Instructions:

Select all the correct answers.

Which equations have one solution?


A) 1/3x+3=26+6/19x-23

B) x+3+3x=-3+4x+6

C) 2(1/5+1/4x)-2x=x-1

D) 4. 3x+2. 5-2. 2x+2. 2-2. 1x=0

E) 2(4x+3)+2x=5(2x+3)

F) 2/5x+10+3/5x=2x+5

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:

40-m=21

40-40-m=21-40

m=21-40

m=-19

Answer: To find the new balance including interest, we need to take into account the interest charged on the current balance and the new purchase.

First, let's calculate the interest charged on the current balance. The monthly interest rate is 18.99% / 12 = 1.5825%.

The interest charged on the current balance is therefore:

interest on current balance = 0.015825 * 9160.00 = 144.98

So the total balance including interest for the current month is:

current balance including interest = 9160.00 + 144.98 = 9304.98

Next, let's calculate the interest charged on the new purchase of $1,098.00. The interest charged on the new purchase is:

interest on new purchase = 0.015825 * 1098.00 = 17.39

So the total balance including interest for the new purchase is:

new balance including interest = 1098.00 + 17.39 = 1115.39

Finally, we add the current balance including interest and the new balance including interest to get the total balance including interest:

total balance including interest = current balance including interest + new balance including interest

total balance including interest = 9304.98 + 1115.39

total balance including interest = 10420.37

Therefore, the new balance including interest is $10,420.37.

Step-by-step explanation:

The expanded form of 2d with an exponent of -5 is 32d⁵

2d with an exponent of -5

[tex] {(2d)}^{ - 5} [/tex]

[tex] = \frac{1}{ {(2d)}^{5} } [/tex]

expand

[tex] = \frac{1}{2d \times2d \times2d \times2d \times2d } [/tex]

[tex] = {32d}^{5} [/tex]

Therefore, 2d with an exponent of -5 is 32d⁵

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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.

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:

d. 1 7/30...............

Answer:

D

Step-by-step explanation:

2/5 + 5/6

Make the denominator same

(2×6)/30 + (5×5)/30

12+25/30

37/30

1 7/30

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 parent function which is represented by the given table as required in the task content is; Choice B. f(x) = |x|.

It follows from the task content that the parent function which is represented by the table is to be determined.

On this note, by observation of the function; the values of y represent the positive version of x.

Consequently, it follows that the table represents the absolute value function.

Therefore, Choice B; f(x) = |x| is correct.

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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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Maybe 9/12? I counted the amount of times 6 or 9 shows up on the graph. :D. Hope that helps.

Answer:

The answer for anle X is 66°

Step-by-step explanation:

Base angles of an isosceles triangle are equal

<x=<y

<x+<y+<w=180

let<x=X

Remember <X=<Y

X+X+48=180

2X+48=180

2X=180-48

2X=132

divide both sides by 2

X=66°

<X=X

<X=66°

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:

25

Step-by-step explanation:

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 range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.

To find the maximum value of f(x), we can take the limit as x approaches infinity:

The value of x is approximately 10.57 and the value of y is approximately 15.25.

In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.

The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.

In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:

105 + (7y + 1) + (7x + 1) + (4y + 14) = 180

Simplifying and solving for x and y, we get:

7x + 4y + 122 = 180

7x + 4y = 58 ......(1)

Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:

105 + (4y + 14) = 180 ......(2)

(7y + 1) + (7x + 1) = 180 ......(3)

Simplifying and solving for y in equation (2), we get:

4y + 119 = 180

4y = 61

y = 15.25

Substituting this value of y in equation (3) and solving for x, we get:

(7x + 1) + (7*15.25 + 1) = 180

7x + 106 = 180

7x = 74

x = 10.57

Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.

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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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The surveyor must test at the slightest 385 voters within the expansive city to build a 95% certainty interim for the extent who bolster the occupant candidate with an edge of blunder no bigger than 0.05.

To discover the test measure required to attain an edge of mistake of no more than 0.05 for a 95% certainty interim, able to utilize the taking after equation:

n = (z[tex]^{2}[/tex] * p * q) / E[tex]^{2}[/tex]

where:

n is the test estimate

z is the z-score related to the specified level of certainty (in this case, 95% corresponds to a z-score of 1.96)

E is the specified edge of blunder (in this case, 0.05)

Substituting the given values, we get:

n = (1.96[tex]^{2}[/tex] * 0.5 * 0.5) / 0.05[tex]^{2}[/tex]

n = 384.16

thus, we get a test measure of 385.

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Applying the Angle Bisector Theorem, the length of the segments are:

AB = 15;    AC = 20.

The Angle Bisector Theorem states that in a triangle, if a line segment bisects an angle of the triangle and intersects the opposite side, then it divides that side into two segments that are proportional to the lengths of the other two sides of the triangle.

Therefore, we would have the following equation based on the angle bisector theorem:

5y/8 = 4y - 1 / 6

Cross multiply:

8(4y - 1) = 6(5y)

32y - 8 = 30y

32y - 30y = 8

2y = 8

y = 4

AB = 4y - 1 = 4(4) - 1 = 15

AC = 5y = 5(4) = 20

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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 volume of the apple would increase by ΔVtotal over the five-week period

The volume of the apple is directly proportional to the cube of its radius. Therefore, if the radius increases by 1/8 inch per week for five weeks, the total increase in radius would be 5/8 inches.

To calculate the change in volume, we can use the formula V = (4/3)πr^3.

Initially, let's assume the radius of the apple is r.

After the first week, the radius would be r + 1/8 inches. Therefore, the new volume would be:
[tex]V_1 = (4/3)\pi(r + 1/8)^3[/tex]

To calculate the change in volume, we can subtract the initial volume from the new volume:

[tex]\DeltaV_1 = V_1 - V_0[/tex]

where V0 is the initial volume of the apple.

Similarly, after the second week, the radius would be r + 2/8 inches, and the new volume would be:

[tex]V2 = (4/3)\pi(r + 2/8)^3[/tex]

The change in volume after the second week would be:

ΔV2 = V2 - V1

We can repeat this process for the remaining three weeks and find the total change in volume by adding all the individual changes:

ΔVtotal = ΔV1 + ΔV2 + ΔV3 + ΔV4 + ΔV5

By simplifying this equation, we get:

[tex]\Delta V_{total }=  (4/3) \pi r^3[(r + 1/8)^3 + (r + 2/8)^3 + (r + 3/8)^3 + (r + 4/8)^3 + (r + 5/8)^3 - 5r^3][/tex]

Therefore, the volume of the apple would increase by ΔVtotal over the five-week period.

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The volume of the apple will increase by [tex](4/3)π[(r0 + 5/8)^3 - r0^3][/tex] during the five-week period.

Assuming that the apple is a perfect sphere, we can use the formula for the volume of a sphere:

[tex]V = (4/3)πr^3[/tex]

where V is the volume of the sphere and r is the radius of the sphere.

Let's start by finding the initial volume of the apple. We are not given the initial radius, so let's assume it to be r0.

[tex]V0 = (4/3)πr0^3[/tex]

After one week, the radius increases by 1/8 inch, so the new radius is r1 = r0 + 1/8. The new volume is:

[tex]V1 = (4/3)π(r0 + 1/8)^3[/tex]

After two weeks, the radius increases by another 1/8 inch, so the new radius is r2 = r0 + 2/8. The new volume is:

[tex]V2 = (4/3)π(r0 + 2/8)^3[/tex]

Similarly, after three weeks, the new radius is r3 = r0 + 3/8 and the new volume is:

[tex]V3 = (4/3)π(r0 + 3/8)^3[/tex]

After four weeks, the new radius is r4 = r0 + 4/8 and the new volume is:

[tex]V4 = (4/3)π(r0 + 4/8)^3[/tex]

Finally, after five weeks, the new radius is r5 = r0 + 5/8 and the new volume is:

[tex]V5 = (4/3)π(r0 + 5/8)^3[/tex]

To find how the volume changes during the five-week period, we need to subtract the initial volume from the final volume:

ΔV = V5 - V0

[tex]ΔV = (4/3)π(r0 + 5/8)^3 - (4/3)πr0^3[/tex]

Simplifying this expression, we get:

[tex]ΔV = (4/3)π[(r0 + 5/8)^3 - r0^3][/tex]

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The "possible-sources" of in the measurement error of an experiment are Instrument error, Human error, sampling error and environmental factors, these sources "may" or "may-not" be enough to account for the percent differences calculated from the data.

There are several possible sources of "measurement-error" in an experiment which affect the accuracy and precision of the results.

These sources include instrument error, human error, environmental factors, and sampling error.

(i) "Instrument-Error" : is defined as inaccuracies in the measuring instruments used in the experiment. This include issues such as calibration errors, sensitivity of the instruments.

(ii) "Human-Error" can arise from mistakes made by experimenters during data collection or analysis, such as misreading measurements or recording data incorrectly.

(iii) "Environmental-Factors", such as temperature, humidity, or electromagnetic interference, can also cause error into experiment if they affect performance of measuring instruments.

(iv) "Sampling-Error" occur when a subset of the population is used for the experiment, and the results are generalized to the entire population.

Depending on the magnitude of these sources of error, they may or may not be enough to account for the percent differences calculated from the data.

If the measurement errors are small and within an acceptable range for the experiment, they may not significantly impact the results.

If the errors are large or systematic, they can introduce significant bias into the data and affect the percent differences calculated.

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The given question is incomplete, the complete question is

Discuss the possible sources of measurement error in an experiment. Are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.

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!

The fireworks will explode after 1.125 seconds of launching Firework B.

Distance = Speed × time

Let time = t

Firework A:

[tex]D(t) = 360t - - - (1)[/tex]

Firework B:

[tex]D(t) = 280(0.25) + 280t[/tex]

[tex]D(t) = 70 + 280t - - - (2)[/tex]

Equate 1 and 2 :

[tex]360t = 280t + 70[/tex]

Collection of like terms

[tex]360t - 280t = 70[/tex]

[tex]80t = 70[/tex]

[tex]t = 70/80[/tex]

[tex]t = 0.875 seconds[/tex]

[tex]0.875 + 0.25 = 1.125 seconds[/tex]

Therefore, the fireworks will explode after 1.125 seconds of launching Firework B.

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A number multiplied by itself.

What is square?

In mathematics, a square is a number that is obtained by multiplying a number by itself. It is also a geometric shape with four equal sides and four right angles. The area of a square is calculated by multiplying the length of one of its sides by itself. The formula for calculating the area of a square is A = s^2, where A is the area and s is the length of one side.

Squares have many important applications in mathematics, including in algebra, geometry, trigonometry, and calculus. They are used in the Pythagorean theorem, which relates to the sides of a right triangle, and they are used to represent variables in algebraic equations. Squares are also important in geometry, where they are used to construct geometric shapes and to calculate their areas and perimeters.

The better definition of squares is:

A number multiplied by itself.

In mathematics, a square refers to the product of a number multiplied by itself. For example, the square of 4 is 16, because 4 multiplied by 4 equals 16. Squares have a variety of important applications in mathematics, including in geometry, algebra, and calculus.

While a result that has been proved to be true is sometimes referred to as a "square" in certain contexts, it is not the primary definition of the term. Similarly, a triangle with a right angle is referred to as a "right triangle" or a "right-angled triangle," but not a square.

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

Step-by-step explanation:

Answer:

Your answer should be A