Find the measure of the indicated arc or angle.

Using compound interest, it is found that they must deposit $9,143.47 in order to have the desired amount.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For this problem, the parameters are:

A(15) = 30000, r = 0.08, n = 4

Then we solve for P to find the initial deposit:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]30000 = P\left(1 + \frac{0.08}{4}\right)^{4 \times 15}[/tex]

[tex]P = \frac{30000}{(1.02)^{60}}[/tex]

P = $9,143.47.

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The length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

The cosine rule is given as;

[tex]c = \sqrt{a^2 + b^2 - 2ab cos \alpha }[/tex]

c = length of the diagonal

a = base length = 22 feet

b = 7 feet

[tex]c = \sqrt{7^2 + 22^2 - 2 * 7 * 22 cos 40}[/tex]

[tex]c = \sqrt{533 - 308 * 0. 7660}[/tex]

[tex]c = \sqrt{533 - 235. 93}[/tex]

[tex]c = \sqrt{297. 072}[/tex]

[tex]c = 17. 24[/tex] feet

Using sine rule

[tex]\frac{a}{sin A } = \frac{c}{sin C}[/tex]

[tex]\frac{a}{sin 70} = \frac{17. 24}{sin 40}[/tex]

Cross multiply

[tex]a[/tex] × [tex]sin 60[/tex] = [tex]c[/tex] × [tex]sin 70[/tex]

[tex]a[/tex] × [tex]0. 8660[/tex] = [tex]17. 24[/tex] × [tex]0. 9397[/tex]

[tex]a = \frac{16. 20}{0. 8660}[/tex]

a = 18. 7 feet long

Thus, the length of the diagonal and the shorter base are 17. 24 feet and 18. 7 feet long respectively.

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The figure that is not equivalent to 2¾ is 2¼ × 2½. That is option B.

Simplification is a process that is used to make a fraction appear in its simplest forms.

The fraction given is = 2¾

The simplification of the fraction= 2^3/4 = 2

But simplification of 2¼ × 2½ is equal to;

2¼= 0.5

2½= 1

Therefore 2¾ is not equivalent to 2¼ × 2½ when simplified.

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle2[/tex]

( by corresponding angle pair )

[tex]\qquad❖ \: \sf \: \angle2 \cong \angle3[/tex]

( given in the question )

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \angle1 \cong \angle3[/tex]

If the length,breadth, height of cuboid are 16 m, 5 m,4 m , slant height of pyramid is 10m,  height be 6 m then the surface area of composite figure be 444 [tex]m^{2}[/tex].

Given that the length,breadth,height of cuboid are 16m,5 m, 4m and slant height be 10 m and height be 6 m.

Surface area is basically sum of area of all the sides of a figure.

Surface area of composite figure =  area of cuboid less area of common side + area of 2 slant sides of pyramid+area of two triangles.

=2(lb+bh+hl)-(lb)+2(slant height*breadth of cuboid)+2[1/2* length of cuboid* height of triangle)

=2(16*5+5*4+4*16)-16*5+2(10*5)+2[1/2*16*6]

=2(80+20+64)-80+2*50+2(48)

=2(164)-80+100+96

=328-80+196

=248+196

=444[tex]m^{2}[/tex]

Hence the surface area of composite figure having a cuboid and pyramid on top is 444[tex]m^{2}[/tex].

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The value of the expression 6/5 * 240 is 288

The expression is given as:

6/5 * 240

Divide 240 by 5

6 * 48

Multiply 6 and 48

288

Hence, the value of the expression 6/5 * 240 is 288

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14 of the $1.50/lb type will you need to obtain the desired mixture.

According to the statement

Chocolate A that sells for $1.50/lb

Chocolate B that sells for $6.50/lb

Then in equation form the quantity of mixture will

A + B = X

then

$1.50A + $6.50(10) = X

1.50A + 65 = X -(1)

after solving the equation the value of a and b will become

A = 14.

So, 14 of the $1.50/lb type will you need to obtain the desired mixture.

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A margin of sampling "error" is a statistical calculation for how accurate a poll's results are.

A population parameter's sampling error is the discrepancy between the sample statistic used to estimate it and the parameter itself. For instance, sampling error is the variance between a population mean and a sample mean.

The sampling errors can be placed into four categories:

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As per inequality, it means that the value of x can be less than or equal to y.

Inequality in Mathematics

The two expressions that make up an equation or an inequality are connected in a mathematical statement. The equal sign (=) in an equation denotes the equality of the two expressions. The symbols >, <, ≤, or ≥ are used to denote an inequality, when the two expressions aren't always equal.

Type of Inequality

The given expression, x <= y denotes the type of inequality where the possible values of x are either less than y or equal to less. The value of x cannot be greater than y in any case.

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Answer:

n = 2.6

Step-by-step explanation:

Hello!

We can create an equation with equivalent fractions. Remember that a ratio can also be represented as a fraction.

We can create two fractions that are equivalent to each other given the ratios.

The value of n is 2.6.

The expanded form of the given expression is 2 × w × z × z

From the question, we are to determine the expanded form of the given expression

The given expression is

2wz²

To write an expression in an expanded form, we will write the expression as a repeated multiplication in the simplest way possible.

To do this, we will first expand the index in the given expression.

The index in the given expression is z²

Thus, we get

z² = z × z

Now, we will include the remaining individual terms in the expression and write them as product.

That is,

2wz² = 2 × w × z × z

Hence, the expanded form of the given expression is 2 × w × z × z

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Answer:

C

Step-by-step explanation:

Example
Find 55% of 200.

200 times 0.55 = 110

Answer: the answer is B

Step-by-step explanation:

if we want to find the percent of 700 people out of 4400 people, we would do 700/4400, which is equal to 0.16, or 16 percent.

Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:

"Zero, because the discriminant is negative".

A quadratic equation is a polynomial of degree 2, in a single variable x.

The standard form of a quadratic equation is ax² + bx + c = 0.

The quadratic formula is used to find the solution(s)/root(s) of this equation.

The quadratic formula is:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

In this formula, [tex]b^2-4ac[/tex] is called the discriminant (D).

The solution(s)/root(s) of the equation, depends on this discriminant value as follows:

In the question, we are given that the simplest form of Quincy's equation in the radical form was,

[tex]x = \frac{-3 \pm \sqrt{-19} }{2}[/tex].

Comparing this to the quadratic formula,

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

we get the discriminant (D) = -19.

Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:

"Zero, because the discriminant is negative".

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For complete question, refer to the attachment.

The other fraction is [tex]1\frac{1}{55}[/tex].

Provided that ,

One fraction = [tex]9\frac{3}{7}[/tex] = [tex]\frac{66}{7}[/tex]

The product of their fraction = [tex]9\frac{3}{5}[/tex] = [tex]\frac{48}{5}[/tex]

We have to find out the other fraction.

When one fraction and their product are given, the formula to find out another fraction = product / one fraction

So, the other fraction = [tex]\frac{48}{5}[/tex] / [tex]\frac{66}{7}[/tex]

= [tex]\frac{48}{5} * \frac{7}{66}[/tex]

= 336/330

= 56/55 [divided both the numerator & denominator by 6]

= [tex]1\frac{1}{55}[/tex]

Therefore it is concluded that the other fraction is [tex]1\frac{1}{55}[/tex] .

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The solution for the questions is mathematically given as

a)

t-distribution.

b)

the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952, 7.3048 )

c) the value of the [tex]\mu_0[/tex] is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_0; otherwise, reject H _0.

d)

you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

Generally, the equation for is mathematically given as

a.

In this case, the standard deviation of the population is unknown.

As a result, we make use of the t-distribution.

b)

We wish to generate a confidence interval with a 98 percent likelihood for the mean.

Because of this,

[tex](\bar{X}-t_{n-1,\alpha/2}\frac{s}{\sqrt{n}},\bar{X}+t_{n-1,\alpha/2}\frac{s}{\sqrt{n}})[/tex]

[tex](6.85-t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}},6.85+t_{148-1,0.02/2}\frac{2.12}{\sqrt{148}})[/tex]

[tex](6.85-t_{147,0.01}\frac{2.12}{12.1655},6.85+t_{147,0.01}\frac{2.12}{12.1655})[/tex]

(6.3952,7.3048)

Therefore, the confidence interval for the mean, based on 98 percent of the sample, is ( 6.3952 , 7.3048 )

c )

If the value of the mu _0 is within the range of the 98 percent confidence interval for the mean, which is between 6.3952 and 7.3048, then accept H_o; otherwise, reject H_0.

d . Here, we want to determine the sample size

Therefore,

[tex]n=t_{n-1,\alpha/2}^2\frac{s^2}{E^2}[/tex]

[tex]n=t_{148-1,0.05/2}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=t_{147,0.025}^2\frac{2.12^2}{0.5^2}[/tex]

[tex]n=2.6097^2\frac{2.12^2}{0.5^2}[/tex]

n=122.4364

In conclusion, you should conduct a poll with around 123 students to determine the average amount of time that students spend sleeping at your institution.

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Answer:

75%

Step-by-step explanation:

9 divided by 12 is 0.75, so 9 is 75 percent of 12.

I hope this helps, have a good day!

like the place where you are applying TURNED TRIANGLE.

coz literrally it means that if the trianlge has for example angle a on its right side then we turn the triangle as a whole and make the turn such that angle a is anywhere else but not on our right side....

I believe the explanation is clear, if not do contact me

The percentage of population has a resting heart rate is 15.7%.

Given that the mean of the data is 70 beats per minute and standard deviation is 4 beats per minute.

A probability distribution is a mathematical function that describes the probability of several possible values ​​of a variable.

Mean, μ=70

Standard deviation, σ=4

Given that the heart rate is resting between 74 and 82.

Now, we will use the standard normal formula

P(x₁<x<x₂)=P((x₁-μ)/σ<x<(x₂-μ)/σ)

Here x₁=74 and x₂=82.

Substitute these values in the formula, we get

P(74<x<82)=P((74-70)/4<x<(82-70)/4)

P(74<x<82)=P(4/4<x<12/4)

P(74<x<82)=P(1<x<3)

P(74<x<82)=P(x<3)-P(x<1)

Now, we will find the values by using the z-table, we get

P(74<x<82)=0.998-0.841

P(74<x<82)=0.157

P(74<x<82)=15.7%

Hence, the percentage of the population has a resting rate between 74 and 82 with the mean data is 70 beats per minute and the standard deviation data is 4 beats per minute is 15.7%.

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Answer:

Yes. If the squares of the 2 short sides add up to the square of the hypotenuse, the triangle contains a right angle. Hope this helped.

Answer:

265

Step-by-step explanation:

You subtract 275 minus 10

$247.5 was the original amount on the credit card

Lets simplify the problem,

Total amount after late fee = $275

Late fee deduction = 10%

Original amount = 275 - 10% of 275

= 275 - 27.5

= $247.5

So $247.5 was the original amount on the credit card before the late fee.

Percentage:

In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol "%" or simply as "percent" or "pct." For example, 35% is equivalent to the decimal 0.35, or the fraction.

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The answer is . one-to-one.

(a) The function is onto because a, b, c, and d are members of its codomain. All points are converted into various points, making it a one-to-one relationship. The response is that it is one-to-one and onto ( A and C).

(b) It is onto because a, b, c, and d are members of the function's codomain. All points are converted into various points, making it a one-to-one relationship. The response is that it is one-to-one and onto (A and B).

(C) The element b is not onto since it is not a part of the function's codomain. All points are converted into various points, making it a one-to-one relationship. One-to-one is the right response.

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The complete question is -

Determine if each of the following functions from {a,b,c,d} to itself is one-to-one and/or onto.

Check ALL correct answers.

(a) f(a)=d,f(b)=a,f(c)=c,f(d)=b

A. onto.

B. neither one-to-one nor onto.

C. one-to-one.

f(a)=b,f(b)=a,f(c)=c,f(d)=d

A. one-to-one.

B. onto.

C. neither one-to-one nor onto.

f(a)=c,f(b)=d,f(c)=a

A. one-to-one.

B. onto.

C. neither one-to-one nor onto.

Answer:

B. (5,12,13)

Step-by-step explanation:

The only answer with two side lengths that are greater than the largest side length.

Answer:

Sum is

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

Answer: Option (1)

Step-by-step explanation:

[tex]\angle DMA[/tex] is another name for angle 3, but not [tex]\angle DME[/tex].

Answer:

For every x value, the y value would be double of the x value. (ex, x=2, y=4)

Step-by-step explanation:

If you look closely at every x value and see their y-values for the ordered pair, you will see that the x-value in question was doubled in order to find the y-value. This will result in the linear equation: [tex]y=2x[/tex].

Answer:

6288388288288828ffjfjjrjir

Answer:

Step-by-step explanation:

Reflection over any line is a rigid transformation that does not change angles or lengths. Dilation is a transformation that changes lengths by the same scale factor, but has no effect on angles. Dilated figures are similar to the original.

When ΔXYZ is reflected over a vertical line, no lengths or angles are changed. When the reflected triangle is dilated by half, we get ...

  Y'X' = (1/2)YX . . . . . . . makes option 3 false

  X'Z' = (1/2)XZ . . . . . . . makes option 4 true

Since no angles are changed, we have ...

  Angle XZY ≅ Angle Y'Z'X'   (another name for angle X'Z'Y')

  ... makes option 2 true

Of course, the resulting triangle is similar to the original, so ...

  △XYZ ~ △X'Y'Z' . . . . . option 1 is true

The number of observation given in the following data set 14. This is also called the size of the population.

It is important to note that the above data possess the minimum value of 12 and the maximum value of 25. As indicated in the attached image, the data set is normally distributed.

The measures of central tendency are given as follows;

Q1 --> 15

Q2 --> 18.5

Q3 --> 22
IQR  = 7

Mean Absolute Deviation (MAD) = 3.5

Min = 12

Max = 25.

It is to be noted that the above indictors are called Descriptive Statistics.

The features of a sample or data set, such as a variable's mean, standard deviation, or frequency, are described or referred to as descriptive statistics.

We can better grasp a data sample's constituent parts by using inferential statistics.

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Answer:

x = [tex]\frac{4}{25}[/tex]

Step-by-step explanation:

1 : x = 6 [tex]\frac{1}{4}[/tex] ← change to improper fraction

1 : x = [tex]\frac{25}{4}[/tex] , then

[tex]\frac{1}{x}[/tex] = [tex]\frac{25}{4}[/tex] ( cross- multiply )

25x = 4 ( divide both sides by 25 )

x = [tex]\frac{4}{25}[/tex]

Answer:

  D.  264 in³

Step-by-step explanation:

The missing edge dimension can be found using the Pythagorean theorem. Then the volume can be found using the appropriate formula.

The missing dimension and the two given for the top triangle will satisfy the Pythagorean theorem. If the missing dimension is represented by 'a', then we have ...

  a² +8² = 10²

  a = √(100 -64) = 6 . . . . inches

The area of the top triangle is ...

  A = 1/2bh . . . . where b and h are the base and height dimensions

  A = 1/2(6 in)(8 in) = 24 in²

The volume of the triangular prism is ...

  A = Bh . . . . . where B is the area of the triangular base, and h is the prism height

  A = (24 in²)(11 in) = 264 in³

The volume of the triangular prism shown is 264 in³.