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3 years ago

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Scott buys candy that costs $7 per kilogram. He will spend at least $35 on candy. What are the possible numbers of kilograms he

will buy? Use p for the number of kilograms Scott will buy. Write your answer as an inequality solved for p.

1 answer:

slega [8]3 years ago

3 0

Answer:

<em>p ≥ 5</em>

<em>Scott will buy at least 5 kilograms of candy.</em>

Step-by-step explanation:

<u>Inequalities</u>

The candy Scott buys cost $7 per kilogram.

Let's set p=number of kilograms of candy Scott will buy.

The money spent to buy p kilograms of candy is 7p dollars.

The condition states he will spend at least $35 on candies, thus the following inequality is formed:

7p ≥ 35

Dividing by 7:

p ≥ 35/7

Operating:

p ≥ 5

Scott will buy at least 5 kilograms of candy.

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Let N be the universal set and A, B, C, D be its subsets given by A={x:xisaevennaturalnumber},B={x:xNandxisamultipleof3} C={x:x

Svet_ta [14]

Answer:

$A^{'}$ = {1,3,5,7,9,....}

$B^{'}$ = {1,2,4,5,7,8,10,11,13,14......}

$C^{'}$ = {1,2,3,4,5}

$D^{'}$ = {10,11,12,13,14,15,......}

Step-by-step explanation:

Solution:

It is given that, Universal set is the set of all Natural Numbers.

and

Set A, Set B, Set C, Set D are subsets of Universal set.

A = {x:x is even natural numbers} = {2,4,6,8,10,.....}

B = {x:x ∈ N and x is a multiple of 3} = {3,6,9,12,15,....}

C = {x:x∈ N and x < 5} = {6,7,8,9,10,.....}

D = {x:x ∈ N and x > 10} = {1,2,3,4,5,6,7,8,9}

U = {1,2,3,4,5,6,7,8,9,10,11,........}

Complements:

$A^{'}$ = U-A = {1,2,3,4,5,6,7,8,9,10,11,........} - {2,4,6,8,10,.....}

$A^{'}$ = {1,3,5,7,9,....}

$B^{'}$ = U-B = {1,2,3,4,5,6,7,8,9,10,11,........} - {3,6,9,12,15,....}

$B^{'}$ = {1,2,4,5,7,8,10,11,13,14......}

$C^{'}$ = U-C = {1,2,3,4,5,6,7,8,9,10,11,........} - {6,7,8,9,10,.....}

$C^{'}$ = {1,2,3,4,5}

$D^{'}$ = {1,2,3,4,5,6,7,8,9,10,11,........} - {1,2,3,4,5,6,7,8,9}

$D^{'}$ = {10,11,12,13,14,15,......}

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3 years ago

(15, 31) is rotated 90 ° counterclockwise which coordinates gives me

dezoksy [38]

Answer:

(-31,15)

Step-by-step explanation:

Rotating 90 degrees clockwise is very simple:

(a,b) 90 degrees= (-b,a)

Very simple.

Just switch sides and add negative to the first term.

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3 years ago

What is the solution to f(-2)=-|-2-2|

nexus9112 [7]

Answer:

f = -4

Explanation:

f(-2) = -|-2 - 2|

Subtract The Numbers: -2 - 2 = 4

f = -| -4|

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3 years ago

Read 2 more answers

#10 i The table shows the admission costs (in dollars) and the average number of daily visitors at an amusement park each the pa

lions [1.4K]

The line of best fit is a straight line that can be used to predict the

average daily attendance for a given admission cost.

Correct responses:

The equation of best fit is; $\underline{ \hat Y = 1,042 - 4.9 \cdot X_i}$

The correlation coefficient is; r ≈<u> -0.969</u>

<h3>Methods by which the line of best fit is found</h3>

The given data is presented in the following tabular format;

$\begin{tabular}{|c|c|c|c|c|c|c|c|c|}Cost, (dollars), x&20&21&22&24&25&27&28&30\\Daily attendance, y&940&935&940&925&920&905&910&890\end{array}\right]$

The equation of the line of best fit is given by the regression line

equation as follows;

$\hat Y = \mathbf{b_0 + b_1 \cdot X_i}$

Where;

$\hat Y$ = Predicted value of the<em> i</em>th observation

b₀ = Estimated regression equation intercept

b₁ = The estimate of the slope regression equation

$X_i$ = The <em>i</em>th observed value

$b_1 = \mathbf{\dfrac{\sum (X - \overline X) \cdot (Y - \overline Y) }{\sum \left(X - \overline X \right)^2}}$

$\overline X$ = 24.625

$\overline Y$ = 960.625

$\mathbf{\sum(X - \overline X) \cdot (Y - \overline Y)} = -433.125$

$\mathbf{\sum(X - \overline X)^2} = 87.875$

Therefore;

$b_1 = \mathbf{\dfrac{-433.125}{87.875}} \approx -4.9289$

Therefore;

The slope given to the nearest tenth is b₁ ≈ -4.9

$b_0 = \mathbf{\dfrac{\left(\sum Y \right) \cdot \left(\sum X^2 \right) - \left(\sum X \right) \cdot \left(\sum X \cdot Y\right)} {n \cdot \left(\sum X^2\right) - \left(\sum X \right)^2}}$

By using MS Excel, we have;

n = 8

∑X = 197

∑Y = 7365

∑X² = 4939

∑Y² = 6782675

∑X·Y = 180930

(∑X)² = 38809

Therefore;

$b_0 = \dfrac{7365 \times 4939-197 \times 180930}{8 \times 4939 - 38809} \approx \mathbf{1041.9986}$

The y-intercept given to the nearest tenth is b₀ ≈ 1,042

The equation of the line of best fit is therefore;

$\underline{\hat Y = 1042 - 4.9 \cdot X_i}$

The correlation coefficient is given by the formula;

$\displaystyle r = \mathbf{\dfrac{\sum \left(X_i - \overline X) \cdot \left(Y - \overline Y \right)}{ \sqrt{\sum \left(X_i - \overline X \right)^2 \cdot \sum \left(Y_i - \overline Y \right)^2} }}$

Where;

$\sqrt{\sum \left(X - \overline X \right)^2 \times \sum \left(Y - \overline Y \right)^2} = \mathbf{446.8121}$

$\sum \left(X_i - \overline X \right) \times \left(Y - \overline Y\right) = \mathbf{-433.125}$

Which gives;

$r = \dfrac{-433.125}{446.8121} \approx \mathbf{-0.969367213}$

The correlation coefficient given to the nearest thousandth is therefore;

<u>Correlation coefficient, r ≈ -0.969</u>

Learn more about regression analysis here:

brainly.com/question/14279500

7 0

3 years ago

The length of a rectangle is 10 meters more than the width. If 3 meters is added to both the length and the width, the new area

Finger [1]

Answer:

L = 20

W = 10

Step-by-step explanation:

L = (w + 10)

NL = (w + 13)

Divide 299 by 13:

299 ÷ 13 = 23

So, 23 x 13 = 299

L = 23

W = 13

Subtract 3 from both to get the original length and width

4 0

3 years ago