Select three expressions equivalent to 28xy + 16x.

Answer:

25

Step-by-step explanation:

In order to change the ratio of toddlers to infants from 7 to 3 to 7 to 5, with an increase of 12 more infants, the number of toddlers in the daycare center has to be 42

Let the coefficient of the ratio be x

Therefore, before the addition of the 12 infants

the number of toddlers = 7x

number of infants = 3x

After the addition of 12 infants

the number of toddlers = 7x

the number of infants = 3x+12

According to the question, new ratio = 7 : 5

[tex]\frac{7x}{3x+12}=\frac{7}{5}[/tex]

5(7x) = 7(3x+12)

35x = 21x + 84

35x - 21x = 84

14x = 84

x = 6

Therefore, the original number of infants = 3 * 6 = 18

the number of toddlers = 7x = 7 * 6 = 42

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If twelve more infants join the day care to change the ratio to 7 to 5, then 126 toddlers are there at this day care center.

Let's first set up the initial ratio using variables: let T represent the number of toddlers and I represent the number of infants. The ratio of toddlers to infants is 7 to 3, so we can write:

T/I = 7/3

To solve for the actual number of toddlers and infants, we need more information. We are told that twelve more infants join the day care, so the new number of infants is I + 12. The new ratio is 7 to 5, so we can write:

T / (I + 12) = 7/5

Now we have two equations with two unknowns, so we can solve for T. First, we can use the initial ratio to solve for I in terms of T:

T/I = 7/3

3T = 7I

I = (3/7)T

Now we can substitute this expression for I into the second equation:

T / (I + 12) = 7/5

T / ((3/7)T + 12) = 7/5

Multiplying both sides by ((3/7)T + 12) gives:

T * (7/5) = ((3/7)T + 12) * (7/5)

Simplifying:

21T / 35 + 84 / 5 = 49T / 35

84 / 5 = 28T / 35

Solving for T:

T = (84/5) * (35/28)

T = 126

Therefore, there are 126 toddlers at this day care center.

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Answer:

To graph this inequality, you can start by graphing the related function y = -x^2 - 1. This is a downward-facing parabola that opens downwards and has a vertex at (0, -1).

To graph the inequality y ≥ -x^2 - 1, you need to shade the region above the graph of the parabola. This is because any point above the parabola will have a y-coordinate that is greater than or equal to the corresponding y-coordinate on the parabola.

So, to graph the inequality, you can shade the region above the parabola. You can use a dotted line to represent the boundary of the inequality, since the inequality includes the possibility of equality (y = -x^2 - 1).

I hope this helps!

Answer:  The theorem states that for any right triangle, the sum of the squares of the non-hypotenuse sides is equal to the square of the hypotenuse. In other words, for a right triangle with perpendicular sides of length a and b and hypotenuse of length c, a2 + b2 = c2.

Step-by-step explanation:

an example if Right triangles that have lengths equaling 3-4-5 or 5-12-13 , or even 7-24-25, are special types of right triangles, because all three lengths are integers that together satisfy the Pythagorean theorem. Such triangles are called Pythagorean triplets.

The equation solved for x can be written as follows:

x = s/(p - q)

just isolate the equation for x, we start wit the equation:

p = q + s/x

Now we can subtract q in both sides:

p - q = s/x

Now we can multiply both sides by the variable x

x*(p - q) =s

Finally, divide both sides by (p - q), in this way you can completley isolate the variable in the left side.

x = s/(p - q)

There you have it.

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The product of 7 and 4 is 28, which is equal to the number of tiles in the product area.

Therefore, this configuration represents the factors of the quadratic expression [tex]x^2 + 9x + 8.[/tex]

To represent the factors of the quadratic expression x^2 + 9x + 8 using algebra tiles, we need to arrange the tiles into two rectangular areas representing the two factors, and the total number of tiles in the product area should be equal to the product of the number of tiles in each factor area.

Based on the information given, we can arrange the tiles as follows:

Factor 1 area: 7 tiles, with 1 x-tile and 6 blank tiles (represented by underscores):

Copy code

x

_

_

_

_

_

_

Factor 2 area: 4 tiles, with 1 x-tile and 3 blank tiles (represented by underscores):

Copy code

x

_

_

_

Product area: 28 tiles, with 1 x^2-tile, 9 x-tiles, 9 negative tiles (represented by red tiles), and 9 blank tiles (represented by underscores):

Copy code

x^2   -     -     -

x     x     x     x

_     _     _     _

_     _     _     _

_     _     _     _

_     _     _     _

_     _     _     _

To check that this configuration represents the given quadratic expression, we can count the number of tiles in each area and verify that the product of the two factors equals the number of tiles in the product area:

Factor 1 area: 7 tiles

Factor 2 area: 4 tiles

Product area: 28 tiles.

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Answer: A

Explanation:

Answer: x-intercept is (3/2, 0),  y-intercept is (0, -3)

Step-by-step explanation:

The number of ways to arrange the letters of PENCIL when the first letter can't be N or L is option (B) 480.

The word PENCIL has 6 letters, here we have to use permutation method.  If all the letters are used, there are 6! = 720 ways to arrange them. However, the first letter can’t be N or L. This means that there are only 4 choices for the first letter (P, E, C, or I). After choosing the first letter, there are 5 letters left to arrange,

So there are 5! = 120 ways to arrange them.

Therefore, the total number of ways to arrange the letters of PENCIL when the first letter can’t be N or L is

4 x 5! = 4 x 120 = 480

Therefore, the correct option is (B) 480.

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The value of angle G is  31⁰.

The value of line GF is 5.

The value of X is 13.

The value of Y is 2.

The value of angle G is calculated as follows;

4x + 7 = 5x - 6

4x - 5x = - 6 - 7

-x = -13

x = 13

Angle H = angle F = 4x + 7

= 4(13) + 7

= 59⁰

Angle G = ¹/₂ (180 - 2x59)

Angle G = ¹/₂(180 - 118)

Angle G = 31⁰

The value of Y is calculated as follows;

y + 3 = 2y + 1

y - 2y = 1 - 3

-y = -2

y = 2

GF = 2y + 1

GF = 2x2 + 1 = 5

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The first point to plot on the mean control chart would be at 1.9 at control chart with both limits.

1. There are four measurements in each sample, as shown in the table.

2. To plot the first point on the mean control chart, we need to calculate the mean of the first sample. Adding up the four measurements from the 10:00 am sample (2.0 + 1.8 + 2.0 + 1.8) gives a total of 7.6. Dividing by the number of measurements in the sample (4) gives a mean of 1.9. Since the mean is within the control limits of 1.8 and 2.2, the first point on the chart would be plotted at 1.9.
1. To determine how many measurements are in each sample, we simply count the number of measurements provided for each time.

10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)

Each sample contains 4 measurements.

2. To plot the first point on a mean control chart, we need to calculate the mean of the first sample (10:00 am).

Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4
Mean = 7.6 / 4
Mean = 1.9

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1. There are 4 measurements in each sample.

2. The first point to plot on the mean control chart would be 1.9, corresponding to the 10:00 am sample.

To determine the number of measurements in each sample, simply count the number of values for each time point.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
There are 4 measurements in each sample.
To plot the first point on the mean control chart, calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4 = 7.6 / 4 = 1.9.

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The greatest common factor of 90 and 315 when divided by the least common multiple of 5 and 15 is 45.

When we multiply all the common prime factors, we get the greatest common factor of the numbers.

These prime factors should come from the prime factorization of the numbers given. These should be in all the unique combinations possible.

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The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

The probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is given by the binomial probability formula:

P(X = k) = (n choose k) [tex]* p^k * (1-p)^(n-k)[/tex]

where X is the random variable representing the number of heads, n is the total number of coin flips, k is the number of heads obtained, and p is the probability of getting a head on any individual flip.

Since we are assuming that the coin is fair, p = 0.5. Let's say you flipped the coin n times and obtained k heads. Then the probability of obtaining exactly k heads with a fair coin is:

P(X = k) = (n choose k [tex]* 0.5^k * ()1-0.5)^(n-k)[/tex]

We don't know what n or k are, so we can't compute the exact probability. However, we can use the fact that the coin is fair to get an estimate. If we assume that the number of heads obtained is roughly half of the total number of flips, then k = n/2. Plugging this into the formula, we get:

[tex]P(X = n/2) = (n choose n/2) * 0.5^(n/2) * (1-0.5)^(n/2)[/tex]

Simplifying this expression, we get:

[tex]P(X = n/2) = (n choose n/2) * 0.5^n[/tex]

Now, we want to find the probability of obtaining exactly as many heads as we just obtained. Let's say we flipped the coin 10 times and obtained 5 heads. Then we want to find P(X = 5), which is:

P(X = 5) = (10 choose 5) [tex]* 0.5^5 * (1-0.5)^(10-5)[/tex] = 0.2461

Therefore, the probability of obtaining exactly as many heads as you just obtained if your coin is the fair coin is 0.2461.

Option C is correct

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The paired t-test results suggest that there is no significant improvement in students' learning after the new unit on factoring, based on a 90% confidence level.

To determine if there has been an improvement in students' learning after a new unit on factoring, we can perform a paired t-test on the pre-test and post-test scores of the five randomly selected students.

The differences between the pre-test and post-test scores for each student are: 3, 3, 4, 8, 0.

The mean of the differences is 3.6, and the sample standard deviation is 2.39.

The t-value for a 90% confidence interval with 4 degrees of freedom is 2.776. Since the calculated t-value of 2.68 (calculated as the mean of the differences divided by the standard error of the mean of the differences) is less than the critical t-value of 2.776, we fail to reject the null hypothesis that there is no improvement in students' learning.

Therefore, there is not enough evidence to conclude that the new unit on factoring has helped students learn based on the sample data.

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Answer:

Assuming that "5 mi Lo" means a sphere with a radius of 5 miles, we can use the formula for the volume of a sphere:

V = (4/3)πr^3

where V is the volume of the sphere, r is the radius, and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting the given radius of 5 miles into the formula, we get:

V = (4/3)π(5^3)

V = (4/3)π(125)

V = (4/3)(3.14159)(125)

V = 523.59833 cubic miles

Therefore, the volume of the sphere is approximately 523.6 cubic miles (rounded to the nearest tenth).

The volume of the sphere is 523.6 mi³

The volume of a sphere is given by V = 4πr³/3 where r = radius of sphere

Since we require to find the volume of the sphere with radius 5 mi, we substitute the value of the radius into the equation.

So, we have that V = 4πr³/3

So, substituting the value of the radius into the equation, we have

V = 4π(5 mi)³/3

= 4π × 125 mi³/3

= 500π mi³/3

= 1570.796 mi³/3

= 523.6 mi³

The volume is 523.6 mi³

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Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.

The missing values in the table that contains the equivalent ratios between X and Y would be = 5

An equivalent ratio is defined as the constant that exists between two different numbers when compared.

The figures in the table is as follows:

X= 1 3 ? 7

y = 5 15 25 35

If X = 1 when y = 5, X= ? when y= 25

That is;

1 =5

?= 25

? = 25/5 = 5

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Replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

Based on the statistical analysis, replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections.

To test this hypothesis, we will use a paired t-test, which compares the means of two sets of paired data. The null hypothesis is that there is no significant difference between the mean accident rates before and after installing roundabouts, while the alternative hypothesis is that the mean accident rate after installing roundabouts is significantly lower than before.

Here are the steps to conduct the paired t-test:

Using the given data, the differences between the accident rates before and after installing roundabouts are:

-0.6, 0.2, 0.6, -0.1, 0

The mean of the differences is 0.02, and the standard deviation is 0.43. There are 5 paired observations, so the degrees of freedom are 4.

Using the formula, we get:

t = 0.02 / (0.43 / √(5)) = 0.14

The critical t-value at a 0.05 level of significance and 4 degrees of freedom is 2.776 from a t-distribution table.

Since the calculated t-value (0.14) is less than the critical t-value (2.776), we fail to reject the null hypothesis. Therefore, we can conclude that replacing stoplights with roundabouts does not significantly reduce the rate of accidents at intersections based on the given data.

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The measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.

A central angle is an angle formed by two radii (or rays) that intersect at the center of a circle. It is an angle whose vertex is at the center of the circle, and its sides are the radii that intersect the circle's circumference.

According to the given information:

To find the measure in degrees of the central angle for the people that chose red, we need to calculate the percentage of people that chose red out of the total number of people surveyed, and then convert that percentage into degrees.

Total number of people surveyed = 180 (brown) + 60 (black) + 90 (red) + 120 (blue) = 450

Percentage of people that chose red = (Number of people that chose red / Total number of people surveyed) * 100 = (90 / 450) * 100 = 20%

Now, we can convert the percentage into degrees using the formula for calculating the central angle in a circle graph:

Central angle = (Percentage / 100) * 360

Plugging in the percentage of people that chose red:

Central angle for red = (20 / 100) * 360 = 72 degrees

So, the measure in degrees of the central angle in the circle graph for the people that chose red is 72 degrees.

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Step-by-step explanation:

where is. the. polynomial.

The population of your friend's town is 300,000 if the population of your town is about 30,000.

To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.

If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.

So, the population of your friend's town is

30,000 x 10 = 300,000

Therefore, your friend's town has a population of about 300,000.

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If the two figures are not related by a dilation with center and scale factor

of 2, followed by a reflection over a line, then Elena's method is not correct. therefore given statement is false.

Elena is claiming that they are similar, and she has shown this by

transforming one figure into the other through a dilation with center and

scale factor of 2, followed by a reflection over a line.

If this is the case, then Elena's method is correct if and only if the two

figures are related by a dilation with center and scale factor of 2,

followed  by a reflection over a line.

A dilation with center and scale factor of 2 will result in a figure that is

twice as large as the original figure, with corresponding sides multiplied

by a factor of 2. If the dilation is followed by a reflection over a line, then

the resulting figure will be similar to the original figure, with

corresponding angles equal and corresponding sides proportional.

However,  In general, two figures are similar if and only if their

corresponding angles are equal and their corresponding sides are

proportional.

There are many ways to show that two figures are similar, including using

transformations such as dilation and reflection, but the specific

transformations used must be appropriate for the figures in question.

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Answer:

It is located at point (-6,-4), and it can reach a distance of 6 units.

Step-by-step explanation:

The equation is a circle equation:

(x-a)²+(y-b)²=r², where a and b are coordinates and r is the radius

We easily see that point a is -6, and point b is -4.

Since the square root of 36 is 6, we see that the radius of the circle is also 6, which is also the signals maximum range.

Hope this helps!

Therefore , the solution of the given problem of probability comes out to be the likelihood that 2 will not occur is 5/6, or roughly 0.8333, or 83.33%.

Any considerations technique's main objective is to determine the likelihood event that a claim is true or that a particular incident will happen. Any number from 0 to 1, where 0 traditionally represents a percentage and 1 typically denotes the degree of certainty, can be used to represent chance. A probability illustration shows the likelihood that a particular event will occur.

Here,

The six possible results on a conventional six-sided die are 1, 2, 3, 4, 5, and 6.

Since there are 5 other numbers on the die in addition to

2 (1, 3, 4, 5, and 6), there are 5 outcomes in which 2 does not appear.

There are six sides to the die, so there are a total of six events that could occur.

The likelihood that the number 2 will not appear on the die is therefore provided by:

Probability is calculated as follows:

=> 5/6 = number of outcomes without 2 out of all possible possibilities.

So, on a typical 6-sided dice, the likelihood that 2 will not occur is 5/6, or roughly 0.8333, or 83.33% (rounded to two decimal places).

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This means that the probability that a randomly selected woman from STEM majors at the university does not meet the age requirement for the internships is approximately 0.0228 or 2.28%.

Without any specific information about the age requirement for the internships or the age distribution of the women in STEM majors at the university, it is impossible to calculate a precise probability.

However, assuming that the age requirement is above the average age of women in STEM majors at the university, we can make a rough estimate.

Let's say that the average age of women in STEM majors at the university is 21 years old, and the age requirement for the internships is 25 years old.

Then, the probability that a randomly selected woman from the STEM majors does not meet the age requirement is the probability that her age is less than 25.

Assuming that the age of women in STEM majors follows a normal distribution with a mean of 21 years old and a standard deviation of 2 years (just for illustration purposes), we can use a standard normal distribution table or a calculator to find the probability that a randomly selected woman's age is less than 25.

Using a standard normal distribution table, we find that the probability of z-score less than (25-21)/2 = 2 is about 0.9772.

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A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution. The correct answer is a.

A probability distribution is a mathematical function that describes the possible values of a random variable and the likelihood of each value occurring. It provides a complete description of the probabilities of all possible outcomes of a random experiment or event.

Probability distributions can be classified into two types: discrete probability distributions and continuous probability distributions. Discrete probability distributions are used when the possible outcomes of a random variable are countable or finite, such as the number of heads in a coin toss.

Continuous probability distributions, on the other hand, are used when the possible outcomes of a random variable are infinite, such as the time it takes for a person to complete a task.

Probability distributions are used in various fields, such as statistics, finance, engineering, and science, to model and analyze random phenomena and make predictions about future events. They are an essential tool for understanding uncertainty and making informed decisions based on probabilistic outcomes.

The correct answer is a.

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Answer:

$13.25 .

Step-by-step explanation:

In case 1 he buys 1 kg of gummy bears and 2 kg of jelly beans .

So By the given condition :-

••••This will serve as equation (1) .

In case 2 he buys 2 kg of gummy bears and 3kg of jelly beans .

So by given condition :-

•••••This will serve as equation (2) .

Solving equation (1) and (2)

From equation (1)

x=38-2y .

we obtain,

2(38-2y)+3y=62.75

76-4y+3y=62.75

y=76-62.75=13.25 .

So cost of 1 kg of jelly bean is $13.25 .

Thus, the in a triangle PQR, with the sides PQ, QR and PR formed a right angled triangle.

If we know the lengths of two of the sides of a right triangle, we can apply the Pythagorean theorem to determine the third side.

Given data:

IN right triangle, the longest side is called the hypotenuse.

So,

hypotenuse H = 25

Now using Pythagorean theorem:

(PR)² = (PQ)² + (QR)²

(25)² = (20)² + (15)²

625 = 400 + 225

625 = 625

LHS = RHS

Thus, the in a triangle PQR, with the sides PQ, QR and PR formed a right angled traingle.

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Complete question:

In a triangle PQR,the sides PQ, QR and PR measure 15 in, 20 in and 25 in respectively. prove that triangle PQR, is the right traingle.