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4 years ago

Find the value of x. Then classify the triangle

Mathematics

1 answer:

kondaur [170]4 years ago

7 0

Answer:

x = 60°

Step-by-step explanation:

This is an equilateral triangle. All angles of this triangle are congruent and have a measure of 60°.

Other method.

We know: the sum of the measures of the angles of the triangle is equal to 180 °.

Therefore we have the equation:

x + x + x = 180°

3x = 180° <em>divide both sides by 3</em>

x = 60°

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A sample of restaurants in a city showed that the average cost of a glass of iced tea is $1.25 with a a standard

FromTheMoon [43]

Answer:

For the restaurant that charges 95 cents, the z-score is -4.29.

For the restaurant that charges $1, the z-score is -3.57.

For the restaurant that charges $1.35, the z-score is 1.43

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average cost of a glass of iced tea is $1.25 with a standard deviation of 7c.

This means that $\mu = 1.25, \sigma = 0.07$

Restaurant that charges 95 cents:

The z-score is found when X = 0.95. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{0.95 - 1.25}{0.07}$

$Z = -4.29$

For the restaurant that charges 95 cents, the z-score is -4.29.

Restaurant that charges $1:.

X = 1

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1 - 1.25}{0.07}$

$Z = -3.57$

For the restaurant that charges $1, the z-score is -3.57.

Restaurant that charges $1.35:

X = 1.35

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.35 - 1.25}{0.07}$

$Z = 1.43$

For the restaurant that charges $1.35, the z-score is 1.43

4 0

3 years ago

Clark and Lana take a 30-year home mortgage of $128,000 at 7.8%, compounded monthly. They make their regular monthly payments fo

svp [43]

Answer:

Step-by-step explanation:

From the given information:

The present value of the house = 128000

interest rate compounded monthly r = 7.8% = 0.078

number of months in a year n= 12

duration of time t = 30 years

To find their regular monthly payment, we have:

$PV = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{r}{n})^{-nt}}{\dfrac{r}{n}} \end {bmatrix}$

$128000 = P \begin {bmatrix} \dfrac{1 - (1 + \dfrac{0.078}{12})^{- 12*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

128000 = 138.914 P

P = 128000/138.914

P = $921.433

∴ Their regular monthly payment P = $921.433

To find the unpaid balance when they begin paying the $1400.

when they begin the payment ,

t = 30 year - 5years

t= 25 years

$PV= 921.433 \begin {bmatrix} \dfrac{1 - (1 - \dfrac{0.078}{12})^{25*30}}{\dfrac{0.078}{12}} \end {bmatrix}$

PV = $121718.2714

C) In order to estimate how many payments of $1400 it will take to pay off the loan, we have:

$121718.2714 = \begin {bmatrix} \dfrac{1300 (1 - \dfrac{12.078}{12}))^{-nt}}{\dfrac{0.078}{12}} \end {bmatrix}$

$121718.2714 = 200000 \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$\dfrac{121718.2714}{200000 } = \begin {bmatrix} (1 - \dfrac{12.078}{12}))^{-nt} \end {bmatrix}$

$0.60859 = \begin {bmatrix} (1 - \dfrac{12}{12.078}))^{nt} \end {bmatrix}$

$0.60859 = (0.006458)^{nt}$

$nt = \dfrac{0.60859}{0.006458}$

nt = 94.238 payments is required to pay off the loan.

How much interest will they save by paying the loan using the number of payments from part (c)?

The total amount of interest payed on $921.433 = 921.433 × 30(12) years

= 331715.88

The total amount paid using 921.433 and 1300 = (921.433 × 60 )+( 1300 + 94.238)

= 177795.38

The amount of interest saved = 331715.88 - 177795.38

The amount of interest saved = $153920.5

6 0

4 years ago

Solve Ax+By=C for x. Provide below

Maru [420]

Answer:

x = $\frac{C-By}{A}$

Step-by-step explanation:

Given

Ax + By = C ( isolate the term in x by subtracting By from both sides )

Ax = C - By ( divide both sides by A )

x = $\frac{C-By}{A}$

8 0

4 years ago

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Point A and point C are shown on the number line below. Point C is located at 4⁄5. The sum of points B and C is equal to point A

11Alexandr11 [23.1K]

1/5 is the answer for your question!!

4 0

3 years ago

A cone has a radius of 6.2 mm and a height of 10.8 mm. What is the volume of the cone to the nearest tenth? use π = 3.14

guapka [62]

$\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}$

Actually Welcome to the Concept of the volumes.

Here given as, r= 6.2 mm, h = 10.8 mm, π=3.14

hence, the volume of the cone is

Volume = 1/3(πr^2h)

===> vol = 1/3(3.14*(6.2)^2*(10.8))

==> Vol = 1/3*(1303.57)

==> Vol = 434.52 mm^3

Hence the volume of the cone is 434.52 mm^3

7 0

3 years ago

Read 2 more answers