Algebra 1 > V.16 Checkpoint: Systems of equations and inequalities LOW
Lisa's dance company is selling candles for a fundraiser. The candles come in two sizes: small
and large. This table shows how many candles Lisa and her friend Kayla sold.
Lisa
Kayla
Small candles Large candles Total sales
16
$360
$400
12
7
22
What was the price of each size candle?
Small candles cost $
Submit
each and large candles cost $
Work it out
each.

Each of Carl's friends will be getting 1/9 of his original collection.

Carl is giving away 1/3 of his collection. Let's assume that the original collection is x. Carl is giving away 1/3 of x.

1/3x divided by 3 = 1/3x x 1/3

                            = 1/9x

In other words, if Carl has a total of 9 baseballs, he wants to give away 1/3 of them which is 3 baseballs. He’s dividing these 3 baseballs among 3 friends, so each friend will get 1/3 of the 3 baseballs which is 1/9 of the original collection.

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The original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size."

a. To find the probability that a randomly selected female has a pulse rate less than 80 beats per minute, we need to standardize the value using the formula z = (x - μ) / σ, where x is the pulse rate we are interested in, μ is the mean pulse rate, and σ is the standard deviation. Thus, we have:

z = (80 - 76) / 12.5 = 0.32

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than 0.32 is approximately 0.6255. Therefore, the probability that a randomly selected female has a pulse rate less than 80 beats per minute is:

P(z < 0.32) = 0.6255

b. Since we are dealing with a sample size of 25 females, we can use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean of μ and a standard deviation of σ / sqrt(n), where n is the sample size.

In this case, we have:

μ = 76.0

σ = 12.5

n = 25

Therefore, the standard deviation of the distribution of sample means is:

σ / sqrt(n) = 12.5 / sqrt(25) = 2.5

To find the probability that 25 randomly selected females have a mean pulse rate less than 80 beats per minute, we need to standardize the value using the formula z = (X- μ) / (σ / sqrt(n)), where X is the sample mean.

Thus, we have:

z = (80 - 76) / (2.5) = 1.6

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than 1.6 is approximately 0.9452. Therefore, the probability that 25 randomly selected females have a mean pulse rate less than 80 beats per minute is:

P(z < 1.6) = 0.9452

c. The normal distribution can be used in part (b) because we are dealing with the distribution of sample means, not individual pulse rates. The central limit theorem states that the distribution of sample means will be approximately normal regardless of the sample size, as long as the sample size is sufficiently large (typically, n ≥ 30). In this case, we have a sample size of 25, which is smaller than 30, but we can still use the normal distribution approximation because the population distribution is assumed to be normal.

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The fixed overhead cost per unit is $3.52. The cost calculation is appropriate as it includes all relevant costs. Accepting the special order would result in a profit of $2.60 per unit, which is lower than the normal profit of $7.60 per unit. Therefore, CMI should not accept the special order.

To calculate the fixed overhead per unit, we need to use the following formula

Fixed overhead per unit = Total fixed overhead / Total units produced

From the given information, we know that CMI is manufacturing 113,000 units of the component and operating at 80% of capacity. So the total units that can be produced are

Total units = 113,000 / 0.8 = 141,250 units

We are also given that the fixed overhead cost is $497,200 per year. To calculate the fixed overhead per unit, we divide this amount by the total units produced

Fixed overhead per unit = $497,200 / 141,250 = $3.52 per unit

Therefore, the fixed overhead per unit is $3.52.

Based on the information given, the cost calculation appears to be appropriate as it includes all the relevant costs such as raw materials, direct labor, variable overhead, and fixed overhead.

However, we cannot determine the accuracy of the cost calculation without knowing the details of how each cost component was determined.

To decide whether to accept the offer from the Italian firm, we need to compare the special order price of $31.50 per unit to the normal selling price of $36.50 per unit, as well as the cost per unit of $28.90. Since the special order price is higher than the cost per unit, accepting the order would generate a positive contribution margin of

Contribution margin = Special order price - Cost per unit

Contribution margin = $31.50 - $28.90 = $2.60 per unit

However, the contribution margin of $2.60 per unit is lower than the normal contribution margin of

Normal contribution margin = Normal selling price - Cost per unit

Normal contribution margin = $36.50 - $28.90 = $7.60 per unit

Therefore, accepting the order would result in a lower contribution margin and lower profitability. However, if CMI has excess capacity and can easily fulfill the order without impacting its normal business, it may still be worthwhile to accept the order.

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The surface area of the cylindrical pottery vase is 177.55 in².

Given that a cylindrical pottery vase has a diameter of 4.3 inches and a height of 11 inches, we need to find the surface area of the vase,

SA of a cylinder = 2π×radius(h+r)

= 2×3.14×2.15(2.15+11)

= 177.55 in²

Hence, the surface area of the cylindrical pottery vase is 177.55 in².

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Answer:

  72°

Step-by-step explanation:

You want the measure of an angle that is 2/3 the measure of its supplement.

Let x represent the angle measure. The problem statement tells us its value is ...

  x = 2/3(180 -x)

  5/3x = 120 . . . . . . . . . . . . . add 2/3x, simplify

  x = (3/5)(120) = 72 . . . . . . multiply by 3/5

The measure of the angle is 72°.

__

Additional comment

The supplement is 180° -72° = 108°. The ratio of the angles is ...

  72°/108° = 2/3

The sale price of the item when displayed on sales costs $8.75 based on the stated original price and percentage discount offered.

The formula to calculate sale price of the item according to discount and original price will be -

Sale price = 25% × original price

Keep the value of original price in the formula to find the sale price

Sale price = 25% × 35

Performing multiplication and division by solving the percentage on Right Hand Side of the equation to find the value of sale price of the item

Sale price = 8.75

Hence, the item on sale costs $8.75.

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Answer: You cannot add (or subtract) fractions with different denominators, so therefore the answer would not be 3/8.

Answer:

a) 16; b) 1/64

Step-by-step explanation:

(1/4)^x

(1^x)/(4^x)

Since 1 to any power 1

Our equation is 1/(4^x)

Answer:

-----------------------

Given expression (1/4)ˣ.

Evaluate this for each value of x.

For x = - 2:

For x = 3:

Answer:

1/9

Step-by-step explanation: 1/3/3

The complex value fraction is simplified and A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

Given data ,

Let the fraction be represented as A

Now , the value of A is

The last denominator of the fraction is

x² / 15x - 1/3x²

On simplifying , we get

( 3x⁴ - 15x ) / ( 15x - 3x² ) , and this fraction is multiplied by the fraction above which is x/( x/3-4 )

So , the above fraction is 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² ) ) / ( x - 12 )

Now , taking the LCM of the denominator of the fraction , we get

( 2/15x ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 ) , we get

( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 )

And , the numerator of the fraction is ( 1/3 ) - ( 3/x² )

On taking the LCM on the numerator , we get

( x² - 9 ) / ( 3x² ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x ) / ( 15x - 3x² )( x - 12 )

The denominator will get multiplied by the reciprocal of the fraction and ,

A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

Hence , the fraction is A = ( x² - 9 ) / ( 3x² ) ( 15x - 3x² )( x - 12 ) / ( 2/15x ) ( 15x - 3x² )( x - 12 ) - 3x ( ( 3x⁴ - 15x )

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The missing quantities are

Social Security= $217

Medicare = $‭50.75‬

Net Pay is $‭2,633.67‬

First, Taxable income is therefore;

= 3,500 - (76.90 x 4 )

= $‭3,192.4‬0

Federal Income Tax (FIT).

With taxable income of $‭3,192.4‬0, the tax is $565.15 plus 28% of anything above $‭3,073.

= 565.15 + (28% x (‭3,192.4‬0 - 3,073))

= 565.15 + 33.43

= $‭598.58

and, Social Security

= Gross pay x 6.2%

= 3,500 x 6.2%

= $‭217‬

and, Medicare

= 3,500 x 1.45%

= $‭50.75‬

Then, the Net Pay

= 3,500 - 598.58 - 217 - 50.75

= $‭2,633.67‬

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The amount of water in the pond after 14 minutes will be 1006 L.

Given that the pound already having 600 L of water is being filled at rate of 29 L per minutes, we need to establish an equation that represent the relation between number of minute and amount of water in the pond.

So,

The relation can be defined as;

W = 600+29T

When T = 14

W = 600+29(14)

W = 1006

Hence, the amount of water in the pond after 14 minutes will be 1006 L.

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(1000-(-800))/(900-300) = 3 (slope)

y=mx+b

1000=3(900)+b

b = -1700
y=3x-1700

Step-by-step explanation:

To solve a two-step equation with fractions, we can use the same steps as we would for a two-step equation without fractions  

Here are the steps:

1.

Simplify both sides of the equation by multiplying both sides by the least common multiple (LCM) of all the denominators in the equation.

2.

Solve the resulting two-step equation using inverse operations.

For example, let's say we have the equation 3/4x - 1/2 = 5/8  

Step 1: Multiply both sides by the LCM of 4, 2, and 8 which is 8. This gives us:

3x - 4 = 5

Step 2: Add 4 to both sides to get:

3x = 9

Step 3: Divide both sides by 3 to get:

x = 3

Therefore, x = 3 is the solution to the equation  

The cost of 1050 bricks is $9,702.00.

The cost of the rectangular prism is given per volume hence we solve for the volume of each brick using:

= length * width * depth

= 7 in x 22 in x 3 in

= 462 cubic inches

The cost of each brick is given to be $0.02 per cubic

inch

To find the cost of 1050 bricks, we can multiply as follows

=  the volume of each brick * 1050 bricks * cost of one brick

=  462 cubic inches x $0.02/cubic inch * 1050 bricks

= $9,702.00

To the nearest cent, the cost of 1050 bricks is $9,702.00.

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The graph of inequality x<-2 is given in the attachment.

The inequality x < -2 represents a portion of the number line to the left of -2, but it does not specify a graph in the traditional sense.

If you want to graph the inequality, you can represent the shaded region of the number line to the left of -2, and you can use an open circle to indicate that -2 itself is not included in the solution set

The open circle at -2 indicates that -2 is not included in the solution set, and the shaded region to the left of -2 represents all the numbers that satisfy the inequality x < -2.

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We can see here that the incorrect statement is #1: The image is located in Quadrant IV.

Transformation in mathematics is a function or a set of rules that converts a collection of points or geometric figures in one coordinate system into a different set of points or geometric figures in a second coordinate system while maintaining some characteristics of the original set.

We can see here that the statement that is incorrect is actually #1: The image is located in Quadrant IV. This is true because the image is in Quadrant I while the transformation is in Quadrant IV.

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1/13 will be the fraction to represent the tosses are tails.

If the ratio of heads to total tosses is 24:26, then we can express the ratio of tails to total tosses as:

Tails : Total Tosses = 2 : 26

Simplifying this ratio by dividing both terms by 2, we get:

Tails : Total Tosses = 1 : 13

Therefore, the fraction of tosses that tail is 1/13.

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The actual length of the yard is 35 feet.

Using the given scale that Adriana used, we know that 2 inches in the drawing represent 5 feet in real life.

Let's set up a proportion to find the length of the actual yard:

2 inches / 5 feet = 14 inches / x feet

Simplifying this proportion, we can cross-multiply:

Therefore, the length of the actual yard is 35 feet.

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The two ways to mark the angle TWV are m∠W or m∠TWX.

We have,

The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.

Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.

Now,

Angle TWV can be written as,

m∠W or m∠TWX

Thus,

The two ways to mark the angle TWV are m∠W or m∠TWX.

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Answer:

Step-by-step explanation: multiply the coins by 7

To find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy, we use the formula for the remainder of the geometric series.

The formula for the remainder of the geometric series is R = a (1 - rn) / (1 - r)Where R is the remaining term of the geometric series, a is the first term of the geometric series, r is the common ratio of the geometric series, n is the number of terms of the geometric series up to the given partial sum.

The formula for the sum of a finite geometric series is: S = a (1 - rn) / (1 - r)

By using the formula for the remainder of the geometric series, the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy is given by:

S - Sn = R

Where, S is the sum of the geometric series, Sn is the sum of the first n terms of the geometric series.

From the given question, the number of terms of the geometric series required to find the sum to the indicated accuracy is not given.

Hence, we cannot find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy.

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Correct question:

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

The relative frequency probability of rain in April is 0.4.This means that it rained on 40% of the days in April in the suburban Maryland neighborhood, which is higher than the average probability of 31%.

The relative frequency probability of rain in April is the proportion of days on which it rained in April out of the total number of days in April.

The total number of days in April is 30, and rain was recorded on 12 of those days.

Therefore, the relative frequency probability of rain in April is:

12/30 = 0.4

This means that it rained on 40% of the days in April in the suburban Maryland neighborhood, which is higher than the average probability of 31%

The relative frequency probability gives us an idea of how often an event is likely to occur based on past occurrences. In this case, it tells us that it rained on 40% of the days in April in the suburban Maryland neighborhood.

Comparing this probability to the average probability of rain in April in the area, which is 31%, we can see that the observed probability is higher. This suggests that this particular April was rainier than usual.

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Answer:

We can start with the left side of the identity and try to manipulate it algebraically to transform it into the right side:

Left side: tan X + cot X

We know that cot X is equal to 1/tan X, so we can substitute this expression in for cot X:

Left side: tan X + 1/tan X

Next, we can use the identity that (a + 1/a) = (a^2 + 1)/a to rewrite the expression as a single fraction:

Left side: (tan^2 X + 1)/tan X

We can then use the trigonometric identity that 1 + tan^2 X = sec^2 X to substitute in for the numerator:

Left side: sec^2 X / tan X

Finally, we can use the identity that csc X = 1/sin X to substitute in for tan X:

Left side: sec^2 X / (sin X / cos X)

We can simplify this expression by multiplying the numerator and denominator by cos X:

Left side: (sec^2 X * cos X) / sin X

We know that sec X is equal to 1/cos X, so we can substitute this expression in for sec X:

Left side: (cos X / cos X * sin X) = cos X * csc X

Therefore, we have shown that the left side (tan X + cot X) is equal to the right side (sec X csc X), and the identity is proven:

tan X + cot X = sec X csc X

The probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

Here, we have to solve the question:

To calculate the probability that a randomly selected part-time student has a gym membership, we need to use conditional probability. Specifically, we need to use Bayes' theorem

P(Gym Membership | Part-Time) = P(Part-Time | Gym Membership) * P(Gym Membership) / P(Part-Time)

Where:

P(Gym Membership | Part-Time) is the probability that a student has a gym membership given that they are part-time.

P(Part-Time | Gym Membership) is the probability that a student is part-time given that they have a gym membership.

P(Gym Membership) is the overall probability of a student having a gym membership (regardless of whether they are full-time or part-time).

P(Part-Time) is the overall probability of a student being part-time (regardless of whether they have a gym membership).

Let's start by filling in the values we know from the table:

P(Part-Time) = (40 + 25) / 155 = 0.5484

P(Gym Membership) = (30 + 25) / 155 = 0.3226

P(Part-Time | Gym Membership) = 25 / (30 + 25) = 0.4545

To find P(Gym Membership | Part-Time), we need to calculate P(Part-Time and Gym Membership). We can use the formula:

P(Part-Time and Gym Membership) = P(Part-Time | Gym Membership) * P(Gym Membership)

Plugging in the values we know, we get:

P(Part-Time and Gym Membership) = 0.4545 * 0.3226 = 0.1463

Now we can use this value, along with P(Part-Time) and P(Gym Membership), to calculate P(Gym Membership | Part-Time):

P(Gym Membership | Part-Time) = 0.1463 / 0.5484 ≈ 0.2667

Therefore, the probability that a randomly selected part-time student has a gym membership is approximately 0.2667 or 26.67%.

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complete question:

a group of 155 students at a private university were asked if they are full-time or part-time and if they have gym memberships. the results are shown in the table below. given that a randomly selected survey participant is part-time, what is the probability that this student has a gym membership?

The maximum quantity of snowfall logged in any one city came out to be an astounding 42 inches.

Most of the data is densely concentrated within the second quarter, spanning between 6 and 14 inches in terms of depth. This surplus can be evidenced by scrutinizing the box plot that has a comparatively slim interquartile range (IQR) within the second quarter with the outline stretching from the bottom quartile (Q1) at 6 inches up to the top quartile (Q3) at 14 inches - denoting that the majority of the numbers lie within this scope, making it the most heavily populated.

In contrast, the data is generally dispersed by the fourth quarter comprising the interval spanning from 30 to 50 inches of snowfall.

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Answer:

x=9

Step-by-step explanation:

Let's start by translating the given sentence into an equation.

"The difference of eight times a number and three is sixty-nine" can be written as:

8x - 3 = 69

where x is the unknown number we're trying to find.

To solve for x, we can start by isolating it on one side of the equation. Adding 3 to both sides, we get:

8x = 72

Dividing both sides by 8, we get:

x = 9

Therefore, the number we're looking for is 9.

Answer:   A

Step-by-step explanation:

If you drew a line that best fits all the dots, that would be the equation they are looking for.

format for a line is:

y=mx+b      m= slope     b=y-intercept

m is not negative, it's an increasing function  so C and D are out

m=1     looks right   m=rise/run  = 1/1 =1

b= -3

put it together

y=x-3       A