the mean rate for satellite television from a sample of households was $49.00 per month, with a standard deviation of $2.50 per month. between what two values do 99.7% of the data lie?

Answer:

 [tex]\frac{(x+2)^2}{121} + \frac{(y-1)^2}{169} = 1[/tex]

Step-by-step explanation:

First, we identify that the vertices are vertical.
(an image below is attached if you want to see a visualization)
Therefore, the equation is such:

[tex]\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1[/tex]

(h,k) is the center of the ellipse, which we could easily calculate by finding the midpoint between any pair of vertices.

This gets us (-2, 1)

Therefore, h = -2, k = 1

Now we want to find a,

we know the length of the major axis is 2a, and in this case, our length of the major axis is 26. So a = 13

Now we want to find b,

We know the length of the minor axis is 2b, and in this case, our length is 22, so b = 11

Now we will just plug in all the values and simplify to get our answer! B)

If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.

Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.

From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.

Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.

So,

length of arc LNM=Circumference of circle-length of arc LKM.

We know that length of an arc =Θr

in which Θ is the angle in radian.

length of arc=70*π[tex]/180*5[/tex]

=70π[tex]/36[/tex]

Circumference of circle=2π*5

=10π

Length of arc LNM=10π-70π[tex]/36[/tex]

=(360π-70π)[tex]/36[/tex]

=290π[tex]/36[/tex]

Put π=3.14

=290*3.14[tex]/36[/tex]

=910.6[tex]/36[/tex]

=25.29m

Hence the length of arc LNM is 25.29 m.

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Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

Two angles are called complementary when their measures add to 90 degrees.

From the diagram; Angle ABD and Angle DBC are complementary angles that add up to make 90 degrees.

Since Angle ABD and Angle DBC are complementary angles, the measure of Angle ABC is 90 degrees.

Hence, option D is the correct answer.

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X= root 6^2 + 10^2

X=2 root 34

So, x is 11.66 to 2d.p

(root means square root)

Hope this helps!

Answer:

x = 11.66

Step-by-step explanation:

Hello!

We can use the Pythagorean theorem to solve for the hypotenuse.

Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]

Plug the values of 6 and 10 into the formula to solve.

The hypotenuse is approximately 11.66.

The cross sectional area of the conduit not part of the 7 cables is; 706.5cm²

It follows from the task content that the conduit in discuss has 7 cables all same diameter and has a circular cross section.

Since, the cross sectional area of the conduit not part of the 7 cables is required; it follows that the cross sectional area of the inside cavity can be evaluated as follows;

where radius, r = D/2 = 30/2.

Area = πr² = 3.14 × (30/2)² = 706.5cm²

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Answer:

46+96=140°_÷__^_^^^^=^

Answer:

E

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

Consider the triangle on the left

3rd angle = 180° - 60° - 90° = 180° - 150° = 30°

the 3rd angle of the triangle on the left = 30° ( vertically opposite angle ), so

∠ 1 = 180° - 30° - 65° = 180° - 95° = 85°

Hi! ◈

Answer:

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

1/4 of the cake was left

Step-by-step explanation:

  Since the total cake is [tex]\sf{\dfrac{4}{4}}[/tex], all we should do is subtract 3 from 4

  [tex]\sf{\dfrac{4-3}{4}}=the \ cake \ that \ was \ left[/tex]

   _____________________

   [tex]\sf{\dfrac{1}{4} \ of \ the \ cake \ was \ left}[/tex]

Hope this made sense to you !!

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

The inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3

The function is given as:

f(x) = 4^(x + 3) -2

Rewrite as:

y = 4^(x + 3) -2

Swap x and y

x = 4^(y + 3) -2

Add 2 to both sides

x + 2 = 4^(y + 3) -2 + 2

This gives

x + 2 = 4^(y + 3)

Take the logarithm of both sides

log(x  + 2)= log(4)^(y + 3)

Apply the base rule of logarithm

log(x  + 2)= (y + 3)log(4)

Divide both sides by log(4)

log(x + 2)/log(4) = y + 3

Apply the change of base rule of logarithm

log₄(x + 2) = y + 3

Subtract 3 from both sides

log₄(x + 2) - 3 = y + 3 - 3

Evaluate the difference

log₄(x + 2) - 3 = y

Rewrite as:

y = log₄(x + 2) - 3

Rewrite as:

f-1(x) = log₄(x + 2) - 3

Hence, the inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3

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Based on the width of the aluminum sheets and the angle of the edges, the depth that allows maximum cross-sectional area is 4 inches.

Assuming that the depth is x, the area would be:

= x (16 - 2x)

= 16x - 2x²

The maximum of the parabola is:

x = -b / 2a

= - 16 / (2 x -2)

= -16 / -4

= 4 inches

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By definition of real field and algebra properties we conclude that the product of three positive integers is always equal to a positive integer.

First, we state the conjecture: The product of three positive integers equals a positive integer. Second, we prove if the conjecture is true:

Integers are part of the real field, which mean that the product of two integers is also an element of that field. By algebra we know that the product of two positive integers is equal to another positive integer. Thus, the product of three positive integers is always equal to a positive integer.

Here is an example:

2 × 5 × 7

10 × 7

70

In a nutshell, the conjecture has been proved true.

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The answer choice which explains that the three segments cannot be used to construct a triangle is; AC + CB < AB.

Since, It follows from the triangle inequalities theorem that sum of the side lengths of any two sides of a triangle is greater than the length of the third side.

Hence, since the sum of sides AC + CB is less than AB, it follows that the required inequality is; AC + CB < AB.

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The mass of radioactive material remaining after 50 years would be 48.79 kilograms

It is important to note that half - life is the time it takes for the amount of a substance to reduce by half its original size.

Given the radioactive decay formula as

m(t)=120e−0.018t

Where

t= 50 years

m(t) is the remaining amount

Substitute the value of t

[tex]m(t) = 120e^-^0^.^0^1^8^(^5^0^)[/tex]

[tex]m(t) = 120e^-^0^.^9[/tex]

Find the exponential value

m(t) = 48.788399

m(t) = 48.79 kilograms to 2 decimal places

Thus, the mass of radioactive material remaining after 50 years would be 48.79 kilograms

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The area enclosed by the given 2 curves is; 8/3 or 2.67

We want to find the area enclosed by the curves;

y = x² - 2x

y = -x² + 2x

The point of intersection of the parabola and the line is given by;

x² - 2x = -x² + 2x

2x² - 4x = 0

Solving this gives;

x = 0, 2

Therefore, the area bounded by the parabola and the line between x = 0 and x = 2 is given as;

A = ∫₀² (-x² + 2x - x² + 2x)

A = ∫₀² (-2x² + 4x)

Using online integration calculator here gives;

A = 2.67

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The possible temperatures are represented by (-∝, 29)

Let the high temperature be x

So, the statement can be represented as:

2x > 5x - 87

Subtract 5x from both sides

-3x > -87

Divide both sides by -3

x < 29

In interval form, we have (-∝, 29)

Hence, the possible temperatures are represented by (-∝, 29)

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The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.

The graph represents a parabola.

The graph can be a function if it passes the vertical line test.

The graph satisfies the vertical line test, it may be said that it reflects a function (C) The graph is accurate if it passes the vertical line test.

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681×239 = 162,759

..... ......

162,759 is answer

happy to help

The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex]  the result of the division is [tex]30.8666667[/tex] in decimal form.

When a large number is distributed into small numbers of equal parts is called division.

The number [tex]1.5[/tex] is not a factor of [tex]46.3[/tex] ,  on dividing them the remainder is not zero.

Therefore,  first convert [tex]1.5[/tex] it into a whole number by multiplying it  [tex]10[/tex] so it becomes [tex]15[/tex] .

Then convert [tex]46.3[/tex]  it into a whole number by multiplying it by [tex]10[/tex] so it becomes [tex]463[/tex]

Here,  [tex]\dfrac{463 \times 10}{15 \times 10}[/tex] which results in [tex]\dfrac{463}{15}[/tex].

Now, divide [tex]\dfrac{463}{15}[/tex] ,  the result will be [tex]30.8666667[/tex].

The solution to the problem when [tex]46.3[/tex] divided by  [tex]1.5[/tex] the result is [tex]30.8666667[/tex].

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The simplified form of the given expression [tex]\frac{x^2-4x-21}{4(x+3)}[/tex] is [tex]\frac{x-7}{4}[/tex].

The steps to simplify a fractional expression are:

The given expression is [tex]\frac{x^2-4x-21}{4(x+3)}[/tex]

Factorizing the numerator:

x² - 4x - 21 = x² - 7x + 3x - 21

                 = x(x - 7) + 3(x - 7)

                 = (x - 7)(x + 3)

Then,

[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{(x-7)(x+3)}{4(x+3)}[/tex]

common factor (x + 3) is canceled out from both the numerator and the denominator

So,

[tex]\frac{x^2-4x-21}{4(x+3)}[/tex] = [tex]\frac{x-7}{4}[/tex]

Therefore, the simplified expression is [tex]\frac{x-7}{4}[/tex].

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Answer:x-3/4

Step-by-step explanation:

(x-3)(x+7)/4(x+7)

=x-3/4

Step-by-step explanation:

38<4x+3+7-3x

4x+3+7>38

4x+3+7<3x

X>7

X<-10

= Ø

Answer:36

Step-by-step explanation:

Let name the missing angle in the triangle w.

We know that x+z+w=180

We also know that z+w=3z=y.

That means that w=2z.

x=2z, so, 2z+2z+z=180

z=36

Answer:

Z=36 degrees

Step-by-step explanation:

Since angles x and y are supplementary, you know that they add up to 180 degrees.

Since we know that:

=x+y

=2z+3z

=5z

=180 degrees

180/5=36 degrees, so Z=36 degrees

Answer:

True

Step-by-step explanation:

So this problem is asking whether Parametric because have an orientation and the short answer to that is that this is true. Parametric curves do have an orientation and we'll just do a little demonstration to share. Why? So let's take these very standard privatization of the unit circle where X is he going to cause of tea and why is equal to sign of tea now? The final part of defining the characterization is defining that the main range of tea on will take t to go from zero to two pi Andi, In this case, this is the this parts of circle going in this direction in the counter clockwise direction. And this is because as X as he goes from zero to play over two x decreases and signed increases on it sets us off on this direction as if that's one orientation off this curve of the circle. But we can alter this curve to get a different orientation. So if we were to take the Parametric equation given by X is equal to the co sign a minus T and why is equal to the sign of minus T in this case? Well again, take the domain to be from 0 to 2 pi. But because of the mind, the sign when it the mind sign doesn't actually affect X, it doesn't effect for co sign Well, it does affect the sign of minus T. So as T increases, the X value still decreases. But the Y value initially decreases as well, so this sets the arrows off on the clockwise direction. So this is another orientation off the same curve. So we've got two very different characterizations that describe the same physical curve. But because of the differences, the curve is constructed in opposite direction, and that is what the orientation defines. So it's very important to make sure that when you're drawing and describing the curve, you're parametric equations are in the correct orientation because otherwise you may encounter some difficulties later on. Because you'll be working with equation start that are, in fact, wrong

Thank you,

Eddie.

The retailer would remit $4,900 to the vendor on July 13.

What is invoice date?

The invoice date is the date written on this which is the same as the date the goods were shipped to customer, in this case, invoice date  is July 1.

Invoice receipt date?

This is the date the customer received the invoice as well as the goods sent by the vendor, which is July 4 in this case.

2/10 means that a discount of 2% is available if the customer pays within the first 10 days, which starts counting from July 4, not July 1, because the customer actually received the invoice on July 4.

From July 4 to July 13 is a period of 10 days, which means that the 2% cash discount that customer would be entitled if payment is made within the first 10 days is still available

discount=2%*$5000

discount=$100

The retailer would remit the invoice price of $5,000 minus the discount.

amount remitted=$5000-$100

amount remitted=$4,900

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Answer:

278,861,394

Step-by-step explanation:

put in the calculator e but then just square the numbers add it and there is your answer

The company's current ratio is 2.6.

Current ratio is an example of a liquidity ratio. Liquidity ratios are financial ratios measure a firm's ability to honour its short terms obligations.

Current ratio = current asset /current liability

$65,000 / 25,000 = 2.6

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Answer: A

Step-by-step explanation:

❄ Hi there,

let us start by considering this: What should we do to get x all by itself?

Since it's

we should

So, let's start.

[tex]\sf{\dfrac{-x}{4}\times4 < 2\times4}}[/tex]

[tex]\sf{-x < -8}[/tex]

[tex]\sf{x > 8}[/tex]

When we divide both sides of an inequality by a negative number, we do "the inequality flip" and flip the inequality sign.

❄

It would take 14 hours for all of them to paint the three houses.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let t represent the time it would take them working together, hence:

(1/24 + 1/26 + 1/20 + 1/21 + 1/27)t = 3

t = 14 hours

It would take 14 hours for all of them to paint the three houses.

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Answer:

144 boxes, 4 popsicles left over

Step-by-step explanation:

# of boxes and the remainder: 1148/8 = 143 boxes 4 popsicles left over

Since they need to buy full boxes we add 1 to 143 = 144 boxes

A full box is 8 and they only need 4 more so they have 4 left over.

Answer:

A' is (-2,-1)

B' is (3,0)

C' is (2,4)

Step-by-step explanation: