Section B
Solve the word problems.
1
During a Science workshop, 685 people attended it on the first day
On the second day, there were 3 times as many people as on the
(a) How many people attended the workshop on the second do
(b) Each person had to pay $8 to attend the workshop
What was the total amount collected for the two days?
685

Answer:

8^(7), which is 2097152

Step-by-step explanation:

8^(4) × 8^(3)

= 8^(4+3)

= 8^(7)

= 2097152

Answer:

The answer is 2097152.

Step-by-step explanation:

1) Use the product rule: x^a x^b = x^ a + b.

[tex] {8}^{7} [/tex]

2) Simplify.

[tex]2097152[/tex]

Thus, the answer will be 2097152.

Answer:

m<PQR = 82°

Step-by-step explanation:

In a Rhombus, the diagonals bisect its angles. This means that they divide each the four angles into two equal parts.

Therefore:

(4x - 27)° = (2x + 7)°

Solve for x

4x - 27 = 2x + 7

Collect like terms

4x - 2x = 27 + 7

2x = 34

Divide both sides by 2

2x/2 = 34/2

x = 17

✔️m<PQR = (4x - 27) + (2x + 7)

Plug in the value of x

m<PQR = (4*17 - 27) + (2*17 + 7)

m<PQR = 41 + 41

m<PQR = 82°

Answer:

A. 25.7°

Step-by-step explanation:

the sum of straight angle is 180°.

so, i subtract 154.3 from 180.

i get 25.7 °

Answer:

A sample size of 385 should be used.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

What sample size should be used (round the number up)

A sample of n should be used.

n is found when M = 5.

We have that [tex]\sigma = 50[/tex]

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]5 = 1.96\frac{50}{\sqrt{n}}[/tex]

[tex]5\sqrt{n} = 1.96*50[/tex]

Simplifying by 10

[tex]\sqrt{n} = 1.96*10[/tex]

[tex]\sqrt{n} = 19.6[/tex]

[tex](\sqrt{n})^2 = (19.6)^2[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample size of 385 should be used.

Answer:

a) 5 cm b) 12in c) 7yd

I think it's so simple. Anyways

This is your answer. If I'm right so,

Please mark me as brainliest. thanks!!!

Answer:

5 cm, 12in, 3.5 yrds

Step-by-step explanation:

to find the radius you divide the diamenter by 2.

Answer:

A=30  B=90  C=60

Step-by-step explanation:

A=30 C=60  B=90

Answer:

Open circle going right. <-- graphed

Step-by-step explanation:

1billion is the correct answerStep-by-step explanation:

Answer:

Center... Mean

Step-by-step explanation:

The mean of a data set is the sum of the values divided by the number of values. The median of a data set is the middle value when the values are written in numerical order.

Answer:

uh i dont know lol im new how do i use this thing bahahaha

Step-by-step explanation:

Answer:

a) The axis of symmetry is the line, y = 2

b)  The vertex  of a parabola is (-3, 2)

c) The focus of the parabola is (0, 2)

d) The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola

Step-by-step explanation:

a) The function for the parabola can be expressed as follows;

12·(x + 3) = (y - 2)²

The general form of the equation of the parabola is x = a·(y - k)² + h

The axis of symmetry is the line, y = k

By comparison, with the given equation of the parabola, we have;

12·(x + 3) = (y - 2)²

x = (1/12)·(y - 2)² - 3

Therefore;

a = (1/12), k = 2, h = -3

The axis of symmetry is y = k

∴ The axis of symmetry is the line, y = 2

b) The vertex  of a parabola = (h, k)

∴ The vertex  of a parabola = (-3, 2)

c) The focus of a parabola is [tex]\left(h + \dfrac{1}{4\cdot a} , \ k\right)[/tex]

Therefore, the focus of the parabola is [tex]\left(-3 + \dfrac{1}{4\cdot \dfrac{1}{12} } , \ 2\right)[/tex] = (0, 2)

The focus of the parabola = (0, 2)

d) The directrix of a parabola is [tex]h - \dfrac{1}{4\cdot a}[/tex]

[tex]\therefore h - \dfrac{1}{4\cdot a} = -3 - \dfrac{1}{4\cdot \dfrac{1}{12} } = -3 - 3 } = -6[/tex]

The directrix of a parabola is, x = -6

e) Please find attached the graph of the parabola, showing the vertex, focus, directrix, and axis of symmetry, created with Microsoft Excel

The axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

It is given that the parabola equation is  [tex]\rm 12(x+3)=(y-2)^2[/tex]

It is defined as the graph of a quadratic function that has something bowl-shaped.

We know the standard form of a parabola is:

[tex]\rm x= a(y-k)^2+h[/tex]  .........(1)

We have the equation of parabola:

[tex]\rm 12(x+3)=(y-2)^2\\\\\rm x+3 =\frac{1}{12} [(y-2)^2]\\\\\rm x =\frac{1}{12} [(y-2)^2]-3\\[/tex]........(2)

a) Axis of symmetry: the axis of symmetry is a straight line that divides the parabola into two identical parts.

By comparing the equation (1) and (2), we get:

Axis of symmetry ⇒ (y - k) = 0 ⇒ (y - 2) = 0 ⇒ y = 2.

b) Vertex of the parabola = (h,k): (-3, 2)

c) The focus of the parabola is [tex]\rm (h+\frac{1}{4a} ,k)[/tex],

[tex]\rm h = -3, a = \frac{1}{12} , k= 2[/tex]

∴ [tex]\rm (-3+\frac{1}{4\times(\frac{1}{12}) } ,2)\\\\\rm (0,2)[/tex]

The focus of the parabola is (0, 2)

d) The directrix of a parabola is [tex]\rm x = h-\frac{1}{4a}[/tex]

[tex]\rm x = -3-\frac{1}{4\times\frac{1}{12} }\\\\\rm x= -3-3\\\rm x= -6[/tex]

The directrix of a is x = -6

e) Shown in the below picture: graph of the parabola and vertex, focus, directrix, and axis of symmetry

Thus, the axis of symmetry of the parabola is y = 2, the vertex of the parabola is (-3, 2), the focus of the parabola is (0, 2) and the directrix of the parabola is x = -6

Know more about the parabola here:

brainly.com/question/8708520

Answer:

D

Step-by-step explanation:

edge

D. approximately 4.3 in. to the right of the center

Problem-solving is the act of defining a problem; figuring out the purpose of the problem; determining, prioritizing, and selecting alternatives for an answer; and imposing an answer.

Problem-solving starts with identifying the issue. As an example, a teacher may need to parent out a way to improve a scholar's overall performance on a writing talent test. To do that, the instructor will overview the writing exams looking for regions for improvement.

Learn more about problem-solving here

brainly.com/question/23945932

#SPJ2

Answer:

1.25 since all prices are sam e

Step-by-step explanation:

area=1/2(AB+0A)Ac=4cm

Answer:

28cm²

Step-by-step explanation:

Area of trapezium = 1/2×(6+8)×4

= 28cm²

Answer:

24 because hsbs. hwhvw w Whelan has w hahaha

9514 1404 393

Answer:

  6/5

Step-by-step explanation:

The slope formula is useful for finding the slope.

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -11)/(-5 -5) = -12/-10

  m = 6/5

The slope of the line through the given points is 6/5.

Answer:

Tiger shows you, step by step, how to solve YOUR Quadratic Equations 3x^2-x-11=0 by Completing the Square, Quadratic formula or, ...

Answer:

1 1/6 ton

Step-by-step explanation:

Answer:

151

Step-by-step explanation:

114+131= 272 376-272=104

Answer:

Around 54% is what I would say.

Step-by-step explanation:

Answer:  12 possible outcomes in total

Step-by-step explanation:

Answer:

Choice 1 is correct: 8/3 x 1/4 = 2/3

Step-by-step explanation:

Answer:

1) 0.4096 = 40.96% of waiting times are between 8 and 10.8 minutes.

2) 0.1401 = 14.01% of waiting times are less than 6.8 minutes.

3) 0.1788 = 17.88% probability that you are late.

4) The cutoff for the top 4% of waiting times is of 14.15 minutes.

5) The waiting time for the 30th percentile is of 8.235 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Average of 9.60 minutes and a standard deviation of 2.60 minutes during peak hours.

This means that [tex]\mu = 9.6, \sigma = 2.6[/tex]

1) What proportion of waiting times are between 8 and 10.8 minutes?

This is the pvalue of Z when X = 10.8 subtracted by the pvalue of Z when X = 8. So

X = 10.8

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{10.8 - 9.6}{2.6}[/tex]

[tex]Z = 0.46[/tex]

[tex]Z = 0.46[/tex] has a pvalue of 0.6772

X = 8

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{8 - 9.6}{2.6}[/tex]

[tex]Z = -0.62[/tex]

[tex]Z = -0.62[/tex] has a pvalue of 0.2676

0.6772 - 0.2676 = 0.4096

0.4096 = 40.96% of waiting times are between 8 and 10.8 minutes.

2) What proportion of waiting times are less than 6.8 minutes?

This is the pvalue of Z when X = 6.8.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{6.8 - 9.6}{2.6}[/tex]

[tex]Z = -1.08[/tex]

[tex]Z = -1.08[/tex] has a pvalue of 0.1401

0.1401 = 14.01% of waiting times are less than 6.8 minutes.

3) You reach Wells Hall parking lot and your class starts in 12 minutes. What is the chance that you are late to class, that is waiting time is at least 12 minutes?

This is 1 subtracted by the pvalue of Z when X = 12. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{12 - 9.6}{2.6}[/tex]

[tex]Z = 0.92[/tex]

[tex]Z = 0.92[/tex] has a pvalue of 0.8212

1 - 0.8212 = 0.1788

0.1788 = 17.88% probability that you are late.

4) Based on your unpleasant experiences in the past you know that your waiting time is in the top 4%. What is the cutoff for the top 4% of waiting times?

The cutoff for the top 4% of times is the 100 - 4 = 96th percentile, which is X when Z has a pvalue of 0.96. so X when Z = 1.75.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.75 = \frac{X - 9.6}{2.6}[/tex]

[tex]X - 9.6 = 1.75*2.6[/tex]

[tex]X = 14.15[/tex]

The cutoff for the top 4% of waiting times is of 14.15 minutes.

5) What is the waiting time for the 30th percentile?

This is X when Z has a pvalue of 0.3. So X when Z = -0.525.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.525 = \frac{X - 9.6}{2.6}[/tex]

[tex]X - 9.6 = -0.525*2.6[/tex]

[tex]X = 8.235[/tex]

The waiting time for the 30th percentile is of 8.235 minutes.

Answer:

A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)

Step-by-step explanation:

Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)

Answer:

Step-by-step explanation:

1. 6.96 in

2. 2.6 in

3. 8.1 in

4. 5.6 m

5. 1.89 cm

6. 6 in

Answer:

Step-by-step explanation:

[tex]\text{Maximize p = 5X1 + 4X2 + 3X3 subject to;} \\ \\ 1X1 + 7X2 + 4X3 <= 90[/tex]

[tex]2X1 + 1X2 + 7X3 <= 96[/tex]

[tex]8X1 + 4X2 + 1X3 <= 90[/tex]

[tex]X1 > = 0[/tex]

[tex]X2 >= 0[/tex]

[tex]X3 >=0[/tex]

[tex]\text{USing LP software, The Optimal Solution: Maximum Contribution} = 90.547;}\\ \\ x1 = 7.07692, \\ \\ x2 = 5.62393, \\ \\ x3 = 10.8889[/tex]