A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 96 students in the high school and found a mean savings of 4000 dollars with a standard deviation of 500 dollars. Determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.

After solving the equations, we know that a total of 25 ladies attended the party.

A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including linear, quadratic, cubic, and others.

So, take dudes as x and ladies as y.

Now, form the required 2 equations as follows:
2x + y = 45 ...(1)

x + y = 35 ...(2)

Work on equation (2):

x + y = 35

x = 35 - y

Now, substitute x = 35 - y in equation (1):

2x + y = 45

2(35-y) + y = 45

70 - 2y + y = 45

-y = -25

y = 25

Since ladies were charged $1 for each ticket, then 25 ladies attended the party.

Therefore, after solving the equations, we know that a total of 25 ladies attended the party.

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The current market price for the bond is $870 the yield to maturity is 14.13%

The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: C = future cash flows/coupon payments. r = discount rate (the yield to maturity)

knowing that:

the formula is:

\(P = (C / (1 + r))^1 + (C / (1 + r))^2 + ... + (C + F) / (1 + r)^n\)

Putting the values:

\($870 = (130 / (1 + r))^1 + (130 / (1 + r))^2 + ... + (130 + 1,000) / (1 + r)^13\)

Using the math we find that the percentage is  approximately 14.13%;

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9n+a-8

=9*(1) + 2 -8

=9+2-8

=3

The simplification of the given expression, 9n+a-8 is 3

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Answer: y = -2x + 1

Step-by-step explanation:

The formula for slope-intercept form is y = mx + b. Keep y and x as the variables. Replace m with the slope, which can be found by doing rise/run, and replace b with the y-intercept. The y-intercept is the spot where the line intersects the y-axis.

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Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Answer: One root

Reason:

The term "root" refers to the x intercept.

We plug in y = 0 and solve for x to get the x intercept

y = 2x-12

0 = 2x-12

2x = 12

x = 12/2

x = 6

The root is 6.

The single x intercept is located at (6,0).

We want to divide

142.45 ÷ 7.4

In order to find the best stimate, we round both numbers.

We have that 142.45 can be rounded to 140 or 150, since it is nearer to 140, then we round:

142.45 ≅ 140

Since 7.4 is near to 7, we can approximate it

7.4 ≅ 7

Then

142.45 ÷ 7.4 ≅ 140 ÷ 7

Since 140 ÷ 7 = 20, then

Answer- D

We have then, that the result for

142.45 ÷ 7.4

must be near to 20 (as we concluded on Part A).

142.45 ÷ 7.4 ≅ 20

Then, if we have 1925, then, the way of placing the decimal point that makes it nearer to 20 is

19.25

Jake says that it is 192.5 but it is farer from 20 than 19.25

Answer- Jake is not correct because 192.5 is far from the stimate. The decimal point belongs after the 9: 19.25

Answer:

2x exponent 2-5x+16

Step-by-step explanation:

Remove Parentheses

-10x *exponent 2* + 9 + 8x *exponent 2* - 5x +7

Group like terms

-10x *exponent 2* +9 + 8x *exponent 2* -5x + 9+7

Add similar Elements: -10x *exponent 2* + 8x *exponent 2* = 2x *exponent 2*

-2x*exponent 2* -5x+9+7

Add the numbers 9 + 7= 16

2x *exponent 2* - 5x + 16 ANSWER

Answer:

3.2 hours.

Step-by-step explanation:

166.4m=52 miles per hour

Now 3.2 would be the accurate hours he drove.

Answer:

1. x^3=27

2. 4^2=64

3. x^4=81

Step-by-step explanation:

Using the value of x, replace x in each equation with three, and raise the number given to the power, or multiply the number by itself __ times, where __ is equal to the smaller number.

The cost of the molding is given as follows:

$119.30.

The circumference of a circle of radius r is given by the equation presented as follows:

C = 2πr.

The parameters for this problem are given as follows:

d = 9 -> r = 4.5.

(as the radius is half the diameter)

Hence the circumference is given as follows:

C = 2 x π x 4.5

C = 28.27 ft.

The cost is of $4.22 per ft, hence the total cost is given as follows:

4.22 x 28.27 = $119.30.

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The true statements are:

A circle is a closed, two-dimensional shape where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the middle.

To identify the true statements, we can first rewrite the given equation of the circle in standard form:

x² - 2x + y² = 8

Completing the square, we get:

(x - 1)² + y² = 9

Now we can identify the true statements:

Therefore, the true statements are:

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Answer: 29, 31, 37, 41, 43, 47, 53.

Step-by-step explanation:

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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Answer:

A = (1/2) × Diagonal × (Sum of heights).

Step-by-step explanation:

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Answer:

$460

Step-by-step explanation:

Because if you put 23% over 100 and multiply it by 20,000 you should get that

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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A' ∩ B ∩ C is region VI where B ∩ C but A is not included.

A Venn diagram can also be referred to as a set diagram or a logic diagram that illustrates various set operations including the intersection, union, and difference of sets. Subsets of a set are also represented using it. A subset of whole numbers, which is a subset of integers, is a collection of natural numbers, as an example.

Given:

The region I represent A.

and, The region III represent B

and, The region VII represent C.

and, the region show A∩B.

and, the region IV shows A ∩ C

and, the region VI shows B ∩ C

and, the region V shows A ∩ B ∩ C.

Now, we want a region where B and C should be intersected but not include region A (A').

So, the regions shows A' ∩ B ∩ C is region VI where B ∩ C but A is not included.

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Part A: The probability of rolling a 5 is 1/6 or approximately 0.167. Part B: the probability of rolling an even number is 3/6 or 1/2 or 0.5.

Probability is a branch of mathematics concerned with measuring the likelihood or chance of an event occurring. It is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability is expressed as a number between 0 and 1, where 0 means that the event will not occur and 1 means that the event will definitely occur. For example, if the probability of an event is 0.5, it means that the event has an equal chance of occurring or not occurring. Probability is used in various fields, such as science, engineering, finance, and statistics, to make predictions and make decisions based on uncertain events.

Part A:

The number cube has six faces, and each face has an equal chance of landing face-up. Therefore, the probability of rolling a 5 is 1/6 or approximately 0.167.

Part B:

The even numbers on a number cube are 2, 4, and 6. There are three even numbers out of a total of six possible outcomes. Therefore, the probability of rolling an even number is 3/6 or 1/2 or 0.5.

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Answer:

Hope you understand not to sure but that's what I got

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


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Answer:

sec(thita)=√8/3 I think that

The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

5.6

Step-by-step explanation:

Answer:

5.6

Step-by-step explanation:

Menjawab:

15cm

Penjelasan langkah demi langkah:

Keliling segitiga adalah jumlah semua sisi segitiga

P = s1 + s2 + s3

Diberikan sisi jika segitiga;

S1 = 5cm

S2 = 7cm

S3 = 3cm

Keliling = 5cm + 7cm + 3cm

Keliling = 15cm

Oleh karena itu, keliling segitiga tersebut adalah 15 cm

The correct answer is B. 195 bpm

Explanation:

In health and related areas, THR or Target Heart Rate zone refers to the range of heart rate an individual should have including the maximum heart rate. In the case of Tierra, her THR zone indicates her maximum heart rate should be 185 beats per minute.

In this context, a heart rate above this number shows Tierra is working too hard or that his heart is doing too much effort, which is dangerous for her health. Thus, the heart rate that shows she is doing too hard is 195 bmp as this is the only one that is above the ideal rate.

The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).

In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:

3(2a^2 - 5a + 2)

Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.

The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:

3(2a - 1)(a - 2)

Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).

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