patricia baked some cupcakes for sale. she put half of the cupcakes equally into 6 big boxes and the other half equally into small boxes. There were 45 cupcakes in 3 big boxes and 8 small boxes altogether.
a) How many cupcakes dud Patricia bake?
b) She sold all the small boxes and collected $189. How much did she sell each small box for?​

Answer:

A

Step-by-step explanation:

For point-slope form, you need a point and the slope.

y - y₁ = m(x - x₁)

Looking at the graph, the points you have are (4, 0) and (-4, -4).  You can use these points to find the slope.  Divide the difference of the y's by the difference of the x's/

-4 - 0 = -4

-4 - 4 = -8

-4/-8 = 1/2

The slope is 1/2.  This cancels out choices C and D.

With the point (-4, -4), A is the answer.

the equation of the line in slope-intercept form is:

y = (1/2)x - 2

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

From the graph, two points on the line are (-4, -4) and (4,0),

The formula for the slope of a line is:

m = (y₂ - y₁) / (x₁ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the given points (-4, -4) and (4, 0), we can calculate the slope:

m = (0 - (-4)) / (4 - (-4))

m = 4 / 8

m = 1/2

Now that we know the slope, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

To find the y-intercept, we can use one of the given points on the line. Let's use the point (-4, -4):

y = mx + b

-4 = (1/2)(-4) + b

-4 = -2 + b

b = -2

Therefore, the slope-intercept form of the line is y = (1/2)x - 2.

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Answer:

Step-by-step explanation:

3x2−5x−2=0

For this equation: a=3, b=-5, c=-2

3x2+−5x+−2=0

Step 1: Use quadratic formula with a=3, b=-5, c=-2.

x= (−b±√b2−4ac )2a

x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)

x= (5±√49 )/6

x=2 or x= −1 /3

Answer:

x=2 or x= −1/ 3

The solutions to the equation are x = -1/3 and x = 2.

Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:

First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Next, we set each factor equal to 0 and solve for x.

(3x + 1)(x - 2) = 0

3x + 1 = 0

3x = -1

x = -1/3

x - 2 = 0

x = 2

Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.

Here is the explanation for each of the steps:

Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.

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Answer:

x = 4.5 ft

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{18}{x}[/tex] = [tex]\frac{8}{2}[/tex] ( cross- multiply )

8x = 36 ( divide both sides by 8 )

x = 4.5

Answer:

2

Step-by-step explanation:

Slope =( difference in the y coordinates)/ (difference in the x coordinates)

= 6/3

= 2

Answer:

13

Step-by-step explanation:

p^2 -6p +6

Let p=-1

(-1)^2 -6(-1) +6

1 +6+6

13

Answer:

4

Step-by-step explanation:

25% of 25

0.25 × 25 = 6.25

15% of 15​

0.15 × 15 = 2.25

Find the difference.

6.25 - 2.25

= 4

Answer:

For the function [tex]f(x)=\frac{1}{x} +3[/tex]. The domain is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex] and the range is  [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

For the function [tex]g(x) =\sqrt{x+6}[/tex]. The domain is [tex]\left[-6, \infty\right)[/tex] and the range is [tex]\left[0, \infty\right)[/tex].

Step-by-step explanation:

The domain of a function is the set of input or argument values for which the function is real and defined.

The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.

[tex]f(x)=\frac{1}{x} +3[/tex] is a rational function.  A rational function is a function that is expressed as the quotient of two polynomials.

Rational functions are defined for all real numbers except those which result in a denominator that is equal to zero (i.e., division by zero).

The domain of the function is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex].

The range of the function is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].

[tex]g(x) =\sqrt{x+6}[/tex] is a square root function.

Square root functions are defined for all real numbers except those which result in a negative expression below the square root.

The expression below the square root in [tex]g(x) =\sqrt{x+6}[/tex] is [tex]x+6[/tex]. We want that to be greater than or equal to zero.

[tex]x+6\geq 0\\x\ge \:-6[/tex]

The domain of the function is [tex]\left[-6, \infty\right)[/tex].

The range of the function is [tex]\left[0, \infty\right)[/tex].

Answer:

 $624.90

Step-by-step explanation:

The total cost is the integral of the marginal cost. Here, you're asked to approximate that integral using 5 equal-width rectangles. The area of each rectangle is the product of its height and width. The height is given by the function value at the left end of the interval.

The table shows the function values at the left end of each of the 5 intervals. The intervals have width 1600/5 = 320. The total estimated cost is the sum of products of 320 and each of the table values. (Of course, 320 can be factored out of the sum to make the math easier.)

The estimated cost is ...

  320(58 + 50.576 + 41.104 + 29.584 +16.016) = 62,489.6 . . . cents

  ≈ $624.90 . . . . cost of manufacturing 1600 yards of fancy ribbon

Answer:

The percent of increase is 25%

Step-by-step explanation:

Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%

Answer:

It's written as

[tex]6.83 \times {10}^{ - 2} [/tex]

Hope this helps you

Answer:

6.83 × 10 -2

hopefully this helped :3

Answer:

[tex]approx. = 85.28 {ft}^{2} [/tex]

Step-by-step explanation:

You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.

(l×w)+(πr^2)/2

(10×7)+((π2^2)/2

79+2π

[tex]approx. = 85.28 {ft}^{2} [/tex]

Answer:

The transformation is rigid because the corresponding side lengths and angles are congruent.

Step-by-step explanation:

Since we have congruent triangles (not similar triangles), they will have to have the same length and angles throughout your transformation. Therefore, our answer is the 1st Option.

Answer:

B) The transformation is rigid because the corresponding side lengths and angles are congruent.

Step-by-step explanation:

Answer:

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

Step-by-step explanation:

Given A=  [tex]\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right][/tex] = B

Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.

so A*B= [tex]\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right][/tex]

Now multiply and add the separate elements of the matrix A*B=

[tex]\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right][/tex]

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.

c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785

Total cost of benefits for all employees at the food truck= 121 + 14= 135

Answer:

The picture isn't very clear but I think this is the answer.

1. 15 cents

2. $1.31

3. 30 cents

Step-by-step explanation:

1. 10+5

2. 50+50+10+10+10+1

3. 25+5

Answer:

A and B are independent because P(A) * P(B) = P(A and B).

Step-by-step explanation:

If A and B are independent, then P(A) * P(B) = P(A and B)

since

P(A)*P(B) = (2/3*1/4) = 2/12 = 1 / 6 = P(A and B)

A and B are independent.

Answer:

YES THANKS FOR 30

Step-by-step explanation:

Answer:

D. A=(9)(4)

Step-by-step explanation:

area= length x width = 9x4

Answer:

Step-by-step explanation:

A=2(3.14)rh+2(3.14)r^2

A=2(3.14)(4.5)(19)+2(3.14)(4.5)^2

A=536.94+127.17

A=664.11

Might want to double the math but the formula is right!

Answer:

y - 2 = (3/2)(x + 1)

Step-by-step explanation:

Start with the point-slope formula y - k = m(x - h).  With m = 3/2, h = -1 and k = 2, we get:

y - 2 = (3/2)(x + 1)

Answer:

The approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=0.15[/tex]

The standard deviation of this sampling distribution of sample proportion is:

 [tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

As the sample size is large, i.e. n = 150 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.

Compute the mean and standard deviation as follows:

[tex]\mu_{\hat p}=0.15\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.15(1-0.15)}{150}}=0.0292[/tex]

So, [tex]\hat p\sim N(0.15, 0.0292^{2})[/tex]

In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the Normal distribution lie within one, two and three standard deviations of the mean, respectively.

Then,

                                  P (µ-σ < X < µ+σ) ≈ 0.68

                                  P (µ-2σ <X < µ+2σ) ≈ 0.95

                                  P (µ-3σ <X < µ+3σ) ≈ 0.997

Then the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

That is:

[tex]P(\mu_{\hat p}-2\sigma_{\hat p}<\hat p<\mu_{\hat p}+2\sigma_{\hat p})=0.95\\\\P(0.15-2\cdot0.0292<\hat p<0.15+2\cdot0.0292)=0.95\\\\P(0.092<\hat p<0.208)=0.95[/tex]

Answer:

c. there might not be any causal relationship between x and y.

Step-by-step explanation:

A correlation can be defined as a numerical measure of the relationship between existing between two variables (x and y).

In Mathematics and Statistics, a group of data can either be negatively correlated, positively correlated or not correlated at all.

1. For a negative correlation: a set of values in a data increases, when the other set begins to decrease. Here, the correlation coefficient is less than zero (0).

2. For a positive correlation: a set of values in a data increases, when the other set also increases. Here, the correlation coefficient is greater than zero (0).

3. For no or zero correlation: a set of values in a data has no effect on the other set. Here, the correlation coefficient is equal to zero (0).

If two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

A causal relation exists between two variables (x and y), if the occurrence of the first causes the other; where, the first variable (x) is referred to as the cause while the second variable (y) is the effect.

A strong linear relationship exists between two variables (x and y), if they both increases or decreases at the same time. It usually has a correlation coefficient greater than zero or a slope of 1.

Hence, if two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

Answer:

  33 units²

Step-by-step explanation:

A (graphing) calculator shows you that f(4) ≈ 8, and f(8) ≈ 8.5. The curve is almost a straight line between, so the area is approximately ...

  A = (1/2)(8 + 8.5)(4) = 33

__

If you do the integration, it gets a bit messy.

  [tex]\displaystyle\dfrac{5}{7}\int_4^8{x^{2/7}}\,dx+\dfrac{1}{2}\int_4^8{x^{4/9}}\,dx+\int_4^8{6}\,dx\\\\=\left.\left(\dfrac{5}{9}x^{9/7}+\dfrac{9}{26}x^{13/9}+6x\right)\right|_4^8\approx 33.16[/tex]

The appropriate answer choice is 33 square units.

Answer:

The width = 38 yard

Step-by-step explanation:

Given

Dimension of Park = 32 by 24 yard

Area = 1748 yd²

Required

Find the width of the park

Given that the park is surrounded by a trail;

Let the distance between the park and the trail be represented with y;

Such that, the dimension of the park becomes (32 + y + y) by (24 + y + y) because it is surrounded on all sides

Area of rectangle is calculated as thus;

Area = Length * Width

Substitute 1748 for area; 32 + 2y and 24 + 2y for length and width

The formula becomes

[tex]1748 = (32 + 2y) * (24 +2y)[/tex]

Open Bracket

[tex]1748 = 32(24 + 2y) + 2y(24 + 2y)[/tex]

[tex]1748 = 768 + 64y + 48y + 4y^2[/tex]

[tex]1748 = 768 + 112y + 4y^2[/tex]

Subtract 1748 from both sides

[tex]1748 -1748 = 768 -1748 + 112y + 4y^2[/tex]

[tex]0 = 768 -1748 + 112y + 4y^2[/tex]

[tex]0 = -980 + 112y + 4y^2[/tex]

Rearrange

[tex]4y^2 + 112y -980 = 0[/tex]

Divide through by 4

[tex]y^2 + 28y - 245 = 0[/tex]

Expand

[tex]y^2 + 35y -7y - 245 = 0[/tex]

Factorize

[tex]y(y+35) - 7(y + 35) = 0[/tex]

[tex](y-7)(y+35) = 0[/tex]

Split the above into two

[tex]y - 7 = 0\ or\ y + 35 = 0[/tex]

[tex]y = 7\ or\ y = -35[/tex]

But y can't be less than 0;

[tex]So,\ y = 7[/tex]

Recall that the dimension of the park is 32 + 2y by 24 + 2y

So, the dimension becomes 32 + 2*7 by 24 + 2*7

Dimension = 32 + 14 yard by 24 + 14 yard

Dimension = 46 yard by 38 yard

Hence, the width = 38 yard

Answer:

Yes.

Step-by-step explanation:

In the future, simply plug both equations into Desmos.

Hey there! I'm happy to help!

The domain is all of the x-values of a relation and the range is all of the y-values. When you write them out, you order the numbers from least to greatest and put it in brackets.

The domain of our relation is the x-values of these points, which are 11, 9, 7, and 5. The domain is  {5,7,9,11}.

The range is the y-values, which are 1, 2, 3, and 4. So, the range is {1,2,3,4}.

Now you can find the domain and range given a few ordered pairs!

Have a wonderful day!

Answer:

The principal amount is $10160

Step-by-step explanation:

Given; Simple interest, I = 7620

Rate, R = 6.25

Time, T = 12

Principal, P =?

The formula for simple interest, I is;

[tex]I = \frac{PRT}{100}[/tex]

Making P the subject of formula;

[tex]P = \frac{I100}{RT}[/tex]

[tex]P = \frac{7620 *100}{6.25*12}[/tex]

[tex]P = \frac{762000}{75}\\P = 10160[/tex]

Therefore, the principal amount is $10160

Answer:

10000

Step-by-step explanation:

If an amount of money, P, called the principal, is invested for a period of t years at an annual interest rate r, the amount of simple interest, I, earned is given by

I=PrtwhereIPrt=interest=principal=rate=time

The following information is given.

Irt=$7,620=0.0635=12 years

Substituting the given information into the simple interest formula and solving for P gives

7,6207,620=(P)(0.0635)(12)=0.762P

Dividing both sides by 0.762, we have

P=7,6200.762=10,000

Thus, the principal amount of the bond was $10,000.

Answer: a) P(1&2 =defect)= 1/800

b)  P(1&2 =defect)= 1/780

Step-by-step explanation:

a) The probability that 1st of the selected fuses is defective is   2/40=1/20 =0.05

So if we replace it by the not defective the number of defective fuses is 1 and total number is 40.

So the probability that 2-nd selected fuse is defective as well is 1/40

The probability both fuses are defective is

P(1&2 =defect)= 2/40*1/40=2/1600=1/800

b) The probability that 1st of the selected fuses is defective is   2/40=1/20 =0.05

SO residual amount of the fuses is 39. 1 of them is defective.

So the probability that 2-nd selected fuse is defective as well is 1/39

The probability both fuses are defective is

P(1&2 =defect)= 2/40*1/39=2/1560=1/780

Answer:

69.9 mg

Step-by-step explanation:

A = A₀ (½)^(t / T)

where A is the final amount,

A₀ is the initial amount,

t is time,

and T is the half life.

A = 400 (½)^(4000 / 1590)

A = 69.9 mg

Answer:

B. No solution.

Step-by-step example

I will try to solve your system of equations.

3x−y=4;6x−2y=7

Step: Solve3x−y=4for y:

3x−y+−3x=4+−3x(Add -3x to both sides)

−y=−3x+4

−y

−1

=

−3x+4

−1

(Divide both sides by -1)

y=3x−4

Step: Substitute3x−4foryin6x−2y=7:

6x−2y=7

6x−2(3x−4)=7

8=7(Simplify both sides of the equation)

8+−8=7+−8(Add -8 to both sides)

0=−1

Therefore, there is no solution, and the lines are parallel.

Answer:

a)

The object slowing down  S = -72 centimetres after t = 4 seconds

b)

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres

Step-by-step explanation:

Step(i):-

Given  S = t³ - 3 t² - 24 t + 8 ...(i)

   Differentiating equation (i) with respective to 'x'

       [tex]\frac{dS}{dt} = 3 t^{2} - 3 (2 t) - 24[/tex]

     Equating Zero

      3 t ² - 6 t - 24 = 0

 ⇒   t² - 2 t - 8   = 0

 ⇒  t² - 4 t + 2 t - 8 = 0

⇒ t (t-4) + 2 (t -4) =0

⇒  ( t + 2) ( t -4) =0

⇒ t = -2 and t = 4

 Again differentiating with respective to 'x'

   [tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6[/tex]

Step(ii):-

Case(i):-

Put t= -2

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( -2) -6 = -12 -6 = -18 <0[/tex]

The  maximum object

S = t³ - 3 t² - 24 t + 8

S = ( -2)³ - 3 (-2)² -24(-2) +8

S = -8-3(4) +48 +8

S = - 8 - 12 + 56

S = - 20 +56

S = 36

Case(ii):-

   put  t = 4

[tex]\frac{d^{2} S}{dt^{2} } = 6 t - 6 = 6 ( 4) -6 = 24 -6 = 18 >0[/tex]

The object slowing down at t =4 seconds

The minimum objective function

S = t³ - 3 t² - 24 t + 8

S = ( 4)³ - 3 (4)² -24(4) +8

S =  64 -48 - 96 +8

S = - 72

The object slowing down  S = -72 centimetres after t = 4 seconds

Final answer:-

The object slowing down  S = -72 centimetres after t = 4 seconds

The speed is decreasing at t = -2 seconds

The objective function  S = 36 centimetres