 psi < X < 31 psi)

[tex]P(27psi<X<31psi) = P(X<31psi)-P(X\leq psi)\\\\P(X<31psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{31-29}{2}) = P(Z<1) = 0.8413\\\\P(X<27psi) = P(\dfrac{x-\mu}{\sigma}\leq \dfrac{27-29}{2}) = P(Z\leq -1) = 1-P(Z<1) = 0.8413\\[/tex]

Therefore, , P(27 psi < X < 31 psi) = 0.8413 - 0.1587 = 0.6826.

To know more about Probability click the link given below.

https://brainly.com/question/18227798

Answer:

[tex]45^{3}[/tex] inches

Step-by-step explanation:

To calculate the volume of a rectangular prism(or in this case, the rectangular box), you need to multiply the length, width and height together.

length x width x height

9 x 5 x 1

=  [tex]45^{3}[/tex] inches

Answer:

The answer is in the picture below

Step-by-step explanation:

Hope this helps!

Figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.

The reflection operator geometrically repositions image elements, or pixel values, in such a way that they are reflected about a user-specified image axis or image point and placed in a new position in a matching output image.

In the given image option fourth is showing the correct reflection of the triangle △MNP over the y-axis to the form △M`N`P'.

It is observed that every point of the triangle MNP is at the same distance from the y-axis as every point of the triangle M'N'P'.

Therefore, figure number four in the image shows △MNP reflected over the y-axis to form △M`N`P`. The correct option is D.

To know more about the reflection of an image follow

https://brainly.com/question/26642069

#SPJ6

Answer:

the answer is -5 -p

Step-by-step explanation:

the reason why this is, because negative 5 is less than (-) the variable p.

Answer:

5800-1160=4640

1160×100÷4640=25

=25%

Answer:

= 0.1 miles per minute

Step-by-step explanation:

= 1.5 miles / 15 min.

= 0.1 miles per minute

Answer:

√2

1.414

Step-by-step explanation:

ⁿ√x₁*x₂*x₃*...*xₙ

√8*1/4

√2

1.414

The geometric mean between 8 and 1/4 is; 1.414.

According to the question:

In essence, the geometric mean can be evaluated as follows;

Read more on geometric mean:

https://brainly.com/question/2292573

Answer:

x^2 -6x +6

Step-by-step explanation:

Square of a difference (can be found in IM2)

Formula: a^2 -2ab +b^2

x= a; 3= b

(x -3)(x -3)

Plug in to formula.

x^2 -2(x)(3) +3^2

Simplify.

x^2 -6x +6

Answer:

[tex](x - 3)^{2}[/tex]

Answer:

[tex]\approx \bold{602\ m}[/tex]

Step-by-step explanation:

Given the following dimensions:

XY=966 ​m

[tex]\angle XYZ[/tex]​ = 38°24', and

[tex]\angle YZX[/tex] = 94°6'

To find:

Distance between points X and Z.

Solution:

Let us plot the given values.

We can clearly see that it forms a triangle when we join the points X to Y, Y to Z and Z to X.

The [tex]\triangle XYZ[/tex] has following dimensions:

XY=966 ​m

[tex]\angle XYZ[/tex]​ = 38°24', and

[tex]\angle YZX[/tex] = 94°6'

in which we have to find the side XZ.

Kindly refer to the image attached.

Let us use the Sine rule here:

As per Sine Rule:

[tex]\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}[/tex]

Where  

a is the side opposite to [tex]\angle A[/tex]

b is the side opposite to [tex]\angle B[/tex]

c is the side opposite to [tex]\angle C[/tex]

[tex]\dfrac{XZ}{sin\angle Y} = \dfrac{XY}{sin\angle Z}\\\Rightarrow \dfrac{966}{sin94^\circ6'} = \dfrac{XZ}{sin38^\circ24'}\\\Rightarrow XZ=\dfrac{966}{sin94^\circ6'} \times sin38^\circ24'\\\Rightarrow XZ=\dfrac{966}{0.997} \times 0.621\\\Rightarrow XZ=601.69 \m \approx \bold{602\ m}[/tex]

Answer: A. The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm

Step-by-step explanation:

Given the following :

Regression equation : ŷ = 0.4 + 0.2x

Price is the response variable (ŷ)

Thickness is the explanatory variable (x)

Relating the equation given to the regression model:

ŷ = c + mx

Here c = intercept ; y = response variable ;x = explanatory variable and m = slope or gradient.

Hence, mx = 0.2x

Where m = 0.2

The slope means :

Change in y / change in x

Changes in the response variable with respect to change in the explanatory variable.

The slope is positive meaning an increase in the thickness will result in a corresponding increase in price.

With a 0.2 gradient value, that means there is an $0.2 average increase in price of soap as the thickness increases by 1 cm.

Answer:

The price of the soap increases by $0.20, on average, when the thickness increases by 1 cm.

Step-by-step explanation:

Answer:

Forecasted earning = $160,200

Tax rate = 27.84%

Step-by-step explanation:

The calculation of forecasted earning and tax rate is shown below:-

Earnings before income and taxes = Sales - Cost of goods sold - Depreciation Expense

= $1,362,000 - $830,000 - $310,000

= $222,000

So,

Forecasted Free cash flow = Net Income + Depreciation  

$470,200 = Net Income + $310,000

Net Income = $470,200 - $310,000

= $160,200

Now, the Tax rate is

Net Income = EBIT × (1 - Tax Rate)

$160,200 = $222,000 × (1 - Tax rate)

(1 - Tax rate) = $160,200 ÷ $222,000

(1 - Tax rate) = 0.721622

Tax rate = 27.84%

Answer:

There are multiple ways this can be said :

Answer:

According to the graph, there are 6 pumpkins with the mass of 9kg to 12kg and 4 pumpkins with the mass of 0kg to 3kg.

In order to find how many pumpkins more, you have to subtract it so it will be 6 pumpkins - 4 pumpkins = 2 pumpkins.

Therefore, there are 2 more pumpkins with the mass of 9 to 12kg compared to the pumpkins with the mass of 0 to 3kg.

Answer:

2

Step-by-step explanation:

Answer:

1.02×10¹ = 10.2

Step-by-step explanation:

We have given a number in scientific notation as follows 1.02×10¹

We need to convert it into standard notation.

1 is in ones place, 0 is in tenths place and 2 is in hundredths place.

[tex]1.02\times 10^1=\dfrac{102}{100}\times 10\\\\=\dfrac{102}{10}\\\\=10.2[/tex]

So, the standard notation of 1.02×10¹ is 10.2

Answer:

The correct option is c.

Step-by-step explanation:

The margin of error is the range of values lower than and more than the sample statistic in a confidence interval. It is the number of percentage point by which the sample result will differ from the population result.

The general formula to margin of error is:

[tex]MOE=CV\times\frac{SD}{\sqrt{n}}[/tex]

Here,

CV = critical value

SD = standard deviation

n = sample size

Now, if the computed minimum sample size needed for a particular margin of error is not a whole number, then round the value of n up to the next larger whole number.

Thus, the correct option is c.

Answer: a.) About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.

b.) The correlation coefficient, r, is -0.736.

Step-by-step explanation:

The coefficient of determination is denoted [tex]R^2 \ or \ r^2[/tex]  which gives the percent of the variance in the dependent variable that is predictable from the independent variable.

Given, [tex]r^2= 0.542[/tex]

That means 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age.

Also, [tex]r=\sqrt{0.542}\approx\pm0.736[/tex] , where r determines the correlation coefficient.

As driver;s age increases the distance he can see decreases, so there is a negative correlation between them.

So r= -736.

Hence, The correlation coefficient, r, is -0.736.

So, the correct options are a.) and b.)

Data

6,9,5,0,5,3,7,5,2,7,10,2,9,8,0,6,2,6,6,3,6,9,7,7,4,1,6,8

Answer:

(a) shown in the attachment

(b) 0.54

(c) 5.32

(a) The frequency distribution table has been added to this response.

The table contains four columns:

First column (x): The discrete values of the marks

Second column (f): The corresponding frequency of the marks

Third column (d) : The difference between each mark(x) and the assumed mean(A). i.e d = x - A (Where A = 6 from the question)

Fourth column (fd): The product of the first column and the third column. i.e f * d

(b) From the table, it can be deduced that the modal score is 6

This is because the score 6 has the highest number of frequency which is 6

(c) If a student is selected at random, the probability P(>5), that the student scored more than 5 is given as follows;

P( >5 ) = [The sum of frequencies of marks greater than 5] / [Total frequency]

P( >5 ) = [6 + 4 + 2 + 3 + 1] / [28]

P( >5 ) = 15 / 28 = 0.54

Therefore, the probability that the student scored more than 5 is 0.54

(d) To get the arithmetic mean, M, from the assumed mean A = 6, we use the following relation;

M = A + [∑fd / N]           -----------(*)

Where

N = total frequency = 28

A = 6

∑fd = sum of the items on the fourth column = -19

Substitute these values into equation (*)

M = 6 + [-19 / 28]

M = 149 / 28

M = 5.32

Therefore, the arithmetic mean is 5.32

Answer:

It might be 168 centimetres

Step-by-step explanation:

Answer:

Total Price = 1.07(0.65x)= 0.6955x.

Step-by-step explanation:

The discount percentage is, d% = 35%.

The sales tax percentage is, s% = 7%.

The variable x represent the original cost of the item(s).

The discount is subtracted from the original amount.

So, the discounted amount will be, 0.65x.

And the sales tax is added to the original amount.

So, the value of tax plus price will be, 1.07x.

Then the final price of the item(s) will be:

Total Price = 1.07(0.65x)= 0.6955x.

Answer:

It's C for those on edgenuity

Step-by-step explanation:

Answer:

Step-by-step explanation: 2y+18 = y+39

y=21

Answer:

y = 21

Step-by-step explanation:

In the figure , 2y + 18 and y + 39 are opposite interior angles . We know that opposite interior angles are equal , so

2y + 18 = y + 39

=> 2y - y = 39 - 18

=> y = 21

Answer:

The inverse represents the temperature F corresponding to a temperature C.

The domain of the inverse function is all real numbers.

194°F

Step-by-step explanation:

Let C= y

y= 5/9 (F - 32),

F= 9/5y + 32

But y= C, hence;

F= 9/5 C +32

The inverse represents the temperature F corresponding to a temperature C.

Given;

F= 9/5 C +32

The domain of the inverse function is all real numbers.

Given C= 90°

F= 9/5 C +32

F= 9/5 (90°) +32

F= 194°F

Answer:

Total number of people in the concert

= 186

Step-by-step explanation:

There are 80 people in level 2

Then in level one

The dimensions of the room are 62 feet by 31 feet.

15 people fit in a 3 feet by 6 feet space.

Area of the room= 62*31= 1922 feet²

area of 15 people space= 3*6= 18 feet²

To know how many 15 people we get in the 2nd level

=Area of room/area of 15 people space

= 1922/18

= 106.77

= 106 (we round down because this is human being.)

Total number of people in the concert

= 106+80

= 186

Answer:

  x ≠ -2 or 3

Step-by-step explanation:

No denominator can be zero, so ...

  x +2 ≠ 0

  x ≠ -2

__

  x -3 ≠ 0

  x ≠ 3

__

  g(x) ≠ 0 . . . . . true for all x; no restriction needed for this

__

The appropriate restrictions are x ∉ { -2, 3 }.

Cross multiply the numbers in the matrix:

1 *2 + 5*x = -13

Simplify:

2 + 5x = -13

Subtract 2 from both sides:

5x = -15

Divide both sides by 5

X = -15/5

X = -3

Because it’s absolute value it needs to be positive so x = 3

Answer:

Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.

Step-by-step explanation:

Se requiere el menor número posible de manzanas y duraznos para obtener el mayor número de cajas. Puesto que no se considera cortar fruta alguna en porciones y sabiendo que hay más manzanas que duraznos, se determina la razón mínima de manzanas por duraznos:

[tex]x = \frac{48\,manzanas}{36\,duraznos}[/tex]

[tex]x = \frac{4 manzanas}{3\,duraznos}[/tex]

Se requiere 4 manzanas por cada 3 duraznos. Entonces, cada caja debe contener 3 duraznos y 4 manzanas. El número máximo de cajas es:

[tex]n = \frac{48\,manzanas}{4\,\frac{manzanas}{caja} } = \frac{36\,duraznos}{3\,\frac{duraznos}{caja} }[/tex]

[tex]n = 12\,cajas[/tex]

Se requiere 12 cajas con 4 manzanas y 3 duraznos cada una.

Answer:

x = (-5 ± 2√10) / 3

Step-by-step explanation:

5 − 10x − 3x² = 0

Write in standard form:

-3x² − 10x + 5 = 0

Solve with quadratic formula:

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ -(-10) ± √((-10)² − 4(-3)(5)) ] / 2(-3)

x = [ 10 ± √(100 + 60) ] / -6

x = (10 ± 4√10) / -6

x = (-5 ± 2√10) / 3

Step-by-step explanation:

[tex]5 - 10x - 3 \times 2 = 0[/tex]

[tex]multiply \: the \: numbers \\ \\ 5 - 10 x- 6 = 0[/tex]

[tex]collect \: like \: terms \\ \\ 5 - 6 - 10x[/tex]

[tex] - 1 - 10x = 0[/tex]

[tex] - 10x = 1[/tex]

[tex]divide \: both \: sides \: of \: the \: equation \: by \: - 10[/tex]

[tex]x = - \ \frac{1}{10} [/tex]

[tex]alt \: form \: = \\ \\ = 0.1 \\ x = - 10 {}^{ - 1} [/tex]

Hope this helps. :)