to prove triangleABC is isosceles, which of the following statements can be used in the proof?
(idk the answer)

Given Information:

Annual interest rate = r = 10%

Accumulated amount = A = $6380.00

Semi-annual compounding = n = 2

Number of years = t = 38/12 = 19/6  

Required Information

Principle amount= P = ?

Answer:

Principle amount= P = $4,684.05

Step-by-step explanation:

The principal amounts in terms of compound interest is given by  

[tex]$ P = \frac{A}{(1 + i)^N} $[/tex]

Where  

i = r/n

i = 0.10/2

i = 0.05

N = n*t

N = 2*19/6

N = 19/3

So, the principal amount is

[tex]P = \frac{6380.00}{(1 + 0.05)^{19/3}} \\\\P= \$4,684.05 \\\\[/tex]

Therefore, you need to invest $4,684.05 at 10% compounded semiannually for 38 months to get $6380.00 in savings.

Answer:

Hello please your question is in-complete attached is the complete question

degree of freedom = -62.90 ( e )

Step-by-step explanation:

The formula for calculating the F-statistic/test statistic is

test - statistic  = Coef ( LBW) / SE Coef ( LBW )

                       = -0.72399 / 0.01151

                       = - 62.90

the degree of freedom the F-statistic has = -62.90

F-statistic test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. the value of the test can be gotten from running an ANOVA test or regression analysis on the statistical models

Using the definition of degrees of freedom, it is found that the F-statistic has 63 df.

When a hypothesis is tested, the number of degrees of freedom is one less than the sample size.

In this problem, the sample size is of n = 64.

Hence:

df = n - 1 = 64 - 1 = 63

The F-statistic has 63 df.

A similar problem is given at https://brainly.com/question/16194574

Answer:

357 mi²

Step-by-step explanation:

The shape is made of a triangle and a half-square

we will calculate the area of each one

let A1 be the area of the half-circle:

A1= (10²*π)/2 = 50π mi²

Let A2 be the area of the triangle:

A2= 10*20=200 mi²

let At be the total area:

At =A1+A2= 200+50π =357.07≈ 357 mi²

Answer:

a. The 95% confidence interval for the mean is (33.52, 35.48).

b. The 95% confidence interval for the mean is (34.02, 34.98).  

c. n=49 ⇒ Width = 1.95

n=196 ⇒ Width = 0.96

Note: it should be a factor of 2 between the widths, but the different degrees of freedom affects the critical value for each interval, as the sample size is different. It the population standard deviation had been used, the factor would have been exactly 2.

d. 5. Quadrupling the sample size while holding the confidence coefficient fixed decreases the width of the confidence interval by a factor of 2.

Step-by-step explanation:

a. We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=34.5.

The sample size is N=49.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{49}}=\dfrac{3.4}{7}=0.486[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=49-1=48[/tex]

The t-value for a 95% confidence interval and 48 degrees of freedom is t=2.011.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.011 \cdot 0.486=0.98[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.98=33.52\\\\UL=M+t \cdot s_M = 34.5+0.98=35.48[/tex]

The 95% confidence interval for the mean is (33.52, 35.48).

b. We have to calculate a 95% confidence interval for the mean.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{196}}=\dfrac{3.4}{14}=0.243[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=196-1=195[/tex]

The t-value for a 95% confidence interval and 195 degrees of freedom is t=1.972.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.972 \cdot 0.243=0.48[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 34.5-0.48=34.02\\\\UL=M+t \cdot s_M = 34.5+0.48=34.98[/tex]

The 95% confidence interval for the mean is (34.02, 34.98).

c. The width of the intervals is:

[tex]n=49\rightarrow UL-LL=33.52-35.48=1.95\\\\n=196\rightarrow UL-LL=34.02-34.98=0.96[/tex]

d. The width of the intervals is decreased by a factor of √4=2 when the sample size is quadrupled, while the others factors are fixed.

Answer:

30 feet

Step-by-step explanation:

We can use ratios to answer this question:

8 foot shadow: 20 feet high

Therefore if we multiply both sides by 1.5

12 foot shadow: 30 feet high

Answer:

n > 1700

Step-by-step explanation:

n ÷ 4 – 125 > 300

Add 125 to both sides.

n ÷ 4 > 425

Multiply both sides by 4.

n > 1700

Answer:

n > 1700

Step-by-step explanation:

n ÷ 4 - 125 > 300

Add 125 to both parts.

n ÷ 4 > 300 + 125

n ÷ 4 > 425

Multiply both sides with 4.

n > 425 × 4

n > 1700

Answer:

6/5

Step-by-step explanation:

you have to flip the numerator and denominator. If it is 5/6 then it would be 6/5.

The reciprocal fraction that is required will be 31/26.

A fraction is a numerical number that is represented in the numerator and denominator form.

We have Two mixed fractions, the First fraction = 4(1/3) and the Second fraction =  5(1/6).

Now,First, convert mixed fractions into simple fractions,i.e.First fraction  = 4(1/3) = 13/3And,Second fraction = 5(1/6) = 31/6

Now, According to the question,

Divide First fraction by Second fraction;i.e.= (13/3) / (31/6)Now simplify,= ( 13 × 6) / (31 × 3)

Now, We get,= 26/31

So, the reciprocal fraction = 31/26.

Hence we can say that the reciprocal fraction that is required will be 31/26.

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Answer:

41.67%  probability of the sum of the dots indicate a sum less than or equal to 6

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes:

In this problem, we have these possible outcomes:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes.

Desired outcomes:

Sum of 6 or less. They are:

(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)

15 desired outcomes

15/36 = 0.4167

41.67%  probability of the sum of the dots indicate a sum less than or equal to 6

Answer:

D. -5 <= x < 1

Step-by-step explanation:

the values under the square-root radical must not be negative, AND

the value of the denominator must not be 0 or negative

x+5 >=0  or x >= -5

and 1-x > 0 or x < 1

So the answer is -5 <= x < 1

Answer:

(B)24 Units

Step-by-step explanation:

Triangle MNO is an equilateral triangle with sides  measuring [tex]16\sqrt{3}[/tex] units.

The height divides the base into two equal parts of lengths [tex]8\sqrt{3}[/tex] units.

As seen in the diagram, we have a right triangle where the:

Using Pythagoras Theorem

[tex](16\sqrt{3})^2=(8\sqrt{3})^2+h^2\\16^2*3-8^2*3=h^2\\h^2=576\\h=\sqrt{576}\\ h=24$ units[/tex]

The height of the triangle is 24 Units.

The height of the given equilateral triangle is gotten as;

B: 24 units

Equilateral Triangles

The height of an equilateral triangle starts from the mid - point of the base to the ap ex.

Now, if the sides of the equilateral triangle are 16√3 units, then it means we can use pythagorean theorem to find the height h.

Half of the base will be; ¹/₂ * 16√3 = 8√3

Thus, the height h can be calculated from;

h²= ((16√3)² - (8√3)²)

h² = 3(256 - 64)

h² = 576

h = √576

h = 24 units

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Answer: x = 120

Step-by-step explanation:

Here we have 3 triangles, one big and two smaller ones, one at the left and other at the right.

Now, the right sides is shared by the right smaller triangle and the big triangle, if this length is Z, we have that (using the angle in top of it, A, such that 64 is adjacent to A.)

Cos(A) = 64/Z

Cos(A) = Z/(64 +225)

We can take the quotient of those two equations and get:

[tex]1 = \frac{64*(64 + 225)}{Z^2} = \frac{18496}{Z^2}[/tex]

Then:

Z = √(18,496) = 136.

now, we have that for the smaller triangle one cathetus is equal to 64 and the hypotenuse is equal to 136.

Then, using the Pythagorean theorem:

64^2 + x^2 = 136^2

x = √(136^2 - 64^2) = 120

Answer:

The correct answer would be C

Step-by-step explanation:

please mark brainliest

The choice which best compares the volume of the cylinders is; Choice B; The volume of cylinder B is the same as that of cylinder A.

From geometry, It can be concluded that the volume of a solid shape is the product of its cross sectional area and the height over which the area spans. On this note, since the volume of a cylinder is dependent on the radius and height of the cylinder, both cylinders have equal volumes.

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Answer:

2.24 s

Step-by-step explanation:

Given:

Δy = 80 ft

v₀ = 0 ft/s

a = 32 ft/s²

Find: t

Δy = v₀ t + ½ at²

80 ft = (0 ft/s) t + ½ (32 ft/s²) t²

t = 2.24 s

Answer:

r = (An−nP)/P

Step-by-step explanation:

A = P(1 + nr)

Divide P on both sides.

A/P = 1 + nr

Subtract 1 on both sides.

A/P - 1 = nr

Divide n on both sides.

A/P/n - 1/n = r

(An−nP)/P = r

The answer is, r = (An−nP)/P

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here, we have,

given that,

A = P(1 + nr)

Divide P on both sides.

A/P = 1 + nr

Subtract 1 on both sides.

A/P - 1 = nr

Divide n on both sides.

A/P/n - 1/n = r

(An−nP)/P = r

hence, answer is (An−nP)/P = r.

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Answer:

Step-by-step explanation:

When two variables vary inversely, it means that an increase in one would lead to a decrease in the other and vice versa. Since the volume of a gas, V in a container varies inversely with the pressure on the gas, P, if we introduce a constant of proportionality, k, the expression would be

V = k/P

If V = 370 in³ and P = 15psi, then

370 = k/15

k = 370 × 15 = 5550

The equation that relates the volume, V, to the pressure, P would be

V = 5550/P

if the pressure was increased to 25psi, the volume would be

V = 5550/25 = 222 in³

Answer:

v=5550/p

222

Step-by-step explanation:

Answer:

It cannot be extended.

Step-by-step explanation:

Consider the function [tex]f(x,y) = \frac{x^2-y^2}{x^2+y^2}[/tex]. To extend this functions so it is continous at (0,0) we must define [tex] f(0,0) = \lim_{(x,y)\to(0,0)\frac{x^2-y^2}{x^2+y^2}[/tex]. However, this implies that the limit exists. So, we should find if the limit exists or not.

In this case, consider the case in which y =0. When y=0 then

[tex]\lim_{(x,y)\to(0,0) \frac{x^2-0^2}{x^2+0^2} = \lim_{x\to 0}\frac{x^2}{x^2}= 1[/tex]

But, when x=0, we get

[tex]\lim_{(x,y)\to(0,0) \frac{0^2-y^2}{0^2+y^2} = \lim_{y\to 0}\frac{-y^2}{y^2}=-1[/tex].

So, since the limit depends on how we approach to the point (0,0) the limit does not exist. So we can't extend f(x,y) so it is continous.

Answer:

The expected value is also known as the expectation, mathematical expectation, mean, average, or first moment.

Answer:

x = 2.

Step-by-step explanation:

3(x + 2) = 12

3x + 6 = 12

3x = 6

x = 2

Hope this helps!

Answer:

4

Step-by-step explanation:

Answer:

Decreases by 2 degrees

Step-by-step explanation:

The expression that describes temperature as a function of latitude is:

[tex]T=110-2(Latitude)[/tex]

This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.

Answer:

(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]

Step-by-step explanation:

Volume of fluid in the tank =1000 gallons

Initial Amount of Salt in the tank, A(0)= 30 pounds

Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.

Rate In=(concentration of salt in inflow)(input rate of brine)

[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]

The resulting mixture is pumped out at the same rate, therefore:

Rate Out =(concentration of salt in outflow)(output rate of brine)

[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]

Therefore:

The rate of change of amount of salt in the tank,

[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]

Complete Question:

You want to install a 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the​ walk? Use 3.14 for pi π.

Answer:

75.36 square yard

Step-by-step explanation:

From the question,

The diameter of this circular pool inside is 23 yd.

This means that the radius = Diameter/2 = 23yd/2 = 11.5 yd.

The formula for the area of a circle =

A = πr²

A = π(11.5)²

A =3.14 × 11.5²

A = 415.265 yd²

This is the Area of the inner circle.

We were told in the question also that he wants to install a walk of 1 yard

Hence, the radius of outer circle =

radius of inner circle +length of the walk

11.5yard + 1 yard

= 12.5 yard

A = πr²

A = 3.14 × (12.5)²

A = 490.625yd²

Area of the walk = Area of the Outer circle - Area of the inner circle

= (490.625 - 415.265)yd = 75.36 yd²

Therefore, the area of the walk is 75.36 square yards.

Answer:

x = 90

y = 100

z = -10

Step-by-step explanation:

To find x and y in the above parallelogram ABCD as shown above, recall that one of the properties of a parallelogram is: the consecutive angles in a parallelogram are supplementary.

This means that the sum of angle A and angle B in the parallelogram ABCD = 180°.

Thus,

(x + 30)° + (x - 30)° = 180°

Solve for x

x + 30 + x - 30 = 180

x + x + 30 - 30 = 180

2x = 180

Divide both sides by 2

2x/2 = 180/2

x = 90

=>Find y:

Also, recall that opposite angles in a parallelogram are congruent.

This means, angle A and angle C in parallelogram ABCD above are equal.

Thus,

(x + 30)° = (y + 20)°

Plug in the value of x to solve for y

90 + 30 = y + 20

120 = y + 20

Subtract 20 from both sides

120 - 20 = y

100 = y

y = 100

=>Find z, if z = x - y

z = 90 - 100

z = -10

Answer:

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Step-by-step explanation:

Step(i):-

Given mean of the Population  'μ'= 25c.m

Given standard deviation of the Population 'σ' = 8c.m

Given sample size 'n' = 256

Let X₁ = 24

[tex]Z_{1} = \frac{x_{1}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{24-25}{\frac{8}{\sqrt{256} } } = -2[/tex]

Let X₂ = 25

[tex]Z_{2} = \frac{x_{2}-mean }{\frac{S.D}{\sqrt{n} } } = \frac{25-25}{\frac{8}{\sqrt{256} } } = 0[/tex]

Step(ii):-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = P(-2≤ Z ≤0)

                     = P( Z≤0) - P(Z≤-2)

                     = 0.5 + A(0) - (0.5- A(-2))

                     = A(0) + A(2)        ( ∵A(-2) =A(2)

                     = 0.000+ 0.4772

                     = 0.4772

Final answer:-

The probability that the mean of my sample will be between 24 and 25 cm

P(24 ≤X⁻≤25) = 0.4772

Answer:

yes

Step-by-step explanation:

y = 19+ 3x

Let x = 3 and y = 28

28 = 19 + 3*3

28 =19+9

28 = 28

This is true so the point is one the line

Answer: your answer should be 103

Answer:

Step-by-step explanation:

103

Answer:

Two Portions!!!

Step-by-step explanation:

Answer:

1/9

Step-by-step explanation:

The probability of picking a even number is 1/3

The probability of picking another even number is 1/3(if u put the first one back)

So u multiply 1/3 times 1/3 which gives u 1/9 which is ur answer hope this helps

Answer:

1/9

Step-by-step explanation:

3 cards total

1 even number

P(even) = even/total

                1/3

Put the card back

3 cards total

1 even number

P(even) = even/total

                1/3

P(even, replace, even) = P(even) * P(even) =1/3*1/3 = 1/9

Answer:

  y = 5 (x + 2)

Step-by-step explanation:

Equations with a different x-coefficient will graph as lines that intersect the given one, so will form a system with one solution.

The equation with the same slope and y-intercept (y = 5(x -2)) will graph as the same line, so will form a system with infinite solutions.

The line with the same slope and a different y-intercept will form a system with no solutions:

  y = 5 (x + 2)

Answer:

B

Step-by-step explanation:

got it on edge