Find the area and perimeter of the parallelogram. (Hint: Don't forget your units!)
7 cm
8 cm
4 cm

The probability of drawing a black card is P(draw a black card) = 0.3 or 30%.

Probability is a branch of mathematics that deals with the study of random events and the likelihood or chance of their occurrence. It is the measure of how likely or unlikely it is for an event to happen. The probability of an event is a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain to occur.

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if we want to calculate the probability of flipping a coin and getting heads, we divide the number of ways to get heads (1) by the total number of possible outcomes (2), which gives us a probability of 1/2 or 0.5.

Probability is used in many real-world applications, such as in the fields of finance, insurance, and engineering, to make informed decisions based on the likelihood of an event occurring. It is also used in statistical analysis to make inferences about a population based on a sample of data.

The total number of cards in the deck is:

Total number of cards = number of black cards + number of red cards = 33 + 77 = 110

The probability of drawing a black card is given by:

P(draw a black card) = (number of black cards) / (total number of cards) = 33 / 110

Therefore, the probability of drawing a black card is:

P(draw a black card) = 0.3 or 30%

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Using curves, we can find that the value of y at the indicated point on the curve is √3.

What is the definition of curves?

A smooth-drawn figure or line with a bend or turns is referred to as a curve. A circle is an illustration of a curved shape. Geometry is a subfield of mathematics that examines the dimensions, characteristics, and shapes of figures.

Here in the question,

Given equation:

x = y² - 2

As a point (1, y) is on the curve, we can put the value of x coordinate in the equation:

1 = y² - 2.

Adding 2 on both sides:

1 + 2 = y² - 2 + 2

⇒ 3 = y²

⇒ y = √3.

Therefore, the value of y at the indicated point on the curve is √3.

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The diagram of the Gateway Arch on the coordinate plane, analyzed using quadratic equations indicates;

1. The vertex point is (50, 630)

2. The solution point are; (20, 0), and (80, 0)

3. Vertex form; f(x) = -0.7·(x - 50)² + 630

4. Factored form; f(x) = -0.7·(x - 20)·(x - 80)

A quadratic equation is an equation of the form f(x) = a·x² + b·x + c

1. The vertex obtained from the graphical diagram of the Gateway Arch indicates that the point corresponding to the vertex point is; (50, 9 × 70 = 630)

The vertex point is; (50, 630)

2. The solution are the points the curve of the Gateway intersects the x-axis, which are points where the y-axis values are zero, therefore;

The solutions are; (20, 0), and (80, 0)

3. The vertex form of a quadratic equation is; f(x) = a·(x - h)² + k

Where;

(h, k) = The coordinates of the vertex

Therefore;

(h, k) = (50, 630)

f(20) = 0 = a·(20 - 50)² + 630

a·(20 - 50)² = -630

a = -630/((20 - 50)²) = -630/900 = -7/10

a = -7/10 = -0.7

The vertex form quadratic equation is therefore; f(x) = -0.7·(x - 50)² + 630

4. The factored form of a quadratic equation is; f(x) = a·(x - r₁)·(x - r₂)

r₁ = 20, and r₂ = 80, a obtained from the vertex is; a = -0.7

The factored form is therefore; f(x) = -0.7·(x - 20)·(x - 80)

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Answer: a. To find the number of barrels that should be refined to maximize profit, we need to find the critical point of the function P(x), which occurs where the derivative of P(x) equals zero.

P(x) = 8x - 0.02x²

P'(x) = 8 - 0.04x

Setting P'(x) = 0, we get:

8 - 0.04x = 0

Solving for x, we get:

x = 200

Therefore, 200 barrels should be refined to maximize the profit.

b. To find the maximum profit, we substitute x = 200 into the profit function P(x):

P(200) = 8(200) - 0.02(200)²

P(200) = 1600 - 800

P(200) = 800

Therefore, the maximum profit is $800.

Step-by-step explanation:

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

The basic probability formula of dividing the number of favorable outcomes by the total number of outcomes.

In this case, we are given the percentage of members in each age group, and we need to find the probability of selecting a member with a certain age range.

Here we have

The table shows the age distribution of members of a gym.  

Age -            Under 21      21 -35     36 - 55   Over 55

percentage       12                42            32          14  

a) To find the probability that the selected member is 21 or more,

Add the percentage of members who are 21-35, 36-55, and over 55 since all of these age groups are 21 or more.

Probability (21 or more)

= Percentage (21-35) + Percentage (36-55) + Percentage (Over 55)

= 42% + 32% + 14%

= 88%

b) To find the probability that the selected member is 55 or less,  

Add the percentage of members who are under 21, 21-35, and 36-55 since all of these age groups are 55 or less.

Probability (55 or less)

= Percentage (Under 21) + Percentage (21-35) + Percentage (36-55)

= 12% + 42% + 32%

= 86%

c) To find the probability that the selected member is not in the 21 to 35 age group,

Add the percentage of members who are under 21, 36-55, and over 55 since all of these age groups are not in the 21 to 35 age group.

Probability (not in the 21 to 35 age group)

= Percentage (Under 21) + Percentage (36-55) + Percentage (Over 55)

= 12% + 32% + 14%

= 58%

Therefore,

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

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Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

The equation [tex]y=\frac{7}{2}x+3[/tex] tells us that, to find y, we must multiply x by [tex]\frac{7}{2}[/tex] and then add 3. Here, we are given the y value. We simply must plug in y and solve for x.

We are given: the equation [tex]y=\frac{7}{2}x+3[/tex], and [tex]y=-4[/tex]

So, we have:

[tex]y=\frac{7}{2}x+3 =\\\\-4 =\frac{7}{2}x+3[/tex]

Solve for the variable x.

[tex]-4=\frac{7}{2}x+3=\\\\\\-7 = \frac{7}{2}x =\\-14 = 7x=\\-2 = x[/tex]

Therefore, when y is equal to -4, x is equal to -2.

still 7 inches since translation and rotation do not affect area, angles and the length of the sides. Therefore, if you look at the angles, CA will be the same as DF

Answer:

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

Step-by-step explanation:

To find the rate of growth of the yeast population, we can use the exponential growth formula:

P(t) = P₀ * e^(kt)

where P(t) is the population size at time t, P₀ is the initial population size, k is the growth rate constant, and t is the time elapsed.

In this case, the initial population size P₀ is 5, the final population size P(5) is 160, and the time elapsed t is 5 hours. We want to find the growth rate constant k.

Plugging in the values, we get:

160 = 5 * e^(5k)

Divide by 5:

32 = e^(5k)

Now, take the natural logarithm (ln) of both sides to isolate k:

ln(32) = ln(e^(5k))

Using the property that ln(a^b) = b * ln(a):

ln(32) = 5k * ln(e)

Since ln(e) = 1:

ln(32) = 5k

Now, divide by 5:

k = (ln(32)) / 5 ≈ 0.4641 (rounded to four decimal places)

So, the growth rate constant k is approximately 0.4641 per hour.

To express the rate of growth as a percentage, multiply the growth rate constant by 100:

0.4641 * 100 ≈ 46.41%

The population of yeast cells is growing at a rate of approximately 46.41% per hour.

The rate of growth of the yeast cells is 31 cells per hour.

The rate of growth of the yeast cells can be calculated by finding the average rate of change in the population over the given time period.

In this case, the population increased from 5 to 160 in 5 hours, so the average rate of growth can be calculated as (160 - 5) / 5 = 31. The rate of growth of the yeast cells is 31 cells per hour.

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Therefore, 65% of all nurses have a starting salary of more than $71,725.31.

Random variable: X, the starting salary of a randomly selected nurse.

b) P(X ≥ 78371.8) = 1 - P(X < 78371.8)

Using the Z-score formula:

z = (X - μ) / σ = (78371.8 - 67694) / 10333 ≈ 1.03

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≥ 1.03) ≈ 0.1492

Therefore, P (X ≥ 78371.8) ≈ 0.1492.

c) P (X ≤ 91407.1)

Using the Z-score formula:

z = (X - μ) / σ = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probability in the standard normal table or using a calculator, we get:

P(Z ≤ 2.30) ≈ 0.9893

Therefore, P (X ≤ 91407.1) ≈ 0.9893.

d) P (78371.8 < X < 91407.1) = P(X < 91407.1) - P(X < 78371.8)

Using the Z-score formula:

z1 = (78371.8 - 67694) / 10333 ≈ 1.03

z2 = (91407.1 - 67694) / 10333 ≈ 2.30

Looking up the probabilities in the standard normal table or using a calculator, we get:

P(Z < 1.03) ≈ 0.8498

P(Z < 2.30) ≈ 0.9893

Therefore, P (78371.8 < X < 91407.1) ≈ 0.9893 - 0.8498 ≈ 0.1395.

e) P (X ≤ 41861.5)

Using the Z-score formula:

z = (41861.5 - 67694) / 10333 ≈ -2.50

Looking up the probability in the standard normal table or using a calculator, we get:

P (Z ≤ -2.50) ≈ 0.0062

Therefore, P (X ≤ 41861.5) ≈ 0.0062.

f) Yes, a starting salary of 41861.5 dollars is unusually low for a randomly selected nurse, because it is more than 3 standard deviations below the mean. A salary this low would be in the bottom 0.62% of all nurse salaries.

g) To find the starting salary that 65% of all nurses have more than, we need to find the z-score that corresponds to the 65th percentile, and then use the Z-score formula to solve for X.

Using a standard normal table or calculator, we find that the z-score corresponding to the 65th percentile is approximately 0.3853.

Using the Z-score formula:

z = (X - μ) / σ

Substituting μ = 67694, σ = 10333, and z = 0.3853, we get:

0.3853 = (X - 67694) / 10333

Solving for X, we get:

X = 10333(0.3853) + 67694 ≈ 71725.31

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Answer:

78.5 cm²

Step-by-step explanation:

Diameter = 10 cm

Formula

Radius ( r ) = Diameter/2

r = 10/2

r = 5 cm

Formula

Area of circle = πr²

Note

The value of π is 3.14 ( approximately )

Area of circle

= 3.14 × 5²

= 3.14 × 5 × 5

= 3.14 × 25

= 78.5 cm²

Hence,

The area of circle is 78.5 cm².

Answer:

Step-by-step explanation:

4-10(9m-7)

4-90m+70

74-90m

56x+24/8

8(7x + 3)/8

7x + 3

24r + 16

8(3r + 2)

is 2m-3 same as 4(1/2m-3)

2m-3 = 2m-12

: no

-2(10-15x) same as 14x-20+16x

-20+30x = -20+30x

: yes

It should be noted that to select the location of -2 and -9 on the number line, the steps are given below.

Draw a number line with zero in the center and a positive direction to the right and a negative direction to the left.

Find the position of -9 by counting 9 units to the left of zero on the number line. Mark this point with a dot or a cross.

Find the position of -2 by counting 2 units to the left of zero on the number line. Mark this point with a dot or a cross.

Label the points as -9 and -2 to indicate their values.

Your number line should now have two marked points at positions -9 and -2.

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Answer:

a) To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:

P(t) = the population at time t

P0 = the initial population (in this case, 5.51 million)

e = the mathematical constant e (approximately 2.71828)

r = the annual growth rate (in decimal form)

t = the number of years

Substituting the given values, we have:

P(t) = 5.51 * e^(0.0382t)

b) To estimate the population of the city in 2018, we can substitute t = 6 (since 2018 is 6 years after 2012) into the exponential growth function:

P(6) = 5.51 * e^(0.0382*6) ≈ 6.93 million

Therefore, the estimated population of the city in 2018 is approximately 6.93 million.

c) To find when the population of the city will be 10 million, we can set P(t) = 10 and solve for t:

10 = 5.51 * e^(0.0382t)

e^(0.0382t) = 10/5.51

0.0382t = ln(10/5.51)

t ≈ 11.7 years

Therefore, the population of the city will be 10 million in approximately 11.7 years from 2012, or around the year 2023.

d) To find the doubling time, we can use the formula:

T = ln(2) / r

Where:

T = the doubling time

ln = the natural logarithm

2 = the factor by which the population grows (i.e., doubling)

r = the annual growth rate (in decimal form)

Substituting the given value of r, we have:

T = ln(2) / 0.0382 ≈ 18.1 years

Therefore, the doubling time for the population of the city is approximately 18.1 years.

Answer:

36 ft

Step-by-step explanation:

9x4=36. if the bulletin board is 9ft on each side, (9x4) the amount of border she needs would be 36ft.

The only observations that are correct are Grace's and Maddy's. The answer is Option C.

We can start by finding the perimeter, area, and volume of one face of the cube, and then see which observation is correct.

The perimeter of one face of the cube is 4 times the length of one edge, which is:

= 4 × 12 inches

= 48 inches. So Grace's observation is correct.

The area of one face of the cube is the length of one edge squared, which is:

= 12 inches × 12 inches

= 144 square inches. So Maddy's observation is also correct.

The volume of the cube is the length of one edge cubed, which is:

= 1 foot × 1 foot × 1 foot

= 1 cubic foot. So Elena's observation is not correct.

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Answer:

1/3 of 24 is 8, so

8 = (2/3)x

x = 8(3/2) = 12

2/3 of 12 is 8.

The measurements for area of Jacobs yard are;

Part A = 6m x 3m = 18m

Part B = 4.5m x 3m = 13 m

Part C = 1/2 x 3m x 3m = 4.5 m²

Total area = 18m² + 13.5m² + 4.5m² = 36m²

To identify sections that would help in calculating area, you need to look for shapes or figures that can be divided into simpler geometric shapes, such as squares, rectangles, triangles, and circles.

Once you have identified the simpler shapes, you can use their formulas to calculate their areas and then add them together to find the total area of the larger shape or figure.

For example, a rectangle can be divided into two triangles or two smaller rectangles, and a circle can be divided into a sector or a ring. Breaking down a larger shape into smaller, simpler shapes can make it easier to calculate their areas accurately.

Jacob is putting tiles on the section of his yard labeled A, B, C. What is the area of the parts that need tiles?

Part A = .............. x ........... = ...........m

Part B = + .............. x ............. = ............ m

Part C = 1/2 x ................. x ............ = ............... m²

Total area = ................... + ..................... + .................. = ..............m

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The solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is p > 6 or p > -3.

A compound inequality is a mathematical statement that involves two or more inequalities joined by either the word "and" or "or". The solution set of a compound inequality is the set of all values that satisfy both (in the case of "and") or either (in the case of "or") of the individual inequalities.

Let's solve each inequality separately:

4p + 1 < −11

Subtracting 1 from both sides, we get:

4p < -12

Dividing both sides by 4 (and remembering to flip the inequality because we are dividing by a negative number), we get:

p > -3

So the solution to the first inequality is:

p > -3

Now let's look at the second inequality:

6p + 3 > 39

Subtracting 3 from both sides, we get:

6p > 36

Dividing both sides by 6, we get:

p > 6

So the solution to the second inequality is:

p > 6

Therefore, the solution to the compound inequality 4p + 1 < −11 or 6p + 3 > 39 is:

p > 6 or p > -3

This can be written more simply as:

p > -3

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Note that the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

To calculate the %DV for saturated fat, we need to first calculate how many grams of saturated fat are in the 2 tablespoon (tbsp) serving size.

From the label, we see that the serving size contains 3.5g of saturated fat.

To calculate the %DV for saturated fat, we use the equation:

%DV = (amount of nutrient per serving / DV) x 100%

Plugging in the values for saturated fat, we get:

%DV = (3.5g / 19g) x 100%

%DV = 0.1842 x 100%

%DV ≈ 18%

Therefore, the %DV for saturated fat in this 2 tbsp serving size is approximately 18%.

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With the help of slope we conclude that Ashley needs to read 100 pages every 10 hours to finish the book in 30 hours.

Slope is a measure of the steepness of a line, and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

To find out how many pages Ashley needs to read every 10 hours, we need to look at the slope of the line on the graph. The slope tells us the rate of change of the number of pages read per hour.

We can use the formula for slope, which is:

slope = (change in y) / (change in x)

In this case, the "change in y" is the number of pages Ashley needs to read in 30 hours minus the number of pages she needs to read in 0 hours (which is the starting point of the graph). The "change in x" is 30 hours minus 0 hours. So we have:

slope = (number of pages in 30 hours - number of pages in 0 hours) / (30 hours - 0 hours)

Using the graph, we can see that the number of pages Ashley needs to read in 30 hours is 300. The number of pages she needs to read in 0 hours (or the starting point of the graph) is 0. So we have:

slope = (300 - 0) / (30 - 0) = 10

This means that Ashley needs to read 10 pages per hour to finish the book in 30 hours. To find out how many pages she needs to read every 10 hours, we can multiply the hourly rate by 10:

10 pages per hour * 10 hours = 100 pages

Therefore, Ashley needs to read 100 pages every 10 hours to finish the book in 30 hours.

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Answer:

The player can expect to lose money over the long run.

Step-by-step explanation:

We would need to know the possible outcomes and the corresponding probabilities of the game to calculate the expectation. Without that information, we cannot calculate the expectation.

The expectation is calculated by multiplying each outcome by its probability and then adding up all the products. In this case, the outcomes are the amounts indicated by the pointer, and the probabilities are the likelihood of the pointer stopping on each amount.

If we knew the probabilities, we could calculate the expected value as follows:

Expected value = (amount 1 x probability 1) + (amount 2 x probability 2) + ... + (amount n x probability n)

We would then subtract the cost to play the game to get the net expected value. If the net expected value is positive, it means that the player can expect to make a profit over the long run, while if it is negative, it means that the player can expect to lose money over the long run.

Answer:

48

Step-by-step explanation:

since you are trying to find the number of pencils altogether, you add 24, 15, and 9. 24+15+9= 48

I hope this helped! :)

The range in ages for the middle 50% of viewers is the interquartile range (IQR), which is the height of the box in the box plot. The best approximation is C) 20.

The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of a dataset. It is a useful measure of spread because it is not influenced by outliers.

Range is a statistical measure that represents the difference between the highest and lowest values in a set of data. It provides a simple indication of the spread or variability of the data.

According to the given information:

A box plot is a graphical representation of the distribution of a dataset. The box in the plot represents the middle 50% of the data, with the lower end of the box representing the 25th percentile (Q1) and the upper end of the box representing the 75th percentile (Q3). The distance between Q1 and Q3, which is represented by the height of the box, is called the interquartile range (IQR).

To answer the question, we need to find the best approximation for the range in ages for the middle 50% of viewers. From the box plot, we can see that the height of the box is approximately 20 units, which is the IQR. Therefore, the best approximation for the range in ages for the middle 50% of viewers is option C) 20. This means that 50% of viewers are between Q1-10 to Q3+10, where Q1 is the 25th percentile and Q3 is the 75th percentile.

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The effective tax rate for a taxable income of $115,500 is A) 18.71%

The introductory $10,275 is subjected to a 10% tax burden, with the converted dollar amount representing $1,027.50 in taxes. The additional taxable sum of $30,900 ($41,175 - $10,275) is accessed at a 12% charge and aggregates to $3,708 worth of duties. An extra levy of 22% is imposed on the total $47,900 that lies between the two stipulated ranges ($89,075 - $41,175). The final evaluation stands at 24%, which provides an identical tax rate for the remaining $25,350 ($115,500 - $89,075). ).

Effective Tax Rate = (Total Tax Paid / Taxable Income) x 100%; which further articulates to ($21,357.50 / $115,500) x 100%,

= 18%

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The correct answer is "Rita read at the faster rate because 227 words per minute > 208 words per minute".

The rate of something is a measure of how fast or slow it changes over time or another variable. The general formula for calculating rate is:

Rate = Change in value / Time interval or Change in value / Change in another variable Rates can be expressed in different units, such as miles per hour, dollars per day, or units per minute. It's important to ensure that the units are consistent throughout the calculation to obtain accurate results. In summary, the rate of something can be calculated by dividing the change in value by the time interval or the change in another variable.

To find out who read at the faster rate, we need to calculate the rate of reading for each person. We can do this by dividing the number of words read by the time taken to read them.

Rita's reading rate = 1362/6 = 227 words per minute

Joy's reading rate = 1456/7 = 208 words per minute

Therefore, Rita read at a faster rate than Joy, with a reading rate of 227 words per minute compared to Joy's reading rate of 208 words per minute.

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Answer:

42.15 as a decimal is 0.4215 and you can multiply 0.4215 by a number to get 42.15 percent of that number.

Step-by-step explanation:

So the answer is 0.4215

Hope this helps! =D

Answer:0.4215

Step-by-step explanation:

42.15%÷100=0.4215

Step-by-step explanation:

2 years and 3 months =  27 months      ( there is 12 months in a year)

7 months of this would be THIS fraction:

7/27