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3 years ago

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Apples cost $1.60 per pound at the farmer’s market. They cost 1.5 times as much at the grocery store. How much do the apples cos

t per pound at the grocery store?

1 answer:

LenKa [72]3 years ago

8 0

Answer: $2.40

Step-by-step explanation: 16 times 15 equals 240 you get your decimal point and move it twice to the the left

You might be interested in

What is -3(-6+8)^3-2(1-3)^3

marin [14]

Assignment: $\bold{Solve \ Equation: \ -3\left(-6+8\right)^3-2\left(1-3\right)^3}$

<><><><><>

Answer: $\boxed{\bold{-8}}$

<><><><><>

Explanation: $\downarrow\downarrow\downarrow$

<><><><><>

[ Step One ] Follow PEMDAS Order Of Operations; Calculate Within Parenthesis

Note: $\bold{PEMDAS: \ Parenthesis, \ Exponents, \ Multiply, \ Divide, \ Add, \ Subtract}$

$\bold{-6+8: \ 2}$

[ Step Two ] Rewrite Equation

$\bold{-3\cdot \:2^3-2\left(1-3\right)^3}$

[ Step Three ] Calculate Within Parenthesis

$\bold{1-3: \ -2}$

[ Step Four ] Rewrite Equation

$\bold{-3\cdot \:2^3-2\left(-2\right)^3}$

[ Step Five ] Calculate Exponents

$\bold{2^3: \ 8}$

[ Step Six ] Rewrite Equation

$\bold{-3\cdot \:8-2\left(-8\right)}$

[ Step Seven ] Multiply

$\bold{2\left(-8\right): \ -16}$

[ Step Eight ] Rewrite Equation

$\bold{-24-\left(-16\right)}$

[ Step Nine ] Subtract

$\bold{-24-\left(-16\right): \ -8}$

[ Step Ten ] Rewrite Equation

$\bold{-8}$

<><><><><><><>

$\bold{\rightarrow Mordancy \leftarrow}$

8 0

3 years ago

Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.

irina1246 [14]

Lagrange multipliers:

$L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)$

$L_x=y^2z^2+\lambda=0$
$L_y=2xyz^2+\lambda=0$
$L_z=2xy^2z+\lambda=0$
$L_\lambda=x+y+z-5=0$

$\lambda=-y^2z^2=-2xyz^2=-2xy^2z$

$-y^2z^2=-2xyz^2\implies y=2x$ (if $y,z\neq0$ )

$-y^2z^2=-2xy^2z\implies z=2x$ (if $y,z\neq0$ )

$-2xyz^2=-2xy^2z\implies z=y$ (if $x,y,z\neq0$ )

In the first octant, we assume $x,y,z>0$ , so we can ignore the caveats above. Now,

$x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2$

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of $f(1,2,2)=16$ .

We also need to check the boundary of the region, i.e. the intersection of $x+y+z=5$ with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force $f(x,y,z)=0$ , so the point we found is the only extremum.

4 0

3 years ago

A department store sells small boxes in which customers can store potpourri. The diagram below shows one of the boxes. The diagr

larisa86 [58]

The lateral area is expressed as the product of the perimeter of the base and the height. While the surface area is the sum of all areas. The lateral area and the surface area of the box is calculated as follows:

LA = Ph
P = 2l + 2w = (2 x 17) + (2 x 5) = 44 cm
LA = 44 cm x 3.12 cm = 137.28 cm

SA = 2(lw + wh + lh)
SA = 2[(17x5) + (5x3.12) + (17x3.12)]
SA = 307.28 cm

Thus, the lateral area and the surface area are 137 cm and 307 cm, respectively.

8 0

3 years ago

\log_{4} x + \log_{4} (x+5) = 6

irina1246 [14]

   log(4)x + log(4)(x + 5) = 6
log(4)x + log(4)x + log(20) = 6
       log(8)x + log(20) = 6
        <u>    - log(20) - log(20)</u>
      <u>log(8)x</u> = <u>6 - log(20)</u>
   log(8)    log(8)
   x ≈ 0.999

8 0

3 years ago

Question 6 (1.25 points)

Lisa [10]

Answer:

Test statistic Z= 1.713

The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the mean annual salary of all lawyers in a city is different from $110,000

Step-by-step explanation:

<u><em>Step(i):-</em></u>

A researcher wants to test if the mean annual salary of all lawyers in a city is

different from $110,000

Mean of the Population μ = $110,000

Sample size 'n' = 53

Mean of the sample x⁻ = $114,000.

standard deviation of the Population = $17,000,

Level of significance = 0.01

Null hypothesis :

There is no difference between the mean annual salary of all lawyers in a city is different from $110,000

H₀: x⁻ = μ

Alternative Hypothesis : x⁻ ≠ μ

<u><em>Step(ii)</em></u>:-

Test statistic

$Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }$

$Z = \frac{114000-110000}{\frac{17000}{\sqrt{53} } }$

Z = 1.7130

Tabulated value Z = 2.576 at 0.01 level of significance

The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance

Null hypothesis is accepted

There is no difference between the mean annual salary of all lawyers in a city is different from $110,000

4 0

3 years ago