Ask question

Ask question

All categories

8 days ago

15

Katie's orange tree has 30 oranges. Katie's tree has three times as many fruits as Lisa's did before Lisa harvested half of her

limes on the tree. How many limes does Lisa have on her tree now?

1 answer:

AnnZ [3.8K]8 days ago

3 0

Response:

15

Detailed reasoning: The answer is 15 since Katie has 30 oranges, while Lisa initially had 10, and after harvesting half, which is 5, her remaining count must be considered.

You might be interested in

The equation of the tangent plane to the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 at the point (x0, y0, z0) can be written as xx0 a2

PIT_PIT [3919]

Answer:

The tangent plane equation for the hyperboloid

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=1$ .

Step-by-step explanation:

We have

The ellipsoid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$

The equation for the tangent plane at the point $\left(x_0,y_0,z_0\right)$

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}+\frac{zz_0}{c^2}=1$ (Given)

The hyperboloid's equation is

$\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}{c^2}=1$

F(x,y,z)= $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{z^2}[c^2}$

$F_x=\frac{2x}{a^2},F_y=\frac{2y}{b^2},F_z=-\frac{2z}{c^2}$

$(F_x,F_y,F_z)(x_0,y_0,z_0)=\left(\frac{2x_0}{a^2},\frac{2y_0}{b^2},-\frac{2z_0}{c^2}\right)$

The tangent plane equation at point $\left(x_0,y_0,z_0\right)$

$\frac{2x_0}{a^2}(x-x_0)+\frac{2y_0}{b^2}(y-y_0)-\farc{2z_0}{c^2}(z-z_0)=0$

The tangent plane equation for the hyperboloid is

$\frac{2xx_0}{a^2}+\frac{2yy_0}{b^2}-\frac{2zz_0}{c^2}-2\left(\frac{x_0^2}{a^2}+\frac{y_0^2}{b^2}-\frac{z_0^2}{c^2}\right)=0$

The tangent plane equation

$2\left(\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}\right)=2$

Hence, the required tangent plane equation for the hyperboloid is

$\frac{xx_0}{a^2}+\frac{yy_0}{b^2}-\frac{zz_0}{c^2}=0$

7 0

12 days ago

Customer: “I would like to purchase 20 products at a cost of $65.00 per product. What will be my total?” Employee: “Your state h

Svet_ta [4321]

1 product = $65.00
20 products = 65 x 20 = $1300

Sales Tax is 3.5% of $1300 = 0.035 x $1300 = $45.50

Grand total = $1300 + $45.50 = $1345.50

--------------------------------------------------------------
Response: $1345.50
--------------------------------------------------------------

8 0

5 days ago

Read 2 more answers

Assume that a study of 500 randomly selected airplane routes showed that 482 arrived on time. Select the correct interpretation

babunello [3635]

Answer: C. Significant at 0.036

Step-by-step explanation:

Given:

Total samples selected Ns= 500

Airplanes that arrived on time Na = 482.

Airplanes that arrived late Nl = 500 - 482 = 18

Calculating the probability of an airplane arriving late:

P(L) = Nl/Ns

P(L) = 18/500

P(L) = 0.036

An event is deemed significant if its probability is equal to or less than 0.05.

As P(L) < 0.05

P(L) = Significant at 0.036

4 0

7 days ago

The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). What is the best inte

AnnZ [3877]

Let

s--------> denote the cube's side length

We know that

the volume of a cube is calculated as

$V(s)= s^{3}$

if the side length s measures $2\ feet$

then

$s=2\ feet$

and thus, the volume is defined as

$V(2)= 2^{3}$

$V(2)= 8\ feet^{3}$

This leads us to conclude

the correct option is

D. A cube with side lengths of 2 feet has a volume of 8 cubic feet.

5 0

11 days ago

Read 2 more answers

Mike runs for the president of the student government and is interested to know whether the proportion of the student body in fa

zzz [4022]

Answer:

We conclude that less than or equal to 50% of the student body supports him significantly.

Step-by-step explanation:

Mike, while campaigning for the student government presidency, is keen to determine if more than 50% of the student body supports him.

A random sample of 100 students was surveyed, with 55 expressing support for Mike.

Let p = the proportion of students backing Mike.

Thus, Null Hypothesis, $H_0$ : p $\leq$ 50% {indicating that the proportion of supporters among the student body is significantly less than or equal to 50%}

Alternate Hypothesis, $H_A$ : p > 50% {indicating that the proportion of supporters among the student body is significantly more than 50%}

The test statistics to be utilized here One-sample z proportion statistics;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = the sampled proportion in favor of Mike = $\frac{55}{100}$ = 0.55

n = number of sampled students = 100

Therefore, test statistics = $\frac{0.55-0.50}{\sqrt{\frac{0.55(1-0.55)}{100} } }$

= 1.01

The z test statistic is 1.01.

At a significance level of 0.05, the z table provides a critical value of 1.645 for a right-tailed test.

Given that our test statistic falls below the critical value of z (1.01 < 1.645), we lack sufficient evidence to reject the null hypothesis as it remains outside the rejection region, leading to failure to reject our null hypothesis.

As a result, we conclude that less than or equal to 50% of the student body is in favor of him or the proportion supporting Mike is not significantly greater than 50%.

4 0

2 days ago