Plot a point that best represents the value of square root 215 on the number line

a. The triangles are not similar as the corresponding angles are different.

b. The triangles are similar as the corresponding angles are similar, so AAA criteria.

c. The triangles are similar as the corresponding angles are similar, so AAA criteria.

Similar triangles have the same shape but varying sizes. Cοrrespοnding angles are identical in similar triangles. Similar triangles have cοrrespοnding sides that have the same ratiο. The ratiο οf the square οf any twο οf their cοrrespοnding sides tο any identical triangle's area is the same.

a. The triangles are not similar as the corresponding angles are different.

45 ° + 45 ° + x = 180°

30 ° + y + y  = 180°

45 ° + 45 ° + x ≠ 30 ° + y + y

b. The triangles are similar as the corresponding angles are similar, so AAA criteria.

90° + 50° + x = 180°

90° + 40° + y  = 180°

40° + y  = + 50° + x

x + y = 40° + 50°

x + y = 90°

90° + 90° = 180°

c. The triangles are similar as the corresponding angles are similar, so AAA criteria.

Opposites angles are similar

45° + 65° + x = 180°

45° + 70°  + y = 180°

65° + x = 70°  + y

x + y =  70° + 65°

x + y = 135°

135° + 45° = 180°

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The value of the variable x for the similar triangles is equal to 25

The triangles BDR and QDC are similar, this implies that the length DC of the smaller triangle is similar to the length DR of the larger triangle

and the length DQ of the smaller triangle is similar to the length DB of the larger triangle

so;

x/(15 + x) = 40/64

64x = 40(15 + x) {cross multiplication}

64x = 600 + 40x

64x - 40x = 600 {subtract 40x from both sides}

24x = 600

x = 600/24

x = 25

Therefore, the value of the variable x for the similar triangles is equal to 25

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Answer:

2 meters

Step-by-step explanation:

If she cut 4 pieces and each was 50 cm, we know that she used 200 cm of ribbon.

Cm to M conversion is that 100 cm = 1 meter, so 200 cm would be 2 meters

Answer: Option A

Step-by-step explanation:

The t-statistic and P-value can be calculated using statistical software or a t-test calculator. Using a two-tailed t-test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), we obtain:

t = -1.4789

P-value = 0.173292

Therefore, the correct answer is A. With a t statistic of -1.4789 and a P-value of 0.173292, we fail to reject the null hypothesis that the prices have not changed significantly since the new owner took over. We cannot conclude that the prices have changed significantly.

With a T statistic of 0.7394 and a P value of 0.478505, fail to reject the no hypothesis that prices have not changed. The correct option is D.

A null hypothesis is a type of statistical hypothesis that asserts that there is no statistical significance in a given set of observations.

Using sample data, hypothesis testing is used to assess the credibility of a hypothesis.

To determine if the prices of goods at a supermarket have significantly changed since the new owner took over, we can perform a two-sample t-test with the null hypothesis being that the mean difference in prices before and after the new owner took over is zero.

Using a significance level of 0.05, the critical t-value for a two-tailed test with 9 degrees of freedom is approximately 2.306.

To calculate the t-statistic, we first need to calculate the mean and standard deviation of the differences in prices:

Mean difference = (0.30 - 0.07) / 10 = 0.023

Standard deviation = 2.967

t-statistic = (0.023 - 0) / (2.967 / sqrt(10)) = 0.7394

The calculated t-value of 0.7394 is less than the critical t-value of 2.306, and the corresponding p-value is 0.4785. This means we fail to reject the null hypothesis that the mean difference in prices is zero.

Therefore, based on the given data and using a significance level of 0.05, the correct P-value and conclusion are:

Thus, the correct option is D.

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Answer:

B

Step-by-step explanation:

x + 3y = 2 → (1)

4x - 3y = 23 → (2)

adding (1) and (2) term by term will eliminate y

(x + 4x) + (3y - 3y) = 2 +  23

5x + 0 = 25

5x = 25 ( divide both sides by 5 )

x = 5

G is the centroid of triangle ABC, AC = 85.5, BG = 38, GC = 23.33 (rounded to two decimal places), AE = 11.67 (rounded to two decimal places).

A triangle is a closed, two-dimensional shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry and is often used in various mathematical and scientific contexts.

The three sides of a triangle are usually named using lowercase letters a, b, and c, and the three angles are named using uppercase letters A, B, and C, with the opposite angles and sides having the same letter. The sum of the angles in a triangle is always 180 degrees, and this property is known as the Angle Sum Theorem.

Triangles can be classified based on their side lengths and angles. Based on the side lengths, triangles can be classified as:

Scalene triangle: A triangle in which all three sides have different lengths.

Isosceles triangle: A triangle in which two sides have the same length, and the third side has a different length.

Equilateral triangle: A triangle in which all three sides have the same length.

We can start by using the fact that G is the centroid of triangle ABC, which means that the medians from each vertex intersect at G. Therefore, we know that:

FC = 2/3 * EA (since FC is a median and EA is the corresponding segment of the opposite side)

AG = 2/3 * DC (since AG is a median and DC is the corresponding segment of the opposite side)

BF = 2/3 * AC (since BF is a median and AC is the corresponding segment of the opposite side)

We can use these relationships to find the lengths of AC, BG, GC, and AE:

AC = 3/2 * BF = 3/2 * 57 = 85.5

BG = 2/3 * AG = 2/3 * 2/3 * AC = 4/9 * 85.5 = 38

GC = 2/3 * FC = 2/3 * 35 = 23.33 (rounded to two decimal places)

AE = EA/2 = 2/3 * FC/2 = 1/3 * 35 = 11.67 (rounded to two decimal places)

Therefore, the answers are:

AC = 85.5

BG = 38

GC = 23.33 (rounded to two decimal places)

AE = 11.67 (rounded to two decimal places)

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The product is decreased by a factor of 16.

What is a factor?

In mathematics, a factor is a number or quantity that, when multiplied with another number or quantity, produces a given result. For example, in the expression 3 x 4 = 12, 3 and 4 are factors of 12. Factors can also refer to algebraic expressions, where they are the expressions that are multiplied together to obtain a larger expression.

Let's say we have two numbers, A and B, and we want to find the product of A and B.

The product of A and B is AB.

If we decrease A by a factor of 2, the new value of A becomes A/2. If we decrease B by a factor of 8, the new value of B becomes B/8.

So the new product of A/2 and B/8 is:

(A/2)(B/8) = AB/16

Therefore, the product is decreased by a factor of 16.

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Answer:

The correct equation that represents the relationship between b and f is:

Ob = (3/2)f

Explanation:

We know that Priya uses 4 cups of flour to make 3 loaves of banana bread.

So, the amount of flour required per loaf of bread is 4/3 cups.

Now, if Andre makes b loaves of bread using f cups of flour, then the amount of flour required per loaf of bread is f/b cups.

We can set up a proportion as follows:

4/3 = f/b

Cross multiplying, we get:

4b = 3f

Dividing both sides by 3, we get:

b = (3/4)f

This means that Andre can make (3/4) loaves of bread per cup of flour.

But the question asks for the relationship between b and f, so we need to rearrange the equation:

b = (3/4)f

Multiplying both sides by (2/3), we get:

(2/3)b = (1/2)f

Simplifying, we get:

Ob = (3/2)f

Therefore, the correct equation that represents the relationship between b and f is Ob = (3/2)f.

Refer to the attached images.

Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

Answer:

Step-by-step explanation: To find the ratio of corresponding sides for the two similar triangles, we need to match up the corresponding sides of the triangles and write the ratios of their lengths.

For Triangle 1, we have:

Side length = 12

Hypotenuse = 15

We can use the Pythagorean theorem to find the length of the blank side:

(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2

(Blank side)^2 = 15^2 - 12^2

(Blank side)^2 = 225 - 144

(Blank side)^2 = 81

Blank side = 9

So, for Triangle 1, we have the following ratios:

Side length : Hypotenuse = 12 : 15

Side length : Blank side = 12 : 9

Hypotenuse : Blank side = 15 : 9

For Triangle 2, we have:

Side length = 4

Hypotenuse = 5

We can use the Pythagorean theorem to find the length of the blank side:

(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2

(Blank side)^2 = 5^2 - 4^2

(Blank side)^2 = 25 - 16

(Blank side)^2 = 9

Blank side = 3

So, for Triangle 2, we have the following ratios:

Side length : Hypotenuse = 4 : 5

Side length : Blank side = 4 : 3

Hypotenuse : Blank side = 5 : 3

Therefore, the ratio of corresponding sides for the two similar triangles is:

Side length : Side length = 12 : 4 = 3 : 1

Hypotenuse : Hypotenuse = 15 : 5 = 3 : 1

Blank side : Blank side = 9 : 3 = 3 : 1

Reducing each ratio to lowest terms, we get:

Side length : Side length = 3 : 1

Hypotenuse : Hypotenuse = 3 : 1

Blank side : Blank side = 3 : 1

So the correct answer is (b) StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction.

All the true statements, if each interior angle measure of a regular polygon is (2x + 20)° include the following:

A. If x = 60, then the regular polygon is a nonagon.

C. If x = 77, then the regular polygon is a 60-gon.

D. If x = 65, then the regular polygon is a dodecagon.

D. If x = 44, then the regular polygon is a pentagon.

In Geometry, the measure of each interior angle of a regular polygon can be calculated by using this mathematical expression:

Interior angle = [180 × (n - 2)]/n

Where:

n represents the number of sides of a regular polygon.

When x = 60, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(60) + 20)° = [180 × (n - 2)]/n

140 = [180 × (n - 2)]/n

140n = 180n - 360

360 = 40n

n = 9 sides.

When x = 77, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(77) + 20)° = [180 × (n - 2)]/n

174 = [180 × (n - 2)]/n

174n = 180n - 360

360 = 6n

n = 60 sides.

When x = 65, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(65) + 20)° = [180 × (n - 2)]/n

150 = [180 × (n - 2)]/n

150n = 180n - 360

360 = 30n

n = 12 sides.

When x = 41, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(41) + 20)° = [180 × (n - 2)]/n

102 = [180 × (n - 2)]/n

102n = 180n - 360

360 = 78n

n = 4.6 sides.

When x = 44, the number of sides of the regular polygon is given by:

(2x + 20)° = [180 × (n - 2)]/n

(2(44) + 20)° = [180 × (n - 2)]/n

108 = [180 × (n - 2)]/n

108n = 180n - 360

360 = 72n

n = 5 sides.

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Answer:

The events are not disjoint because it is possible to receive an accurate order from Restaurant A.

Step-by-step explanation:

The probability of getting an order from Restaurant A or an order that is accurate is 0.907.

Add up all numbers in the table. 1121.

Add up all numbers in the order accurate data set plus the A order, not accurate data set. 1017

Take 1121/1017=0.907

The events are not disjoint because it is possible to receive an accurate order from Restaurant A.

Answer:

$85

Step-by-step explanation:

340*0.25

The domain is all real numbers, The range is all real numbers and There is one y-intercept is true from the given option in context of all linear functions. option B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept is right choice.

All linear functions have a domain that includes all real numbers, a range that includes all real numbers, and exactly

one y-intercept.

The rate of change of a linear function is non-zero only if the function is not constant (i.e. its slope is not zero).

However, there are linear functions that have a slope of zero, such as the function f(x) = 2, which is a horizontal line.

This means that statement A is not true of all linear functions.

Furthermore, there are linear functions that have no x-intercept (if the line is parallel to the x-axis) or that have more

than one x-intercept (if the line intersects the x-axis more than once).

Therefore, statement D is also not true of all linear functions.

The correct answers to this question are B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept.

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Answer:

C

.........................

Answer: the answer is A

Step-by-step explanation: The process of nuclear fusion is the union of two light atomic nuclei into one heavier one while releasing enormous quantities of energy.

The cost of the utility pole is $127.36.

Answer:

by ASA rule

they are congruent

The formula that could help Jim find Ann’s number, n as soon as he is given the result, r is n = (r - 7) / 5.

Formula 1;

Let the unknown number Ann thought of = n

(n × 5) + 7 = r

5n + 7 = r

If Jim is given Ann's number n if given the results, r

This means Jim will make Ann's number n the subject of the formula;

5n + 7 = r

Subtract 7 from both sides

5n = r - 7

divide both sides by 5

n = (r - 7) / 5

Therefore, the formula written in terms of n is n = (r - 7) / 5

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Answer:

Step-by-step explanation:

To find the area of the upper surface of the pool, we need to know the dimensions of the pool. If we assume the pool has a rectangular shape, we can use the formula:

Area = length x width

We can find the length and width by using the given volume and depth. Since the volume of the pool is 800 cubic cm and the depth is 8cm, we can find the length and width using the formula:

Volume = length x width x depth

800 = length x width x 8

length x width = 800/8

length x width = 100

Now, we do not have enough information to determine the exact dimensions of the pool. However, we do know that the area of the upper surface of the pool is equal to the length times the width. Therefore, the area of the upper surface is 100 square cm.

Answer:

5

Step-by-step explanation:

S1=R1²=*3²=9 (the outer circle)

S2=R2²=*2²=4 (the inner circle)

S=S1-S2=9-4=5 (the shaded ring)

Answer:

Step-by-step explanation:

Mean is when you add all the numbers toghther and then you divide it by how many numbers there are so for example we would add 15 + 15+8+12+15+8+20+12+10+12 and we get 127 from there we divide it by 10 because there are 10 numbers and we get 12.7

Range is simple all you do is subtract the biggest number by the smallest number and you get 20 - 8 = 12. SO the range is 12

Using the compound interest formula it is obtained that the loans which will have the lowest total cost is option C) - 30 years at 5% interest.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

We can use the formula of compound interest [tex]A = P\big(1 + \frac{r}{n} \big)^{(nt)}[/tex] to calculate the total cost (A) of each loan, where P is the principal (the initial amount borrowed), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the total number of years.

For all loans, the principal P is $380,000.

For Loan A, the annual interest rate is 10%, and the interest is compounded 12 times per year (monthly), so r = 0.1/12 and n = 12.

The total time is 20 years, so t = 20.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.1/12)^{(12 \times20)} = $1,245,956.70[/tex]

For Loan B, the annual interest rate is 6.5%, and the interest is compounded 12 times per year (monthly), so r = 0.065/12 and n = 12.

The total time is 25 years, so t = 25.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.065/12)^{(12 \times25)} = $844,275.92[/tex]

For Loan C, the annual interest rate is 5%, and the interest is compounded 12 times per year (monthly), so r = 0.05/12 and n = 12.

The total time is 30 years, so t = 30.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.05/12)^{(12 \times30)} = $766,726.73[/tex]

For Loan D, the annual interest rate is 4%, and the interest is compounded 12 times per year (monthly), so r = 0.04/12 and n = 12.

The total time is 35 years, so t = 35.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.04/12)^{(12 \times35)} = $810,780.25[/tex]

Therefore, Loan C with 30 years at 5% interest has the lowest total cost, with a total cost of $766,726.73.

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The value of n (S) is 5, n (T) is 7, n (∪) is 11 and n (∩) is 1. The solution has been obtained by using the given sets.

What is a set?

Sets are represented as a collection of well-defined objects or elements and it does not change from person to person. A set is symbolised by a capital letter. The number of items in the finite set is known as the cardinal number of a set.

We are given two sets as S = {r, e, l, a, x} and T = {i, t, s, o, k, a, y}.

Now,

n (S) = 5

This is because there are 5 elements in this set.

n (T) = 7

This is because there are 7 elements in this set.

S ∪ T = {r, e, l, a, x, i, t, s, o, k, y}

n (∪) = 11

This is because there are 11 distinct elements in the sets.

S ∩ T = {a}

n (∩) = 1

This is because there is only 1 element common in the sets.

Hence, the required solution has been obtained.

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Answer:

Step-by-step explanation:

34,05m my love

Answer:

The height of the tree is approximately 15.14 meters, rounded to the nearest hundredth of a meter.

Step-by-step explanation:

Let's call the height of the tree "h". We can use similar triangles to set up an equation involving Joseph's height, the length of his shadow, the height of the tree, and the length of the tree's shadow.

The two triangles we're interested in are:

Joseph's triangle: This triangle has a height of 1.75 meters (Joseph's height) and a base of x meters (the length of Joseph's shadow).

Tree's triangle: This triangle has a height of h meters (the height of the tree) and a base of 29.7 - x meters (the length of the tree's shadow).

Since the two triangles are similar, we can set up the following proportion:

h / (29.7 - x) = 1.75 / x

To solve for h, we can cross-multiply and simplify:

h * x = 1.75 * (29.7 - x)

h * x = 52.075 - 1.75x

h = (52.075 - 1.75x) / x

Now we need to find the value of x that makes the tips of the two shadows meet. From the problem statement, we know that x + 34.05 = 29.7, so:

x = 29.7 - 34.05

x = -4.35

This means that the tips of the shadows don't actually meet, but the problem is likely assuming that the tips of the shadows are very close together, so we can use the value x = -4.35 to approximate the height of the tree.

Substituting x = -4.35 into our equation for h, we get:

h = (52.075 - 1.75(-4.35)) / (-4.35)

h = 15.14

Answer:

the next term will be 15

Step-by-step explanation:

a=81/25

r(common ratio)=t2/T1=5/3

so,t4=ar^(n-1)

=81/25×5/3^(4-1)

= 81/25×125/27

=15

Well for each person, the probability is 1/3. This is because they all have 2 out of 6 possible outcomes.