Miguel went shopping for a new phone. Sales tax where he lives is 4%. What number should he multiply the price of the phone by to find the total plus tax in one step?

t-3.2 ≤ 7.5

"at most" means less than or equal to

Answer:

z=3

Step-by-step explanation:

1. collect like terms

5z-5=25-5z

2. Move the variable to the left hand side and change its sign

5z-5+5z=25

3. Collect like terms

10z=25+5

4. Divide both sides of the equation by 10

z=3

The solution to the equation is z = 3.

To solve for z in the equation 3z - 5 + 2z = 25 - 5z, we can simplify and combine like terms on both sides:

3z + 2z + 5z = 25 + 5

Combining the terms on the left side gives:

10z = 30

Next, we isolate the variable z by dividing both sides of the equation by 10:

(10z)/10 = 30/10

This simplifies to:

z = 3

Therefore, the solution to the equation is z = 3.

To know more about equation:

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Answer:

Time taken for pump B to empty pool = 1 hour.

Step-by-step explanation:

Given:

Time taken for pump A to empty pool = 4 hour

Time taken together = 48 minutes = 48 / 60 = 4/5 hour

Find:

Time taken for pump B to empty pool

Computation:

Assume;

Time taken for pump B to empty pool = a

1/4 + 1/a = 1 / (4/5)

1/4 + 1/a = 5/4

1/a = 5/4 - 1/4

1/a = (5 - 1) / 4

1/a = 1

a = 1

Time taken for pump B to empty pool = 1 hour.

9514 1404 393

Answer:

  90° CCW

Step-by-step explanation:

The transformation from B to B' is ...

  B(-4, 1) ⇒ B'(-1, -4)

  (x, y) ⇒ (-y, x) . . . . . matches the transformation for 90° CCW

Answer:

90 degrees

Step-by-step explanation:

Answer:

Option B. A = (5/6)^-⅛

Step-by-step explanation:

From the question given above, we obtained:

(5/6)ˣ = A¯⁸ˣ

We can obtain the value of A as follow:

(5/6)ˣ = A¯⁸ˣ

Cancel x from both side

5/6 = A¯⁸

Recall:

M¯ⁿ = 1/Mⁿ

A¯⁸ = 1/A⁸

Thus,

5/6 = 1/A⁸

Cross multiply

5 × A⁸ = 6

Divide both side by 5

A⁸ = 6/5

Take the 8th root of both sides

A = ⁸√(6/5)

Recall

ⁿ√M = M^1/n

Thus,

⁸√(6/5) = (6/5)^⅛

Therefore,

A = (6/5)^⅛

Recall:

(A/B)ⁿ = (B/A)¯ⁿ

(6/5)^⅛ = (5/6)^-⅛

Therefore,

A = (5/6)^-⅛

Answer:

Step-by-step explanation:

From the given information:

a)

Assuming the shape of the base is square,

suppose the base of each side = x

Then the perimeter of the base of the square = 4x

Suppose the length of the package from the base = y; &

the height is also = x

Now, the restriction formula can be computed as:

y + 4x ≤ 99

The objective function:

i.e maximize volume V = l × b × h

V = (y)*(x)*(x)

V = x²y

b) To write the volume as a function of x, V(x) by equating the derived formulas in (a):

y + 4x ≤ 99   --- (1)

V = x²y          --- (2)

From equation (1),

y ≤ 99 - 4x

replace the value of y into (2)

V ≤ x² (99-4x)

V ≤ 99x² - 4x³

Maximum value V = 99x² - 4x³

At maxima or minima, the differential of [tex]\dfrac{d }{dx}(V)=0[/tex]

[tex]\dfrac{d}{dx}(99x^2-4x^3) =0[/tex]

⇒ 198x - 12x² = 0

[tex]12x \Big({\dfrac{33}{2}-x}}\Big)=0[/tex]

By solving for x:

x = 0 or x = [tex]\dfrac{33}{2}[/tex]

Again:

V = 99x² - 4x³

[tex]\dfrac{dV}{dx}= 198x -12x^2 \\ \\ \dfrac{d^2V}{dx^2}=198 -24x[/tex]

At x = [tex]\dfrac{33}{2}[/tex]

[tex]\dfrac{d^2V}{dx^2}\Big|_{x= \frac{33}{2}}=198 -24(\dfrac{33}{2})[/tex]

[tex]\implies 198 - 12 \times 33[/tex]

= -198

Thus, at maximum value;

[tex]\dfrac{d^2V}{dx^2}\le 0[/tex]

Recall y = 99 - 4x

when at maximum x = [tex]\dfrac{33}{2}[/tex]

[tex]y = 99 - 4(\dfrac{33}{2})[/tex]

y = 33

Finally; the volume V = x² y is;

[tex]V = (\dfrac{33}{2})^2 \times 33[/tex]

[tex]V =272.25 \times 33[/tex]

V = 8984.25 inches³

9514 1404 393

Answer:

  А. Зп > 9

Step-by-step explanation:

The inequality of A may or may not be true. (It is true only if n > 3.) All of the others are definitely false.

Answer:

The maximum height of the basketball is of 24.25 feet.

Step-by-step explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

[tex]f(x) = ax^{2} + bx + c[/tex]

It's vertex is the point [tex](x_{v}, y_{v})[/tex]

In which

[tex]x_{v} = -\frac{b}{2a}[/tex]

[tex]y_{v} = -\frac{\Delta}{4a}[/tex]

Where

[tex]\Delta = b^2-4ac[/tex]

If a<0, the vertex is a maximum point, that is, the maximum value happens at [tex]x_{v}[/tex], and it's value is [tex]y_{v}[/tex].

Height of the basketball:

Given by the following function:

[tex]h(t) = -4t^2 + 10t + 18[/tex]

Which is a quadratic function with [tex]a = -4, b = 10, c = 18[/tex]

What is the maximum height of the basketball?

y(in this case h) of the vertex. So

[tex]\Delta = b^2-4ac = 10^2 - 4(-4)(18) = 388[/tex]

[tex]y_{v} = -\frac{388}{4(-4)} = 24.25[/tex]

The maximum height of the basketball is of 24.25 feet.

Answer:

At this pace the country will have only 237.6 million acres of forest left in 44 years.

Step-by-step explanation:

Given that a certain country has 586.08 million acres of forest, and every year, the country loses 7.92 million acres of forest mainly due to deforestation for farming purposes, to determine, if this situation continues at this pace, how many years later will the country have only 237.6 million acres of forest left, the following calculation must be performed:

Current amount - (amount lost per year x number of years) = 237.6

586.08 - (7.92 x X) = 237.6

586.08 - 7.92X = 237.6

-7.92X = 237.6 - 586.08

-7.92X = -348.48

X = -348.48 / -7.92

X = 44

Therefore, at this pace the country will have only 237.6 million acres of forest left in 44 years.

Answer:

a) The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).

b) The margin of error is of 0.05.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

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

In a sample of 400 students, 60% of them prefer eBooks.

This means that [tex]n = 400, \pi = 0.6[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.054[/tex].

Margin of error -> Question b:

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

[tex]M = 2.054\sqrt{0.6*0.4}{400}}[/tex]

[tex]M = 0.05[/tex]

The margin of error is of 0.05.

A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.

Sample proportion plus/minus the margin of error.

0.6 - 0.05 = 0.55

0.6 + 0.05 = 0.65

The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).

Answer:

35

Step-by-step explanation:

AEC and AEB form a straight angle(180°)

180-40=140

AEV and AED are equal

140 divided by 4 = 35

Answer:

Step-by-step explanation:

Answer:

1.) A negative linear pattern

2.) Y = - 0.298X1 + 22.241

3.) slope = - 0.298 ; intercept = 22.241

Kindly check explanation

Step-by-step explanation:

Fitting the time series data using technology, the regression equation obtained is :

Y = - 0.298X+ 22.241

Where ; y = percentage of adults who smoke

x = year

Comparing with the linear equation model :

y = b1x + b0

y = - 0.298x + 22.41

-0.298 = slope

22.41 = intercept

The mean squared error, MSE = 0.512

To achieve, percentage users of 12% or less :

y = 12

Y = - 0.298X+ 22.241

12 = - 0.298X + 22.241

12 - 22.241 = - 0.298X1

-10.241 = - 0.298X

X = 10.241 / 0.298

X = 34.365

X = 35 years

From the model OSHA is not on target to meet it's goal as it will take 35 - 11 = 24 years from the last year of the data to achieve a smoker percentage less Than 12%

Answer:

Given the following algebraic expression 5x² + 10 Which statement is true?

a. The coefficient is 5. ( true)

b. The constant is 2

C. The power is 10

d. The constant is 5

Answer:

115.5 cm

Step-by-step explanation:

A^2 + B^2 = C^2

41^2 + 108^2 = C^2

C^2 = 13345

C = 115.5 cm

[tex]{ \bf{ \underbrace{Given :}}}[/tex]

Radius of the circle "[tex]r[/tex]" = 10 cm.

[tex]{ \bf{ \underbrace{To\:find:}}}[/tex]

The circumference of the circle.

[tex]{ \bf{ \underbrace{Solution :}}}[/tex]

[tex]\sf\orange{The\:circumference \:of\:the\:circle\:is\:20\:π\:cm.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

We know that,

[tex]\sf\purple{Circumference\:of\:a\:circle \:=\:2πr }[/tex]

[tex] = 2 \: \pi \times 10 \: cm \\ \\ = 20 \: \pi \: cm[/tex]

Therefore, the circumference of the circle is 20 π cm.

[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]

Answer:

City B experienced a bigger temperature change than City A.

Step-by-step explanation:

From the graph of the temperature given, using visual inspection, we can see how the graph of both cuties change, for city A, the change in temperature, very low as the highest temperature is about 80 and the lowest temperature value is about 76 ;

However. For city B, the highest temperature value is about 100 and the lowest is about 76

Hence, City B experienced a bigger temperature change than A.

For low temperature, the low temperature in city A and B are the same with a value of about 76°

Answer:

Correct.

Step-by-step explanation:

It looks good to me.

Good job!

Answer:

as the sample size increases, the margin of error decreases

Answer:

[tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]

Step-by-step explanation:

Just to make it easier to see, [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex] and [tex]\sqrt[5]{x} = x^{\frac{1}{5} }[/tex]  This way we could more easily use the power rule of derivatives.

So if f(x) = [tex]x^{2} +x^{\frac{1}{2} } +x^{\frac{1}{5} }[/tex] then f'(x) will be as follows.

f'(x) = [tex]x^{1} +\frac{1}{2} x^{-\frac{1}{2} } +\frac{1}{5} x^{-\frac{4}{5} } = x +\frac{1}{2x^{\frac{1}{2} }} +\frac{1}{ 5x^{\frac{4}{5} }} = x +\frac{1}{2\sqrt{x}} +\frac{1}{ 5\sqrt[5]{x^4} }[/tex]

to find f'(3) just plug 3 into f'(x) so [tex]3 + \frac{1}{2\sqrt{3} } + \frac{1}{5\sqrt[5]{81} }[/tex]

Answer:

Auto Credit Express, Carvana, Capital one auto loan

Answer:

80 ft²

Step-by-step explanation:

You are given the formula

a = (1/2)bh

Just plug in the base and height, then multiply

a = (1/2) * 8 *20

a = (1/2) * 160

a = 80 ft²

Answer:

80 [tex]ft^{2}[/tex]

Step-by-step explanation:

Area = [tex]\frac{1}{2} bh[/tex]

Area = [tex]\frac{1}{2}[/tex] 8 · 20

Area = [tex]\frac{1}{2}[/tex] 160

Area = 80 [tex]ft^{2}[/tex]

The answer is B

the method use to solved this is called foil

Answer:

c

Step-by-step explanation:

Answer:

(-1.5, 0.5)

Step-by-step explanation:

x = -1.5

y = 0.5

(-1.5, 0.5)

Answer:

the answer is 3.5

Step-by-step explanation:

Use the following property below:

[tex] \large \boxed{ \sqrt[n]{a} \times \sqrt[n]{a} \times \sqrt[n]{a} = { (\sqrt[n]{a}) }^{3} }[/tex]

Therefore,

[tex] \large{ \sqrt[7]{x} \times \sqrt[7]{x} \times \sqrt[7]{x} = { (\sqrt[7]{x}) }^{3} }[/tex]

Then we use next property.

[tex] \large{ \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } }[/tex]

Hence,

[tex] \large{ \sqrt[7]{ {x}^{3} } = {x}^{ \frac{3}{7} } }[/tex]

Answer

Answer:

Let the retail cost be x and the wholesale cost be y

Step-by-step explanation:

x = y + 0.50y

x = 1.50y

Therefore the retail cost is 1.50 times the wholesale cost.